Following a brief report on high-temperature superconductivity in B-doped Q-carbon [Bhaumik et al., ACS Nano 11(6), 5351–5357 (2017)], we present detailed structure-property correlations to understand the origin of superconductivity in strongly bonded lightweight materials and methods to further enhance the superconducting transition temperature (Tc). Nanosecond melting of carbon in a super undercooled state and rapid quenching result in a strongly bonded unique phase of B-doped Q-carbon. The temperature-dependent resistivity and magnetic susceptibility measurements demonstrate type II superconductivity in this material with a transition temperature of 36.0 ± 0.5 K and an upper critical field of 5.4 T at ∼0 K. It has also been shown that in B-doped Q-carbon, the upper critical magnetic field (Hc2(T)) follows Hc2(0) [1-(T/Tc)2.1] temperature dependence and is consistent with the Bardeen–Cooper–Schrieffer formalism. In the present study, B-doped Q-carbon thin films are formed on sapphire substrates by employing pulsed laser annealing (PLA) using a nanosecond excimer laser. This process involves the rapid quenching of highly undercooled melt of homogenously mixed B and C. Through the structure-property correlation measurements in B-doped Q-carbon, we estimate a higher electronic density of states near the Fermi level. Higher density of states near the Fermi-level along with higher Debye temperature and phonon frequency are responsible for the enhanced Tc. As a result of rapid melting and quenching, we can achieve 17.0 ± 1.0 or higher atomic % of B in the electrically active sites of Q-carbon which leads to the formation of shallow electronic states near the valence band maximum. From the critical current density versus field moments, the value of critical current density (Jc (2T)) in B-doped Q-carbon at 21 K is calculated as 4.3 × 107 A cm−2, which indicates that this novel material can be used for the persistent mode of operation in MRI and nuclear magnetic resonance applications. This discovery of high-temperature superconductivity in B-doped amorphous Q-carbon shows that the non-equilibrium synthesis technique using the super undercooling process can be used to fabricate materials with greatly enhanced physical properties.

The versatility in the arrangements of C atoms to form various allotropes and phases has led to the discovery of several new structures with unique properties. One of them is the evolution of superconductivity in carbon-based materials. In principle, high-temperature superconductivity can be achieved in structures with strongly bonded light C atoms due to the large Debye frequency. However, the lack of strong electron-phonon coupling and electronic density of states near the Fermi level in the pure C structures limits to achieving higher superconducting transition temperatures (Tc). The superconductivity has been observed in carbon-based materials, e.g., graphite intercalated superconductors (Tc ∼ 15 K),1 single-walled carbon nanotubes (Tc ∼ 15 K),2 alkali doped fullerenes (Tc ∼ 40 K),3 B-doped diamond (Tc ∼ 11 K),4 etc. Superconductivity in the bulk B-doped diamond is limited to 11 K, where it is caused by a strong electron-phonon mediated pairing of the charge carriers, well established by the Bardeen–Cooper–Schrieffer formalism.5,6

Superconductivity in B-doped diamond is the most studied subject due to its broad applications in electronics.7,8 It is shown experimentally that Tc ranging from 4 K to 11 K is achieved in B-doped diamond with increasing boron concentration in the substitutional lattice sites of diamond.4,7,9 According to theoretical predictions, without considering the electronic compensating defects, Tc in B-doped diamond can be increased up to 55 K with ∼20 at. % B.10 Increasing the concentration of B dopant (n > 1020 cm−3) decreases the activation energy and it exhibits a metal-like behavior.9 Achievement of such higher concentrations by equilibrium Chemical Vapor Deposition (CVD) methods is a major challenge. Therefore, non-equilibrium methods based upon energetics of plasma and lasers, are needed to attain a concentration beyond the thermodynamic solubility limits. However, theoretical studies also indicate that the B atoms, beyond the solubility limits generate strains and form dimers in the B-doped diamond.11 This pairing leads to the symmetric and anti-symmetric combinations of bound states of B, which do not contribute to the density of states at the Fermi level, and adversely affect the value of Tc.11 This remains a major challenge in improving the superconducting properties of B-doped diamonds, grown by CVD based techniques.4,12,13 The CVD process is close to an equilibrium synthesis method and it restricts the B-doping in substitutional sites above the thermodynamic solubility limits, which is about 2.0 at. % in diamond.

Non-equilibrium processes, such as pulsed laser deposition (PLD), pulsed laser annealing, plasma enhanced CVD, and ion implantation, allow dopant concentration exceeding the thermodynamic solubility limits. The doping by non-equilibrium laser quenching is a primary focus of the present work. It has also been established that the amorphous/disordered counterparts of the crystalline phases exhibit higher Tc. Recently, the reports indicate experimentally measured superconductivity in amorphous Bi (Tc = 6 K) which is significantly higher than that in crystalline Bi (Tc = 53 mK).14 This is due to the increased number of electronic density of states near the Fermi level and strong electron-phonon coupling in amorphous Bi.15 It is also been suggested that the mobility of the Cooper pairs in the amorphous structure is not hindered by the transition from semi-metallic to metallic behavior of Bi during the amorphization process.15 Based on these experimental studies and theoretical predictions, we embarked upon the creation of a new class of strongly bonded carbon-based amorphous materials where the dopant concentration can be exceeded beyond the thermodynamic limits.

Recently, we have reported the formation of a novel phase of carbon (Q-carbon) by melting of carbon layers in a super undercooled state by using pulsed laser annealing and subsequent quenching of molten carbon layers.16–18 Q-carbon is formed after nanosecond laser melting and subsequent quenching of the amorphous carbon thin film deposited on c-sapphire. This phase is a new state of carbon which comprises of a mixture of mostly four-fold sp3 (75%–85%) and the rest three-fold sp2 bonded carbon (with distinct entropy).16–18 Upon pulsed laser irradiation, electrons are excited into the conduction band and these excited electrons transfer their energy quickly (within about a picosecond) to phonons, leading to rapid heating and melting. Depending on the laser energy density and the physical properties of the amorphous film and the substrate, a process of super undercooling and quenching takes place which leads to the formation of a metastable state of amorphous Q-carbon structure possessing unique properties.16 High Tc in strongly bonded lightweight materials can be achieved if doping is high enough to sustain a moderate electron-phonon coupling. Q-carbon consists of a phase mixture of sp3 (>80%) and sp2 bonded C atoms and exhibits interesting properties, such as low electron affinity in electric field, room temperature ferromagnetism, etc.17 Undoped Q-carbon shows room-temperature ferromagnetism with a Curie temperature above 570 K. Upon doping with B, Q-carbon turns diamagnetic and exhibits high-temperature superconductivity with Tc ≥ 36 K. We have employed the nanosecond pulsed laser annealing on the B/amorphous C multilayer structures to synthesize B-doped Q-carbon. The structure, properties, and distribution of B atoms in Q-carbon are characterized by various nanoscopic and microscopic spectroscopic techniques, such as secondary ion mass spectroscopy (SIMS), electron energy-loss spectroscopy (EELS), energy dispersive spectroscopy (EDS) in a scanning transmission electron microscope (STEM), Raman spectroscopy, scanning electron microscopy (SEM), and X-ray photoelectron spectroscopy (XPS). We examine the superconductivity behavior of B-doped Q-carbon using the resistance versus temperature and the temperature-dependent magnetic susceptibility measurements in the physical property measurement system (PPMS) and the superconducting quantum interference device (SQUID), respectively. We reported initial results19 on the discovery of high-temperature superconductivity in B-doped Q-carbon. In this paper, we present the details of laser-solid interaction modeling and melting, experimental procedures, critical current versus temperature, and temperature versus field and possibilities of higher Tc > 37 K with increasing boron concentration. Finally, we discuss the origin and nature of superconductivity in B-doped Q-carbon. With this study, we expect that the non-equilibrium undercooling assisted synthesis methods can be used to fabricate highly doped materials, which have greatly enhanced superconducting properties.

Alternating layers of boron and amorphous carbon thin films are deposited onto c-sapphire using pulsed laser deposition (PLD) with a total thickness ranging from 100 to 500 nm in the temperature range of 300–570 K and 1.0 × 10−7 Torr operating pressure (base pressure). This operating pressure was achieved in less than three hours by employing an (oil-free) scroll pump in conjunction with a turbo molecular pump. The PLD can be made a highly nonequilibrium forward-directed process by controlling the laser spot size. For the PLD process, the KrF excimer laser (laser wavelength = 248 nm, pulse duration = 25 ns) was used. The pulsed laser beam is rastered through the glassy carbon and B (sector) targets mounted on the same target holder during the growth process. The laser energy density used during the deposition process ranges from 3.0–3.5 Jcm−2. Before the start of thin film deposition, the targets are pre-ablated to eliminate surface contaminants. Subsequently, these B-doped amorphous carbon thin films are irradiated with the nanosecond ArF excimer laser (laser wavelength = 193 nm, pulse duration = 20 ns) using a laser energy density of 0.6–1.0 J cm−2. The pulsed laser annealing technique melts the B-doped carbon film in a highly super undercooled state, followed by quenching to complete the whole process within 200–250 ns. This leads to the conversion of amorphous carbon films into the B-doped quenched carbon structure where the B concentration can exceed the thermodynamic solubility limit. The characterization of the B-doped Q-carbon phase was carried out using Raman spectroscopy, XPS, SIMS, EELS, Field emission scanning electron microscopy (FESEM), and SQUID magnetometry. An Alfa300 R superior confocal Raman spectroscope with a lateral resolution less than 200 nm was employed to characterize the Raman-active vibrational modes. Crystalline Si was used to calibrate the Raman spectra, which has its characteristic Raman peak at 520.6 cm−1. High-resolution SEM with sub-nanometer resolution was carried out using FEI Verios 460L SEM to characterize the as-deposited and the laser-irradiated films. The B atoms are incorporated into Q-carbon during rapid liquid-phase growth and solute trapping, where dopant concentrations can exceed far beyond the thermodynamic solubility limits. High-resolution SEM measurements were carried out using the field emission mode in FEI Verios 460L SEM. A Time-of-Flight Secondary Ion Mass Spectrometer (TOF-SIMS) with a lateral resolution of <300 nm was used to detect the presence of C, O, B, Al, and other trace impurity elements in the B-doped Q-carbon thin films. XPS with an X-ray energy of 10–14 kV for Al/Mg and Al/Ag sources employing a superior analyzer (PHOIBOS 150) having <1 eV resolution were used for the collection of XPS data. FEI Quanta 3D FEG with dual beam technology employing both electron and ion beam guns was used for preparing cross-sectional TEM samples. A low energy ion beam (5 kV, 10 pA) was used to cleanup the FIB surface damage. Aberration-corrected STEM-FEI Titan 80–300 was used in conjunction with EELS with a resolution of 0.15 eV to acquire high-angle-annular-dark-field (HAADF) images and EELS spectra of B-doped Q-carbon thin films. The electron probe current used in the experiment was 38 ± 2 pA. The EELS data was acquired with a collection angle of 28 mrads. The quantum design magnetic property measurement system (MPMS3) was used to measure the magnetic properties of thin films. VSM and DC modes were used for measuring field- and temperature-dependent magnetization. The magnetic measurements were made with samples mounted parallel to the magnetic field. The SQUID magnetometer can detect the magnetic field with ∼10−8 emu sensitivity and has a working temperature range: 1.8–400 K. The temperature stability is ±0.5% and the magnetic field uniformity is 0.01% over 4 cm (sample length). The magnetic field strength of as high as 7 Tesla (with a field charging resolution of 0.33 Oe) was used to perform the field dependent measurements in B-doped Q-carbon samples. Temperature-dependent resistivity measurements were carried out in the physical property measurement system (PPMS) at zero magnetic field.

Figures 1(a) and 1(b) represent the TOF-SIMS results of as-deposited B&C and B-doped Q-carbon thin films, respectively. As is evident from Fig. 1(a), there are alternating layers of B and amorphous carbon in the as-deposited thin films. The as-deposited layered thin films are engineered to have a top amorphous carbon layer. This results in an enhanced laser coupling due to low reflectivity and high absorption of amorphous carbon as compared to metallic B at 193 nm. An effective coupling is required during the pulsed laser annealing (PLA) process20,21 to cause melting and subsequent quenching to form B-doped amorphous Q-carbon structures. The C and B concentration profiles in the as-deposited sample exhibit periodic variation. However, after the pulsed laser annealing the B and C concentration profiles are uniform, as shown in Fig. 1(b). The high-energy laser photons cause an avalanche of electrons in the conduction band which interact with phonons, thereby melting amorphous carbon and B composite layers. The high concentration of free electrons caused by laser excitation leads to a non-equilibrium phase transition with a considerable modification of the interatomic bonding. The energy is transferred from the excited electrons to phonons thereby causing a homogeneous melting of the laser annealed region. During this melting process, the B dopants diffuse into molten Q-carbon to form a homogeneous mixture. The PLA process is completed in less than 200–250 ns, the details of which are explained in Sec. III J. Using the two-dimensional diffusion equation [X = 2(D*t)0.5], the diffusivity coefficient (D) is calculated as ∼2 × 10−4 cm2/s. This high value of diffusivity is consistent with the diffusion of B in liquid carbon during the PLA process. The high diffusivity in the liquid phase helps the formation of homogeneous B-doped Q-carbon, with B concentrations exceeding the thermodynamic solubility limits of 2.0 at. % in diamond. The higher B concentration is crucial for superconductivity in this material. The results from SIMS spectra also indicate that the as-deposited and PLA samples do not contain any impurities within a resolution of a few ppm.

FIG. 1.

SIMS profiles of (a) as-deposited boron and carbon layers with the inset showing a schematic of the alternating layers of amorphous carbon and boron deposited on c-sapphire using the pulsed laser deposition technique and (b) pulsed laser annealed (B-doped Q-carbon) thin films with the inset showing a schematic of B-doped amorphous Q-carbon formed on c-sapphire.

FIG. 1.

SIMS profiles of (a) as-deposited boron and carbon layers with the inset showing a schematic of the alternating layers of amorphous carbon and boron deposited on c-sapphire using the pulsed laser deposition technique and (b) pulsed laser annealed (B-doped Q-carbon) thin films with the inset showing a schematic of B-doped amorphous Q-carbon formed on c-sapphire.

Close modal

Figure 2(a) depicts the unpolarized Raman spectroscopy of as-deposited B-C, B-doped Q-carbon, and hot-filament chemical vapor deposition (HFCVD) grown B-doped diamond (formed from B-doped Q-carbon) using 532 nm as the excitation source. There is a considerable increase in the sp3 fraction in PLA B-doped Q-carbon (85%) as compared to the as-deposited B-C sample. The inset in Fig. 2(a) shows the fitted cumulative curve in B-doped Q-carbon from which the sp3 fraction can be extracted. In the range of 900–2000 cm−1, the spectrum can be deconvoluted into three Raman-active vibrational modes centered at 1105 cm−1, 1322 cm−1, and 1567 cm−1. The peak centered at 1105 cm−1 corresponds to the sp2 dangling bonds on the surface of nanodiamonds. The unsaturated sp2 bonds are predominantly seen in nanodiamonds as compared to microdiamonds or large area single crystal diamonds. The second and third peaks correspond to the presence of nanodiamonds and graphitic entities (G peak), respectively. The undoped phase of Q-carbon which is formed by nanosecond laser irradiation and subsequent quenching process, contains 75%–85% sp3 bonding. The sp3 fractions calculated in B-doped Q-carbon superconducting thin films after curve fitting vary from 83 to 86%. The low intensity of the G peak is indicative of less graphitization in B-doped Q-carbon samples. The HFCVD prepared B-doped diamond, by using B-doped Q-carbon as a template, has a sharp diamond peak centered at 1331 cm−1 and a graphitic hump at 1557 cm−1. B-doped Q-carbon thin films have nuclei of B-doped diamond which grow during the HFCVD process. This leads to the formation of B-doped diamond at lower temperatures and time as compared to previously reported CVD synthesized B-doped diamond. Due to the presence of quantum mechanical interference between the zone-center Raman active optical phonon and the continuum of electronic states created by B atoms, there occurs an asymmetry and red-shift of the diamond peak in the B-doped Q-carbon thin films. In the case of B-doped polycrystalline diamond samples, there are vibrational modes between 475 and 1225 cm−1 which are due to maximas in the phonon density of states (PDOS).22 These peaks in B-doped diamond thin films suggest distortion and the presence of defects in the diamond lattice. Reports also indicate that these peaks originate from local vibrational modes of B pairs present in the interstitial sites.23 High-resolution Raman spectroscopy of B-doped Q-carbon thin films shows the absence of these peaks, suggesting B doping in electrically active sites of Q-carbon. The vibrational mode, centered at ∼500 cm−1 in B-doped diamond, suggests the presence of B pairs in the interstitial sites of the diamond. This causes a distortion of the hole-hole interaction at lower temperatures, thereby reducing Tc in B-doped diamond to 25.0 ± 0.5 K from 36.0 ± 0.5 K in B-doped Q-carbon. The electronic Raman spectra of B-doped Q-carbon, as-deposited B-C, B-doped diamond (by HFCVD), and c-sapphire substrate, are shown in Fig. 2(b). The results show a distinct shallow acceptor energy level at 33.3 meV in B-doped amorphous Q-carbon, as compared to the previously reported value of 37.0 meV in heavily B-doped crystalline diamond.24 As is evident from Fig. 2(b), there are no electronic Raman transitions from 150 to 400 cm−1 in c-sapphire (substrate) and as-deposited B-C thin films. In the B-doped diamond thin films, there are various electronic transitions at 31.2 meV, 35.3 meV, and 41.6 meV. The first transition at 31.2 meV corresponds to 1s to 3s electronic transition, whereas the other two correspond to 1s to 4s transition. It has already been reported that at low B concentrations (<1 × 1018 cm−3) the electronic transitions, pertaining to only 1s(p3/2) → 1s(p1/2), occur.25 This transition is seen in extremely low-concentration B-doped diamond samples at ∼16 cm−1.25 Lyman series electronic transitions corresponding to 1s to ns transitions are predominantly seen in heavily B-doped diamond samples.24 There also occurs spin-orbit splitting (formation of p3/2 and p1/2) of the acceptor states whose value linearly increases with the increase in the principal quantum number. The value of spin-obit splitting in B-doped Q-carbon is found to be ∼7 meV as compared to ∼6 meV in B-doped diamond24 and ∼6.3 meV in HFCVD B-doped diamond. This coupling causes a considerable overlap of the electronic acceptor states thereby increasing the density of the electronic density of states near the Fermi energy level. The schematic of electronic transitions and the energy levels is shown in Fig. 2(c). The presence of a shallow acceptor state at ∼37 meV and ∼6 meV spin-orbit splitting of the valence band in B-doped diamond cause superconductivity in B-doped diamond. This acceptor state is associated with the formation of metallic B-C nanosheets.24 In B-doped Q-carbon, the formation of a shallow acceptor energy level at ∼33 meV results from the enhanced B concentration, and it is situated near the valence band maximum. The spin-orbit splitting associated with this energy level is ∼7 meV. This causes an increase in the density of the electronic acceptor states near the Fermi level, which leads to high Tc superconductivity in B-doped Q-carbon. As compared to the previously reported value of the shallow acceptor state at ∼37 meV in B-doped diamond (Tc = 5 K), the HFCVD B-doped samples show the presence of an acceptor state at 35.3 meV, situated close to the valence band maximum. The B-doping in Q-carbon introduces a phonon softening of the diamond-related zero-optical phonon peak (from 1332 cm−1 in diamond to 1322 cm−1 in B-doped Q-carbon). A similar downshift is observed in the case of B-doped diamond thin films which is related to electron-phonon coupling thereby leading to superconductivity.26,27 The softening of phonon modes and the creation of new vibrational modes also cause an increase in the Tc of the HFCVD prepared B-doped diamond prepared using B-doped Q-carbon as the template. There is no evidence of the formation of crystalline B-C phases. B-doped carbon nanotubes (Tc = 12 K) have a characteristic radial breathing mode (RBM) at ∼200 cm−1, which denotes the out-of-plane phonon vibrational mode. The pressure induced Tc as observed in these materials is directly related to an increase in the phonon frequency of RBM.28,29 BC3 and BC5 phases have distinct Raman-active vibrational modes centered at ∼500 and 1200 cm−1. In addition to that, these B-C phases are crystalline in nature and have a XRD peak at 2θ ∼ 10°.30 The XRD of B-doped Q-carbon contains no diffraction peaks corresponding to B-C crystalline phases, and there are no Raman peaks at 200 and 500 cm−1.

FIG. 2.

(a) Raman spectroscopy of B-doped Q-carbon, B-doped diamond, and as-deposited B-C thin films with the inset showing 84.3% sp3 in B-doped Q-carbon; (b) electronic Raman spectra of B-doped Q-carbon, B-doped diamond, as-deposited B-C, and c-sapphire substrate; and (c) the energy-level schematic diagram of B acceptor states in B-doped Q carbon (green band:33.3 meV) and B-doped diamond (31.2, 35.3, and 41.6 meV). The sapphire peak in figure (b) is indicated by *.

FIG. 2.

(a) Raman spectroscopy of B-doped Q-carbon, B-doped diamond, and as-deposited B-C thin films with the inset showing 84.3% sp3 in B-doped Q-carbon; (b) electronic Raman spectra of B-doped Q-carbon, B-doped diamond, as-deposited B-C, and c-sapphire substrate; and (c) the energy-level schematic diagram of B acceptor states in B-doped Q carbon (green band:33.3 meV) and B-doped diamond (31.2, 35.3, and 41.6 meV). The sapphire peak in figure (b) is indicated by *.

Close modal

The X-ray diffraction spectrum of B-doped Q-carbon is shown in Fig. 3(a). The diffraction peak at 42.23° (2θ) corresponds to (0006) of the c-sapphire substrate. There are no other peaks in the x-ray scan, thereby indicating that the synthesized B-doped Q-carbon samples are pristine in nature. The spectrum also indicates that the B-doped Q-carbon is amorphous. Figure 3(b) depicts the XPS survey scans of as-deposited and B-doped Q-carbon thin films. The inset in Fig. 3(b) shows the high-resolution XPS scan of the PLA sample in the binding energy range of 186–198 eV. There is a clear increase in the C/O ratio after laser annealing. This is an indication of the laser annealing assisted reduction process, where the oxygen-rich functional group carbon-based material is ablated off from the surface of the thin film. The absence of impurity peaks in the survey scan shows that the as-deposited as well as laser-annealed samples are largely impurity-free. Deconvolution of the high-resolution XPS scan in the range of 188–196 eV gives rise to two peaks. The two peaks are centered at 188.5 eV and 192.0 eV and are attributed to the B1s and B-O electronic states, respectively.31 It has been reported that the strength of the peak centered at 192.0 eV increases with oxidation (formation of B3+).31 This peak in the PLA sample suggests the presence of B-O electronic states near the surface. Since PLA is a laser-assisted reduction process, there is a decrease in the volume fraction of oxygen present in the few surface layers. So, the amount of B-O present in the PLA samples is too low to perturb the superconducting properties of the B-doped Q-carbon structure.

FIG. 3.

(a) XRD scan of B-doped Q-carbon and (b) XPS survey scan of B-C and B-doped Q-carbon thin films. The inset in figure (b) illustrates a high-resolution XPS scan showing the presence of B-O and B-1s peaks.

FIG. 3.

(a) XRD scan of B-doped Q-carbon and (b) XPS survey scan of B-C and B-doped Q-carbon thin films. The inset in figure (b) illustrates a high-resolution XPS scan showing the presence of B-O and B-1s peaks.

Close modal

Figures 4(a) and 4(b) depict the high-resolution FESEM images of a B-doped Q-carbon sample. The inset of Fig. 4(a) shows the dense structure of B-doped Q-carbon which is formed after melting and subsequent quenching of C and B mixed molten layers. The filamentary structure is formed due to interfacial instability during the super undercooling process by the nanosecond ArF laser.17 Formation of nano- and micro-diamonds is observed occasionally at the triple junctions and is shown in figure 4(b). The B-doped Q-carbon structures have a negative electron affinity and it glows under the application of a stage bias. Previous reports on Q-carbon (using Kelvin probe force microscopy) also indicate a negative electron potential with respect to diamond-like carbon.17 The filamentary structures of the B-doped Q-carbon are disconnected, as shown by the white arrows in the inset of Fig. 4(b). Homogeneous and heterogeneous nucleation of diamonds can occur from Q-carbon thereby forming diamonds having ⟨110⟩ and ⟨111⟩ out of plane orientation, respectively.17 Figure 4(c) shows the FESEM image of B-doped diamond formed using the HFCVD technique where the B-doped Q-carbon acts as a template. As evident from figure 4(c), the diamond crystallites are preferentially oriented along ⟨111⟩ indicating heterogeneous nucleation of diamond from Q-carbon on the (0001) sapphire substrate. The resulting B-doped diamond structures have a Tc of 25.0 ± 0.5 K, which is ∼14 K higher than the B-doped diamond samples prepared by the plasma enhanced chemical vapor deposition (PECVD) technique.4 The detailed structural and property correlations of HFCVD prepared B-doped diamond from B-doped Q-carbon will be discussed elsewhere.32 

FIG. 4.

(a) and (b) High-resolution FESEM images showing filamentary structures of B-doped Q-carbon with the insets in (a) and (b) showing dense and (some) disconnected filamentary structures of B-doped Q-carbon (indicated by white arrows) formed due to interfacial instability, respectively, and (c) FESEM image of B-doped diamond formed using B-doped Q-carbon as a template.

FIG. 4.

(a) and (b) High-resolution FESEM images showing filamentary structures of B-doped Q-carbon with the insets in (a) and (b) showing dense and (some) disconnected filamentary structures of B-doped Q-carbon (indicated by white arrows) formed due to interfacial instability, respectively, and (c) FESEM image of B-doped diamond formed using B-doped Q-carbon as a template.

Close modal

Figure 5(a) shows the cross-sectional HAADF image of the B-doped Q-carbon on the c-sapphire substrate. The elemental maps of B and C [Figs. 5(b) and 5(c)], obtained by EELS, clearly demonstrate the homogeneous distribution of B in Q-carbon throughout the analyzed region [in-boxed region in Fig. 5(a)], which is consistent with SIMS results (Fig. 1). A representative EELS spectrum is presented in Fig. 5(d), showing the K-edges of B and C. The spectrum contains the characteristic π* and σ* peaks associated with the K-edge of B and C, showing the presence of B and C bonded in both the sp3 and sp2 hybridized state. The EELS quantification33 estimates the average B concentration to be 17.0 ± 1.0 at. % in the Q-carbon. The HRTEM, HAADF, and convergent beam electron diffraction (CBED) results show the Q-carbon structure to be amorphous, which is consistent with X-ray diffraction. Our EDS elemental mappings show that B is homogeneously distributed in the amorphous carbon. We have also collected the HAADF image of B-doped Q-carbon and performed X-ray EDS elemental mapping of B, Al, and C, whose concentrations are consistent with EELS data.19 The homogeneous dispersion of B atoms, as a result of laser melting and quenching, is crucial for high-temperature superconductivity in B-doped Q-carbon thin films. No evidence for B clusters is found in the EDS maps, suggesting that the melting of B and C layer occurs during pulsed laser melting. The calculated sp3 fraction from C edges by EELS quantification is in agreement with the measured values by Raman spectroscopy. The sp3 fraction of B as calculated from the K-edge of B in EELS is 0.6. The B in its sp3 electronic state resembles the substitutional B atom in the diamond lattice. On the other hand, a fraction of the sp2 B electronic states are in the interstitial B states which act as shallow electron donors (free π electrons) thereby perturbing the superconducting properties of B-doped Q-carbon. There is an excellent correlation between the sp3 fraction in B with Tc and electron-phonon coupling parameter as discussed below.

FIG. 5.

(a) Cross-sectional high-angle annular dark field (HAADF) image of the formed B-doped Q-carbon on the c-sapphire substrate; (b) B-EELS mapping; (c) C-EELS mapping; (d) EELS spectrum revealing characteristic K edges of B and C with estimated 17.0 ± 1.0 at. % of B in amorphous Q-carbon; (e) fitted EELS spectrum revealing the B K edge having 62 sp3%; and (f) fitted EELS spectrum revealing the C K edge having 80 sp3%. The scale bars shown in figures (b) and (c) correspond to 10 nm.

FIG. 5.

(a) Cross-sectional high-angle annular dark field (HAADF) image of the formed B-doped Q-carbon on the c-sapphire substrate; (b) B-EELS mapping; (c) C-EELS mapping; (d) EELS spectrum revealing characteristic K edges of B and C with estimated 17.0 ± 1.0 at. % of B in amorphous Q-carbon; (e) fitted EELS spectrum revealing the B K edge having 62 sp3%; and (f) fitted EELS spectrum revealing the C K edge having 80 sp3%. The scale bars shown in figures (b) and (c) correspond to 10 nm.

Close modal

The magnetization vs. temperature plot in zero field cooled (ZFC) and field cooled (FC) conditions are performed at 60 Oe applied magnetic fields for Q-carbon doped with 17.0 ± 1.0 at. % boron and is shown in Fig. 6(a). From these measurements, the Tc for B-doped Q-carbon was estimated to be 36.0 ± 0.5 K. The Tc for crystalline diamond doped prepared from B-doped Q-carbon using HFCVD was found to be 25.0 ± 0.5 K. As it is quite evident from the plots, the value of magnetic moment increases as a function of the magnetic field. The bifurcation with the application of magnetic field occurs at Tc (36.0 ± 0.5 K). This is as result of trapping of magnetic fluxes in a superconducting material below Tc after the application of an external magnetic field. Our results on B-doped Q-carbon and diamond follow the characteristics of superconductivity in bismuth, where Tc for amorphous bismuth is 6.8 K,34 compared to 53 mK for the bismuth single crystal.14 This trend in bismuth has been correlated to enhanced electron-phonon coupling and higher density of states at the Fermi level in amorphous Bi compared to the single-crystal Bi.15 There is a large difference in the magnetic moment between the ZFC and FC curves indicating the presence of large flux pinning forces in the material. This leads to trapping of magnetic flux in the FC condition. The transition temperature is shifted to lower values after application of the magnetic field, suggesting inhomogeneous superconductivity in the B-doped Q-carbon thin films. Figure 6(b) illustrates the magnetic moment versus applied magnetic field plots at different temperatures (below Tc) in the B-doped Q-carbon thin film. This is also referred to as the “butterfly hysteresis” at different temperatures (below Tc). The values of Hc1(T) and Hc2(T) were calculated from the hysteresis loops. The magnetic field value for the highest point in the negative magnetic moment (4th quadrant) in the hysteresis loop corresponds to Hc1(T). The value of Hc2(T) was determined as the field from which M(H) deviated first from the background (X axis).35 The Hc2(T) is found to vary at a faster rate than predicted by the Werthamer–Helfand–Hohenberg (WHH) model.35 According to the WHH model, the value of Hc2(0) is calculated using the equation

H c 2 0 = 0.69 ( d H c 2 / d T ) T c ,
(1)

where d H c 2 / d T denotes the slope at Tc. Solving this equation yields the value of Hc2(0) as 6.9 T, which is also shown in Fig. 6(c). In B-doped Q-carbon thin films, the value of Hc2(0) as calculated from the intersection of the extrapolated trend curve with the Y axis, is 5.4 T. The Ginzburg–Landau (GB) coherence length (εL) can be calculated using the equation

ε L = Φ 0 / 2 π H c 2 ( 0 ) 0.5 .
(2)
FIG. 6.

(a) Magnetic moment vs. temperature plots of the B-doped Q-carbon thin film showing Tc = 36.0 ± 0.5 K; (b) depicts M-H loops at a constant temperature below Tc; (c) upper critical field and lower critical field in B-doped Q-carbon thin films along with the WHH curve and the inset depicting deconvolution of the lower critical field to Hc1(σ) and Hc1(π) peaks in B-doped Q-carbon thin films; and (d) shows critical current density versus applied magnetic field at various temperatures below Tc with the inset showing Jc (1 T) at various temperatures. The error bars (5%) are shown in figure (c).

FIG. 6.

(a) Magnetic moment vs. temperature plots of the B-doped Q-carbon thin film showing Tc = 36.0 ± 0.5 K; (b) depicts M-H loops at a constant temperature below Tc; (c) upper critical field and lower critical field in B-doped Q-carbon thin films along with the WHH curve and the inset depicting deconvolution of the lower critical field to Hc1(σ) and Hc1(π) peaks in B-doped Q-carbon thin films; and (d) shows critical current density versus applied magnetic field at various temperatures below Tc with the inset showing Jc (1 T) at various temperatures. The error bars (5%) are shown in figure (c).

Close modal

Using the value of Hc2(0) as 5.4 T, εL is calculated as 79.3 Å. The value of penetration depth ( λ d) can also be calculated using the equation

H c 1 ( 0 ) = ( Φ 0 / 4 π λ d 2 ) ln ( λ d / ε L ) .
(3)

The value of λ d is calculated as 82.8 Å. The Ginzburg–Landau parameter (k) is calculated to be 1.04 (>1/20.5) thereby showing that B-doped Q-carbon is a type II superconductor.36 The zero-temperature energy gap (Δ(0)) in B-doped Q-carbon is calculated as 5.5 meV using the equation: Δ(0) = 1.8 kBTc. The value of the exponent (n) is calculated using the power law [Eq. (4)]11 

H c ( T ) H c ( 0 ) = 1 ( T T c ) n .
(4)

From the Hc2(T) data fitting, the value of n is derived to be 2.1 for the case of Hc2(T), which is consistent with the BCS formalism. There is a downward curvature ∼0 K in the case of Hc1(T), which can be explained by the increased contribution from Hc1σ(T) as compared to Hc1π(T).37 

From the viewpoint of practical applications, the critical current density of a superconductor as a function of temperature and field is the most important parameter. The critical current density (Jc) is calculated using the Bean's formula [Eq. (5)] and is shown in Fig. 6(d) 

J c = 20 Δ M t w 2 l w 3 ,
(5)

where Δ M is the difference in magnetization values (+M and −M) at a particular magnetic field, and t, w, and l are the thickness, width, and length of the sample. The value of Jc (0 Oe) at 2 K is calculated as 2.7 × 109 A/cm2 which is quite large as compared to B-doped diamond. The large value of Jc(0 Oe) in B-doped Q-carbon is due to its small dimension. A large value of Jc (0 Oe) is also indicative of flux-melting in this material. The inset in Fig. 6(d) indicates a logarithmic plot of Jc versus magnetic field. The dark dotted line indicates the value of Jc (1 T) at 2, 6, 16, and 21 K. The values of Jc (1 T) and Jc (2 T) at 21 K are found to be 1.6 × 108 A/cm2 and 4.3 × 107 A/cm2, respectively. As is evident from Fig. 6(d), there is a sharp decrease of Jc with an increase in the magnetic field. There occurs a transition from the superconducting state to the normal state in a type-II superconductor above the upper critical field. The ability to transmit the critical current (with no heat loss) in a superconductor can cease much below the upper critical field. The corresponding magnetic field is termed as the irreversibility field (H* ∼ 2.5 T), whose value is approximately half of that of Hc2 (∼5.4 T). Above H*, the Lorentz force which is created on the magnetic vortices causes depinning and thereby drastically reduces the critical current density. An increase in the value of H* is possible by introducing pinning centers in the matrix of a superconductor which in turn adversely affects the value of maximum critical current density. The high value of the Jc (0 Oe) can also be predicted from the sharp fall in the magnetic moment at Tc in the zero field cooled condition [Fig. 6(a)]. The high critical current density of B-doped Q-carbon (at low magnetic fields) makes it an ideal candidate for low field nuclear magnetic resonance (NMR) inserts.

The temperature dependence of the critical field (at 0 Oe) can be fitted with Jc (T) = Jc (0) [1–(T/Tc)]. The value of Jc (0) is extracted as 2.5 × 109 A/cm2. At 4.2 K, the value of Jc (0 Oe) is calculated as ∼107 A/mm2 which is much higher than found in Nb-Ti, Nb3Sn, and YBCO superconductors (<105 A/mm2).38 The energy per unit volume (ΔGns) of the superconducting state relative to the normal state can be represented using the equation: Δ G n s = 0.5 μ 0 H c 2 ,39 where μ 0 and Hc denote the magnetic permeability (in vacuum) and upper critical field (at ∼0 K), respectively. The values of Hc in Nb3Sn and B-doped Q-carbon are 27.0 T and 5.4 T, respectively. So, Δ G n s (of B-doped Q-carbon) = 0.04 ×  Δ G n s (of Nb3Sn). The high values of Jc in B-doped Q-carbon are due to the fact that the energy required to exclude the magnetic field is extremely low in the case of B-doped Q-carbon (0.04 × energy required for Nb3Sn superconductors). A weaker dependence of Jc at higher fields is also observed in B-doped Q-carbon. This can be due to the presence of a large number of weakly coupled superconducting regions.40 The larger values of Jc at lower temperatures are due to the presence of pinned states. Q-carbon may also contain diamond and DLC inclusions due to inhomogeneous melting, which can enhance flux pinning. Therefore, larger current density is required to move the pinned vortices. At larger magnetic field, this phenomenon is negligible due to the presence of an external magnetic field which assists the movement of the pinned states. It is well known that in a pure annealed superconductor, the values of Jc are low due to the presence of flux lattice lines (FLLs), which dissipate the energy and the superconductor eventually turns “normal”. The refinement of the superconducting grain size introduces pinning centers in a superconductor. This causes an increase in the value of Jc.

Figure 7 depicts the temperature dependence of critical current density in B-doped Q-carbon at ∼0 Oe. It is clearly evident that Jc decreases with an increase in temperature. Interestingly, it is seen that there is a crossover from the Ambegaokar–Baratoff (AB) model to the Ginzburg–Landau (GB) model at ∼15 K in B-doped Q-carbon. According to the AB temperature dependence, the critical current density is proportional to (1-T/Tc), whereas GL predicts (1-T/Tc)1.5.41 As is evident from Fig. 7, the solid curve (AB) fits better (than the dotted curve) at lower temperatures (≤15 K) whereas at higher temperatures (>15 K) up to Tc, the dotted curve (GL) fits better (than the solid curve). The AB temperature dependence at low temperatures is due to the presence of weak Josephson coupling and is observed in granular superconductors.42 Above 15 K up to Tc, GL dependence is observed in B-doped Q-carbon due to the presence of the current-induced gap suppression effect. It has also been argued that an increase in the coherence length can also increase the crossover temperature in high-temperature superconductors.42 The crossover point also indicates an equality of the Josephson coupling energy and the superconducting condensation energy, which is ∼15 K in the case of B-doped Q-carbon. The ratio of Josephson coupling energy to the superconducting condensation energy (ε0) can be calculated using the equation41 

ε 0 = 1 0.882 1 T x T c ,
(6)

where Tx denotes the crossover temperature. Using the value of Tx as 15 K, the dimensionless quantity ε0 is calculated as 0.7. This indicates a moderate Josephson-coupling in B-doped Q-carbon which causes the crossover between the AB and GL theory. The ratio ε0 is also inversely proportional to the electronic density of states near the Fermi level (N(0)).41 The value of ε0 is less than 1 thereby indicating an increase in the density of states near the Fermi level. This increase in N(0) may produce a moderate electron-phonon coupling in the B-doped Q-carbon structure. The current-induced gap suppression above ∼15 K (in B-doped Q-carbon) indicates the formation of a core of radius εL (T) in its vortex state. With a decrease in temperature, there occurs a shrinkage of the core which causes the crossover to the AB theory (critical current density versus temperature dependence). The depairing current density (j0) in B-doped Q-carbon can be estimated as 1.6 × 1010 A/cm2 by using j 0 = 0 ( 3 3 π λ 2 ξ ) , where 0 , λ , and ξ represent the flux quantum, penetration depth, and coherence length, respectively. This indicates that we have achieved ∼15% of the depairing current (at ∼0 Oe) in B-doped Q-carbon. A further enhancement in Jc can be envisaged by increasing the B concentration and pinning centers.

FIG. 7.

The temperature dependence of critical current density in B-doped Q-carbon. There occurs a crossover between the AB and GL model at ∼15 K.

FIG. 7.

The temperature dependence of critical current density in B-doped Q-carbon. There occurs a crossover between the AB and GL model at ∼15 K.

Close modal

The coherence length, εL is calculated as 79.3 Å in B-doped Q-carbon samples. This coherence length can be compared to the size of the superconducting regions. So the reduced size of superconducting regions in B-doped Q-carbon causes an increase in the value of Jc. The Tc for phonon-mediated superconductivity can be calculated using the McMillan formula [Eq. (7)]23 

T c = ω log 1.2 exp ( 1.04 1 + λ λ μ * ( 1 + 0.62 λ ) ) ,
(7)

where ω log is the logarithmic average of phonon frequencies, μ * is the screened Coulomb pseudopotential, and λ is the measure of average electron-phonon coupling. Using the value of ω log , μ * , and Tc as 67.4 meV,39 0.1,27,40 and 36.4 K, respectively, the calculated value of λ is 0.8, which is consistent with theoretical calculations of Moussa and Cohen for B-doped diamond.10 The value of λ is indicative of moderate electron-phonon coupling in B-doped Q-carbon. This can be explained by the relation between λ , the density of states at the Fermi energy (N(0)), mass (M), average square of electron-phonon matrix element (⟨I2), and the characteristic phonon frequency averaged over the phonon spectrum (⟨ω2). The average electron-phonon coupling parameter is related to the above variables by the following equation:

λ = ( N 0 I 2 ) / ( M ω 2 ) .
(8)

Hall Effect measurements indicate a composite carrier concentration of ∼1022 cm−3 in B-doped Q-carbon samples. This indicates a substantial value of N(0) in these films. The atomic mass is also quite low. But the moderate value of λ in B-doped Q-carbon is due to the presence of strong covalent bonds (stronger than diamond),17 thereby dramatically increasing the value of ⟨ω2. In the B-doped Q-carbon thin films, all the valence states are of σ electronic states with stronger electron-phonon coupling as compared to B-doped diamond. The presence of substitutional disorder can quench Tc in B-doped diamond by opening a gap in the valence states. The value of Tc rises monotonically by increasing the B concentration (in the substitutional sites) in diamond. To date, the highest value of Tc achieved in the diamond-5% B thin film synthesized using the PECVD technique is 11 K.4 At higher B concentrations, B-doped diamond enters into the dirty type II superconductor regime where scattering of Bloch states by impurities does not play an important role. The substitutional disorder states are not formed during the ultrafast pulsed laser annealing of Q-carbon. This gives rise to high Tc in the B-doped Q-carbon structure. The substitutional B in B-doped Q-carbon acts as a shallow acceptor in the valence band. This gives rise to the formation of holes which strongly couple with phonons thereby giving rise to high Tc superconductivity. There exists highly inhomogeneous nature of electron-phonon coupling in the disordered matrix. In the highly disordered B-doped Q-carbon structures, the high value of Tc may also result from the magnetic flux percolation through regions possessing an above average electron-phonon coupling value. Due to the presence of σ and π electronic states in B-doped Q-carbon, there could exist two distinct superconducting gaps. It has been shown that the critical magnetic fields can be analyzed according to a theoretical model.37 In this model, the σ and π electronic states are separated by a Josephson contact (interband coupling). At lower temperatures, the contribution from the π electronic states are predominant and this gives rise to an upward curvature in the doped thin films (having a significant π fraction). This can be explained by an increased electronic scattering in the π band of the doped superconductor. As is evident from the inset of Fig. 6(c), the Hc1 follows a downward curvature at lower temperatures. This is indicative of predominant σ band contribution as compared to π band scattering. This is also consistent from the Hc2 plot. B-doped Q-carbon thin films have a superconducting property due to the presence of shallow acceptor electronic states associated with B. Deconvolution of the Hc1 curve gives rise to two peaks centered at 3.2 K and 16.4 K belonging to Hc1(σ) and Hc1(π), , respectively. The Hc1(σ) fraction calculated from the fitting program is 0.63. This is in excellent agreement with the B σ electronic state fraction (0.62) calculated from the B K edge in EELS. The quantification routine in the EELS spectra takes into account the electronic density of states which cause the critical magnetic field in magnetic materials. Detailed theoretical modeling of the superconductivity in B-doped Q-carbon and diamond is under progress and will be reported elsewhere.32 

In amorphous B-doped Q-carbon where B doping exceeds the retrograde solubility limits (2.0 at. % in diamond), a massive number of carriers in the form of positive holes are formed. These massive number of carriers create strong interaction with the hard phonons. The density functional theory (DFT) calculations10 indicate that at lower B concentrations (less than 5 at. %), there occurs phonon mediated hole scattering to high energy optical phonon modes, thereby causing superconductivity in B-doped diamond. Acoustic modes provide a negligible contribution to superconductivity. The phonon states of B atoms play a vital role in the coupling of optical modes. The increased B concentration (in the substitutional sites) therefore causes an increase in the electron-phonon coupling strength leading to an increase in the Tc. A detailed theoretical study suggests that the density of electronic states near the Fermi energy level is predominantly characterized by the electronic states in the substitutional B atom. Therefore, it can be assessed that an increase in Tc is directly related to an increase in the electronic density of states near the Fermi level. Theoretical studies predict that in the superhard material, BC5 with 16.7 at. % of B, the electronic density of states near the Fermi energy level is 2.1 times higher than that in 2% B-doped diamond.43 This provides a direct evidence of increase in the number of charge carriers induced by B doping. From the phonon density of states and energy calculations in BC5, it has been found that higher energy modes (115–160 meV) correspond to C-C vibrations, whereas the lower energy modes (<100 meV) are due to vibrations pertaining to B and its neighboring C atoms.36 There is also a direct evidence of increase in the intensity of the phonon density of states corresponding to lower energy with an increase in B doping. This is due to better coupling of low energy modes in highly doped samples. Therefore, superconductivity in B-doped carbon samples is attributed to vibrations associated with B atoms and its neighboring electronic concentration. In the superhard materials, with large values of elastic constant and strong chemical bonds, there are high-energy phonons and increased electronic charge densities.44 These properties can cause superconductivity in the superhard materials if they possess moderate to large electron-phonon coupling constants.

Figure 8(a) shows the magnetic moment versus temperature plots of the c-sapphire substrate used in this work. Zero-field-cooled (ZFC) and field-cooled (FC) curves indicate the pristine nature of the substrate. The background substrate corrections were done by using the magnetic plots of the substrate under identical conditions. Figure 8(b) shows the temperature-dependent magnetic moment curves of crystalline diamond doped with 17.0 ± 1.0 at. % boron. The ZFC and FC (at 100 Oe) curves indicate a transition temperature (Tc) of 25.0 ± 0.5 K in the B-doped diamond samples. This transition temperature is higher than the previously experimentally reported value of Tc in B-doped diamond. Figure 8(c) illustrates the temperature-dependent magnetic moment plots at various applied magnetic fields in B-doped Q-carbon thin films. As is quite evident from the plots, the value of magnetic moment increases as a function of the magnetic field. The bifurcation with the application of magnetic field occurs at Tc (36.0 ± 0.5 K). This occurs as a result of trapping of magnetic fluxes in a superconducting material below Tc after the application of an external magnetic field.

FIG. 8.

Magnetic moment vs temperature plots of (a) sapphire substrate; (b) HFCVD grown B-doped diamond using B-doped Q-carbon as the template; and (c) B-doped Q-carbon at different applied magnetic fields.

FIG. 8.

Magnetic moment vs temperature plots of (a) sapphire substrate; (b) HFCVD grown B-doped diamond using B-doped Q-carbon as the template; and (c) B-doped Q-carbon at different applied magnetic fields.

Close modal

The temperature-dependent (normalized) resistivity measurements of B-doped Q-carbon thin films are shown in Fig. 9(a). It shows a clear evidence of the onset of superconducting transition below ∼38 K. The zero-resistivity (Tc off) condition is observed at 35.5 K. The sharper superconducting transition in B-doped Q-carbon indicates the presence of a high-quality superconducting phase. The inset in Fig. 9(a) shows the temperature derivative plot to depict the maximum resistivity drop at 37.8 K (shown by *). Figure 9(b) shows the enlarged view of the superconducting transition of B-doped Q-carbon. The transition width (ΔT) is calculated to be 1.5 K. This transition width is comparable to that of high-temperature oxide superconductors 45,46 but much wider than that observed in single-crystal metallic superconductors (∼10−4 K).47 The transition width in a zero magnetic field condition is also dependent on the crystalline nature of a sample, with the single-crystal sample having a more narrow transition than their polycrystalline counterparts.48 An increase in the transition width in B-doped Q-carbon demonstrates its amorphous nature. The conditions of field and temperature necessary for the establishment of superconductivity in an amorphous sample will vary from one region of the sample to another in correspondence with the local value of the mean free path.49 This may also lead to magnetic field percolation through the regions of large electron-phonon coupling, thereby causing high-temperature superconductivity in B-doped Q-carbon.

FIG. 9.

(a) Temperature-dependent (normalized) resistivity measurements of B-doped Q-carbon thin films showing the onset temperature of superconducting transition temperature at 37.8 K and zero-resistivity condition at 35.5 K with the inset showing the temperature derivative measurements to depict the maximum resistivity drop at 37.8 K (shown by *) and (b) the enlarged view of the superconducting transition showing the transition width (ΔTc) to be 1.5 K. The transition width is calculated using the equation: ΔTc = T90%-T10%.

FIG. 9.

(a) Temperature-dependent (normalized) resistivity measurements of B-doped Q-carbon thin films showing the onset temperature of superconducting transition temperature at 37.8 K and zero-resistivity condition at 35.5 K with the inset showing the temperature derivative measurements to depict the maximum resistivity drop at 37.8 K (shown by *) and (b) the enlarged view of the superconducting transition showing the transition width (ΔTc) to be 1.5 K. The transition width is calculated using the equation: ΔTc = T90%-T10%.

Close modal

Figure 10(a) shows the variation of the electron-phonon coupling parameter with Tc in B-doped Q-carbon using the McMillan equation. It is evident from the plot that the Tc dependence on the electron-phonon coupling parameter is not strong at low values of λ (<0.40). When the values of λ are in the moderate-coupling regime (greater than 0.45), Tc increases rapidly. This is a characteristic feature of a superconducting material and it is due to the exponential relation between Tc and λ. A value of electron-phonon coupling of 0.2 is calculated in 2.0 at. % B-doped diamond which has a Tc of 4 K. The value of the electron-phonon coupling in B-doped amorphous Q-carbon is calculated as ∼4 times as that in B-doped diamond. This suggests stronger electron-phonon coupling in B-doped Q-carbon as compared to B-doped crystalline diamond, thereby leading to high-temperature superconductivity in B-doped Q-carbon. The EELS quantification50 in B-doped Q-carbon provides a valuable insight into the origin of superconductivity in this novel material prepared by ultrafast melting and subsequent quenching process. Electronic states corresponding to the σ bonding are present in both C and B in B-doped Q-carbon. After using the EELS quantification routine, the σ fractions calculated for C and B are 0.8 and 0.6, respectively. As discussed earlier, the B at % present in B-doped Q-carbon is 17.0 ± 1.0%. Therefore, the fraction of B contributing to the sp3 bonding (σ electronic state) is 0.1 (10.5 at. %). It is envisaged that the B electrons present in the σ electronic states play an important role in the superconductivity in B-doped Q-carbon. These electronic states act as a shallow acceptor and are situated close to the Fermi level. When B-doped Q-carbon is cooled below ∼36 K, hole Cooper pairs are formed. These Cooper pairs are mediated by the phonons and cause high-temperature superconductivity in B-doped diamond. On the other hand, B atoms present in the π electronic states have delocalized electrons (donor states) and can thwart the formation of hole Cooper pairs. This will lead to a reduction in Tc in B-doped Q-carbon. Figure 10(b) shows the density functional theory (DFT) calculation of electron-phonon coupling and Tc in B-doped diamond and their dependence on B at %.10 In these calculations, the substitutional disorder (randomness) arising from the B doping is not considered. Furthermore, these calculations pertain to B-doped σ electronic states only. As is evident from the plots in Fig. 10(b), a 10.5 at. % of B sample (doped in the sp3 hybridized electronic sites) gives rise to a value of 0.8 for the electron-phonon coupling parameter. This translates to a Tc value of ∼38 K. In the present case, 10.5 at. % B-doped in the sp3 electronic sites of Q-carbon results in a Tc value of 36.0 ± 0.5 K and λ as 0.8. This is in excellent agreement with the DFT calculated values in B-doped diamond10 (without considering the substitutional disorder). Thus the high-temperature superconductivity in B-doped Q-carbon is due to the B doping in the sp3 electronic sites of Q-carbon.21 B doping in sp3 bonded carbon causes the formation of positively charged holes (p-type) which plays an important role in the superconducting behavior of B-doped Q-carbon. The highest value of Tc (superconducting critical temperature) which was achieved in B-doped diamond was ∼11 K.4 Increasing the B concentration in B-doped diamond causes the formation of substitutional disorder and B-interstitials (n-type). These factors quench the Tc in highly B-doped diamond. B-doped Q-carbon is formed by nanosecond melting and subsequent rapid quenching of the super undercooled state. This facilitates increased concentration (exceeding the retrograde solubility limit) of B in C. The structure of B-doped Q-carbon comprises of 85% sp3 and the rest sp2. The presence of sp2 bonded C in B-doped Q-carbon plays an important role in reducing the formation of B dimers and interstitials, which causes a reduction in Tc.

FIG. 10.

(a) Variation of Tc with λ for B-doped Q-carbon and (b) variation of Tc and λ with at% B in B-doped diamond10 (the blue dotted line corresponds to 10.5 B at. % in B-doped diamond).

FIG. 10.

(a) Variation of Tc with λ for B-doped Q-carbon and (b) variation of Tc and λ with at% B in B-doped diamond10 (the blue dotted line corresponds to 10.5 B at. % in B-doped diamond).

Close modal

Calculation of the threshold energy is crucial for this study, as it will determine the minimum laser energy required for melting amorphous carbon/B thereby leading to the formation of B-doped Q-carbon structures. We have employed the SLIM (solid laser interaction in materials) programming51 to simulate the laser-solid interactions. These calculations involve an extremely accurate finite difference method to calculate the melt depth and temperature profile in the laser annealed samples. The initial layered structure consists of amorphous carbon/B/sapphire. The threshold energy ( E t h ) required for melting few layers of the amorphous carbon/B thin film can be calculated using the equation51 

E t h = K s T m ζ 0.5 ( 1 R l ) D 0.5 .
(9)

K s  = thermal conductivity of amorphous carbon (=0.3× T−0.53 W cm−1 K−1).

T m  = difference between the substrate temperature of c-sapphire and melting temperature of amorphous carbon (=3523 K).

ζ  = pulsed laser width (=20 ns).

R l  = reflectivity of the amorphous carbon at 193 nm (=0.1).

D  = diffusivity of amorphous carbon at room temperature (=2 cm2 s−1).

The thickness of the melted region varies linearly with the pulse energy density. The surface starts to melt slowly due to the sudden change in reflectivity during the phase transition. As the laser pulse terminates, the melt front recedes back to the surface. The initial stages of solidification see a low velocity but quickly reach the maximum when the steady state condition is achieved. With the increase in pulse duration, the onset of melting decreases with a decrease in solidification velocity. The maximum depth of melt also decreases with the increase in pulse duration. There is an increase in the time of peak melt depth with increasing laser pulse width.

The maximum melt depth ( Δ x ) is calculated by Eq. (10)

Δ x = C 1 ( E E t h ) ,
(10)

where

C 1 = ( 1 R l ) / ( C v T m + L ) .
(11)

In Eq. (11), C v is the volume heat capacity of amorphous carbon at its melting point (=2.1 J cm−3 K−1) and L is latent heat of fusion of amorphous carbon (= 19 775 J cm−3).

The melt in velocity ( v i n ) is calculated using equation

v i n = Δ T K 1 / L Δ x ,
(12)

where Δ T is the temperature difference between maximum temperature and melting point of amorphous carbon.

Again, Δ T is calculated using the equation

Δ T = L C 1 2 K l ζ ( E E t h ) 2 .
(13)

It was also calculated that the melt depth increases with the increase in substrate temperature. In all the above-mentioned calculations the substrate temperature was considered as 300 K. The relatively low plasma frequency of amorphous carbon helps for better material-laser coupling when the 193 nm excimer laser is used. With the incidence of laser densities having energies more than the melting point of carbon, melting occurs of the carbon/B layers. This homogeneous metallic melt triggers the liquid phase diffusion process, where the dopant concentrations exceed the retrograde thermodynamic solubility limits. As is evident from the temperature profile in Fig. 10, the onset of melting occurs at ∼20 ns after the laser is incident on the layered structure. The dotted line denotes the melting point of C. The melting point of B is ∼2349 K. As evident from the temperature profile, B and C form a homogeneous melt when laser energy densities greater than 0.6 J/cm2 are employed for the PLA process. A flatter temperature profile with time is essential for a better formation of a homogeneous melt. As seen in Fig. 11, there is a large overshoot of temperature when a laser energy density of 0.8 J/cm2 is used, and this annealing condition should be avoided. Insufficient laser energy densities (lower than 0.4 J/cm2) do not cause melting of carbon and thus are not effective in the PLA technique. The homogeneous melt cools down with high solidification velocities (30–40 m/s). This causes sufficient undercooling to form B-doped amorphous Q-carbon. It should be noted that large and small undercooling causes formation of Q-carbon and diamond, respectively.17 

FIG. 11.

Temperature versus time profile after PLA using different laser energy densities and simulated using SLIM programming.47 The dotted red line corresponds to the melting point of carbon. The inset represents a schematic diagram of the initial arrangement of C and B layers and the nanosecond laser used for the simulation purpose. A melt depth of ∼500 nm with solidification velocities 30–40 m/s was calculated using the simulation program.

FIG. 11.

Temperature versus time profile after PLA using different laser energy densities and simulated using SLIM programming.47 The dotted red line corresponds to the melting point of carbon. The inset represents a schematic diagram of the initial arrangement of C and B layers and the nanosecond laser used for the simulation purpose. A melt depth of ∼500 nm with solidification velocities 30–40 m/s was calculated using the simulation program.

Close modal

The mechanism of annealing depends critically on laser and substrate parameters. Redistribution of dopants by laser annealing cannot be explained by diffusion in solid, as the diffusion time is ultrafast in nature. The diffusion coefficients in liquid counterparts are much higher than its solid phase and cause shallow and sharp dopant profile after laser annealing.21 It has been seen that there are significant modifications taking place in the implanted region of Si lattice as a result of laser annealing. There occurs a substitution of the dopant atoms in Si lattice sites. Ion backscattering and ion channeling techniques help to determine this lattice substitution in crystalline solids.21 The lattice contraction (after substitution of lower atomic radii elements) and expansion can be measured by X-ray diffraction and ion channeling techniques. The lattice always expands or contracts 1D in out of plane conditions. High dopant concentrations can also cause a measurable strain in the substrate lattice. The time associated with laser annealing is too small, less than a microsecond (critical time for dislocation nucleation) to cause the formation of misfit dislocations which tend to relieve the strain and destroy the one-dimensional change of the lattice parameter.21 In this case, there occurs the formation of B-doped amorphous Q-carbon after the PLA process which involves melting and subsequent quenching from the super undercooled state. During the melting, B and C diffuse rapidly into liquid with a diffusivity of ∼10−4 cm2/s, and produce the homogeneous molten state. Upon quenching of the super undercooled state, this B-doped Q-carbon phase is created with B concentrations exceeding thermodynamic solubility limits via solute trapping. This gives rise to the formation of shallow acceptor electronic states and moderate electron-phonon coupling in B-doped Q-carbon which causes the high-temperature superconductivity in this material.

Type II superconductivity in B-doped Q-carbon with a Tc of 36.0 ± 0.5 K and an upper critical field of 5.4 T at ∼0 K is achieved. This novel phase is formed as a result of nanosecond laser melting of boron and carbon layers in a super undercooled state and rapid quenching subsequently. This process of rapid nanosecond melting and quenching has been modeled to obtain detailed temperature distribution, melting, and quenching kinetics. This process can enhance the dopant concentrations beyond the thermodynamic solubility limits, via solute trapping, which can be incorporated into substitutional sites without affecting their energy levels and ionization efficiencies. The dopants can be substituted in the electrically active sites thereby giving rise to interesting magnetic and electrical properties. It has been observed both experimentally (TOF-SIMS, HAADF, and EELS) and theoretically (SLIM Modeling) that the melting of C and B layers occurs during the PLA technique. The liquid phase diffusivity of B in C causes an increase in the atomic concentration of B in C beyond the retrograde solubility limits to 17.0 ± 1.0 at. % in Q-carbon as compared to the thermodynamic solubility limit of 2.0 at. % in diamond. This increase in B at % in B-doped Q-carbon plays an important role in high-temperature superconductivity. It has been shown that in B-doped Q-carbon, the upper critical magnetic field Hc2(T) follows Hc2(0) [1–(T/Tc)2.1] temperature dependence and is consistent with the BCS formalism. The moderate electron-phonon values of 0.8 and high electronic density of states near the Fermi energy level result in high-temperature superconductivity in B-doped Q-carbon. EELS and Raman spectroscopy of B-doped Q-carbon illustrate the structure, bonding, and sp3 fraction in this novel material which ultimately leads to high-temperature superconductivity. The EELS quantification of the sp3 fraction in B reveals that 10.5 at. % of B is doped in the sp3 electronic states of Q-carbon. According to the DFT calculations in B-doped diamond10 (without considering the substitutional disorder electronic states), Tc and λ values are calculated as ∼37 K and 0.8, respectively. This is in excellent agreement with the corresponding values measured in B-doped Q-carbon, where the substitutional disorder is minimized as a result of the amorphous structure. This suggests that the high-temperature superconductivity in B-doped Q-carbon is due to the B doping in the sp3 electronic sites of Q-carbon. The electronic Raman spectra of B-doped Q-carbon reveal an acceptor energy level at ∼33 meV with the spin-orbit splitting energy value of ∼7 meV. This energy state corresponds to ∼37 meV and ∼6 meV (spin-orbital splitting) found in the B-doped diamond. The presence of this electronic state near the valence band maximum indicates an increase in the density of shallow acceptor electronic states near the Fermi energy level. Therefore, the moderate electron-phonon values and high electronic density of states near the Fermi energy level result in high-temperature superconductivity in B-doped Q-carbon. The EELS quantification estimates the average 17.0 ± 1.0 at. % B in the B-doped Q-carbon, which is crucial for the high-temperature Tc in this material. The critical current density dependence with temperature and field in B-doped Q-carbon indicate that this novel material can be used for MRI and NMR applications. The critical current densities with field show considerably large values (4.3 × 107 A cm−2 at 21 K and 2 T) than typical oxide superconductors (BSCCO: 1.2 × 105 A cm−2 at 4.2 K), which is an important consideration for practical applications.38 We have obtained Tc > 57 K with increasing B concentration to 27% atomic, the details of these results will be reported shortly. This discovery of high-temperature superconductivity in B-doped Q-carbon will stimulate further research in strongly bonded carbon-based materials in the search for near room temperature superconductivity.

We are grateful for the Fan Family Foundation Distinguished Chair Endowment for J. Narayan. Ritesh Sachan acknowledges the National Academy of Sciences (NAS), USA for awarding the NRC research fellowship. This work was performed under the National Science Foundation (Award No. DMR-1560838). We used the Analytical Instrumentation Facility (AIF) at the North Carolina State University, which is supported by the State of North Carolina. Critical discussions with Professor Marvin L. Cohen of U.C. Berkeley are gratefully acknowledged.

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