Thermal transport and mixed valence in ZrTe₃ doped with Hf and Se

Interplay between the charge density wave (CDW) and conventional superconductivity (SC), both Fermi surface instabilities and low-temperature collective orders caused by a strong electron-phonon coupling, has been a subject of extensive investigations over recent decades.¹ CDW instability commonly arises in a metallic one-dimensional (1D) chain at zero temperature due to Fermi surface nesting, i.e., energetically favorable lattice reconstruction under electronic perturbation with a momentum space peridicity of q = 2$kF$⁠, where $kF$ is the Fermi wavevector; in the case of a single half-filled band, this leads to metal-insulator transition.² In 1D metals with Kohn anomaly, the CDW is typically found below temperature $TCDW$⁠, developing a BCS-type energy gap.³ Over the course of years, it has been recognized that the CDW may also arise due to strong enhancement in the electron–phonon coupling at some wavevectors unrelated to the nesting condition or to the electron-electron interaction in materials with strong Coulomb energy.^4,5

Layered ZrTe₃, an interesting metallic member of MX₃ (M = Hf, Zr; X = S, Se, Te) TMTCs, has been attracting extensive attention. It features low-dimensional atomic arrangement in its unit cell of $P21/m$ symmetry [Fig. 1(a)].^6–9 ZrTe₃ undergoes a nesting-type CDW transition that opens only a partial gap at the Fermi surface below $TCDW$ ∼ 63 K since multiple bands cross the Fermi surface. Its crystal structure is quasi two-dimensional (2D) with vdW gap, but it hosts two quasi 1D trigonal prismatic ZrTe₆ chains with inversion symmetry that propagates along the b-axis; in addition, there are Te2-Te3 chains along the a-axis [Fig. 1(a)]. The CDW originates from nesting in an electron pocket with highly directional Te 5p_x orbital character along the chains, whereas other parts of the Fermi surface are unaffected.^10–16 In contrast to NbSe₃, the CDW-induced resistivity anomaly is observed in electrical resistivity for the current path along the a-axis but is absent for the current path along the b-axis due to the nesting wavevector $q→≡(114,0,13)$⁠.^11,17,18 Band structure calculation and angular resolved photoemission (ARPES) measurements revealed that the Fermi surface (FS) consists of a three-dimensional (3D) FS sheet at the Brillouin zone (BZ) center and quasi-1D FS sheets parallel to the inclination of the BZ boundary.^19–22 The Kohn anomaly associated with a soft phonon mode and CDW fluctuations have been identified.^23–26 While the strong electron-phonon coupling is important for CDW formation in ZrTe₃, structural changes are detected at the onset of pressure-induced superconductivity.^27,28

Below $TCDW$⁠, ZrTe₃ shows a filamentary-to-bulk SC at $Tc$ ∼ 2 K with local pair fluctuations; the SC first condenses into filaments along the a-axis and then becomes phase coherent below 2 K. Bulk SC with an enhanced $Tc$ is observed by applying pressure, intercalation, substitution, and disorder with suppression of the CDW order.^29–39 Pressure-induced reentrant SC in ZrTe₃ implies the possible unconventional Cooper pairing mechanism,²⁹ yet the ultra-low-temperature thermal conductivity indicates multiple nodeless gaps in ZrTe_3−xSe_x.³⁶ ZrTe_3−xSe_x displays SC with the T_c up to 4.4 K for x ∼0.04, where the CDW-related modes in Raman spectra are observable while the long-range CDW order vanishes.¹⁵ In contrast to ZrTe₃, the isostructural HfTe₃ undergoes a CDW transition at $TCDW$ ∼ 93 K without the appearance of SC down to 50 mK at ambient pressure; the SC pairing starts to occur only within the 1D Te2-Te3 chain but no phase coherence between the SC chains can be realized under pressure.^40–42 

In superconducting ZrTe_2.96Se_0.04, CDW fluctuation-induced electronic correlations were proposed since heavy-fermion-like mass enhancement of mass tensor anisotropy has been detected.¹⁵ In addition, the mixed valence of Zr in ZrTe₃ nanoribbons was observed.⁴³ Valence segregation is associated with superconductivity in transition metal oxides with both weak and strong electronic correlations and has been discussed in connection with superconducting mechanisms and electron-phonon coupling.^44–47 Thermal transport is an efficient method to characterize the nature and sign of carriers as well as the correlation strength in superconductors, whereas x-ray photoemission spectroscopy (XPS) and Raman measurements are good probes of the valence state and phonon vibrations in transition metal compounds.^48–51 

Here, we examine the electronic correlation strength and Zr valence in superconducting ZrTe₃ single crystals doped with Se on Te and contrast this with ZrTe₃ doped with Hf on Zr atomic sites when the electrical and thermal current flow is restricted along the ZrTe₆ chains, i.e., the b-axis. We observe a decrease in Zr–Te bond lengths in both Hf- and Se-doped crystals, consistent with smaller unit cells of HfTe₃ and ZrSe₃. Thermal transport and Raman measurements show an increase in $TCDW$ with Hf substitution and a rapid suppression of $TCDW$ with Se doping. Significant mixed-valent disproportion in ZrTe₃ is reduced in bulk superconducting ZrTe_2.96Se_0.04 as well as in non-superconducting Zr_0.95Hf_0.05Te₃. The tendency toward equivalent metal valence with completely suppressed CDWs in ZrTe_2.96Se_0.04 is similar to superconducting Ba_1−xK_xSbO₃.⁴⁷ 

Single crystals of ZrTe_3−xSe_x (x = 0, 0.01, and 0.04) and Zr_1−yHf_yTe₃ (y = 0.01 and 0.05) were fabricated by the chemical vapor transport method.¹⁵ A mixture of pure elements Hf, Zr, and Te and Se powder was sealed with ∼5 mg cm⁻³ iodine as the transport agent in an evacuated quartz tube. The furnace gradient was kept between 1023 and 923 K after heating at 973 K for two days. The actual elemental ratio was checked by using energy-dispersive x-ray spectroscopy in a JEOL JSM-6500 scanning electron microscope (SEM). The x-ray absorption near edge structure (XANES) and extended x-ray absorption fine structure (EXAFS) spectra were measured at the 8-ID beamline of the National Synchrotron Light Source II (NSLS II) at Brookhaven National Laboratory (BNL) in the fluorescence mode and processed using the Athena software package. The extracted EXAFS signal $χ(k)$ was weighed by k³ to emphasize the high-energy oscillation and then Fourier-transformed to analyze the data in the R space. Thermopower and electrical resistivity were measured in Quantum Design PPMS-9 with a standard four-probe technique with thermal gradient and electrical current flow directed along the b-axis. The sample dimensions were measured by an optical microscope Nikon SMZ-800 with 10 μm resolution. XPS measurements were carried out in an ultrahigh-vacuum (UHV) system with 3 × 10^–10Torr base pressure, equipped with a SPECS Phoibos 100 spectrometer and a non-monochromatized Al-K_α x-ray source (⁠$hν$ = 1486.6 eV). XPS peak positions were calibrated using metallic Te 3$d5/2$ at 573.0 eV. The single selected point unpolarized Raman spectrum experiment was performed using WITec confocal Raman microscope alpha 300 equipped with an solid-state laser (λ = 532 nm), an electron multiplying CCD detector, and an 100×/0.9 NA objective lens. Raman scattered light was focused onto a multi-mode fiber and a monochromator with a 1800 line/mm grating. In XPS and Raman measurements, samples were sputtered in UHV by 2 × 10^–5Torr of Ar⁺ ions with a kinetic energy of 2500 eV for 60 min in order to remove surface oxygen contamination. The Raman spectra were measured right after the samples were taken out from the UHV chamber. The Raman shows no difference between Ar sputtered and freshly exfoliated samples.

Figure 1(b) shows the normalized Zr K-edge XANES spectra. The Zr K-edge absorption energy at ∼18.008 keV for ZrTe₃ indicates a dominant Zr⁴⁺ state;⁵² yet it slightly shifts to lower energies with Hf and Se doping implying valence changes. Figure 1(c) depicts the corresponding Fourier transform EXAFS of indicated samples. EXAFS could be described in a single-scattering approximation by⁵³ 

where N_i is the number of neighboring atoms at a distance R_i from the photoabsorbing atom. $S02$ is the passive electrons reduction factor, $fi(k,Ri)$ is the backscattering amplitude, λ is the photoelectron mean free path, δ_i is the phase shift, and $σi2$ is the correlated Debye–Waller factor measuring the mean square relative displacement of the photoabsorber-backscatter pairs. For ZrTe₃, the main peak at 2.76 Å corresponds to the six nearest Zr–Te bonds, while the peaks at 3.18 and 3.52 Å can be assigned to the next-nearest Zr–Te1 and Zr–Zr bonds, respectively. With Hf and Se substitution, all three peaks shift to smaller bond distances of 2.67, 3.13, and 3.50 Å, reflecting smaller unit cell volumes of HfTe₃ and ZrSe₃ when compared to ZrTe₃.^34,40,54 This indicates increased metal-chalcogen hybridization.

Figures 2(a) and 2(b) exhibit the temperature dependence of normalized resistivity $ρ/ρ300K$⁠. It shows a typical metallic behavior without resistivity anomaly for all investigated samples. An abrupt resistivity drop is seen in Se-doped ZrTe₃ [the inset in Fig. 2(a)], signaling the onset of SC. Zero resistivity is observed at $Tc$ = 4.4 and 3.4 K for ZrTe_2.99Se_0.01 and ZrTe_2.96Se_0.04, respectively. In contrast to ZrTe_3−xSe_x, no SC above 2 K was observed for Zr_1−yHf_yTe₃ [Fig. 2(b)]. Figures 2(c) and 2(d) show the temperature dependence of thermal conductivity κ(T) for the indicated samples. The room temperature κ shows a relatively low value of 2.83 W/K $·$ m for pure ZrTe₃, caused by the combination of low crystal symmetry and chemical composition with heavy elements and lower than in polycrystalline samples due to the absence of grain boundaries. A kink in κ(T) is observed at $TCDW$ for ZrTe₃ and Zr_1−yHf_yTe₃, indicating strong electron-phonon coupling, which is absent in ZrTe_3−xSe_x. Moreover, all the κ(T) data are weakly temperature-dependent above 100 K. The absence of a commonly observed maximum in κ(T) is probably related to its rather low value, demonstrating a significant acoustic phonon scattering.⁵⁵ 

Figures 2(e) and 2(f) display the temperature dependence of thermopower S(T) for the indicated samples. All the values of S(T) are positive, indicating dominant hole-like character of the 3D FS sheet at the BZ center. In the high-temperature regime, the S(T) curve is weakly temperature-dependent and shows a quasi-T-linear behavior. With decreasing temperature, the S(T) of ZrTe₃ changes its slope below $TCDW$⁠, reflecting the reconstruction of the Fermi surface, in contrast to no anomaly detected in resistivity and in agreement with previous report.¹⁶ 

In general, the S(T) is discussed in terms of two contributions, i.e., the diffusion term $Sdiff$⁠, and the phonon drag contribution $Sdrag$ due to the electron-phonon coupling. The $Sdrag$ term gives $∝T3$ for $T≪ΘD, ∝T−1$ for $T≫ΘD$⁠, and a peak structure at $∼ΘD/5$⁠, where $ΘD$ is the Debye temperature. The peak feature at 37(5) K in pure ZrTe₃ might be attributed from the phonon-drag effect since the peak temperature is very close to $ΘD/5≈$ 36.8(1) K. However, the phonon drag should diminish by $T−1$ at high temperatures, which is not found here, pointing to the presence of diffusion contribution as well. With Se doping at Te sites, there is no CDW anomaly as well as peak feature. In contrast, the Hf substitution stabilizes the CDW order in Zr_1−yHf_yTe₃ with the $TCDW$ gradually shifting to 72 K for Zr_0.95Hf_0.05Te₃ [Fig. 2(f)].

At low temperatures, the diffusive Seebeck response of the Fermi liquid dominates and is also expected to be linear in T [Fig. 3(a)]. In a single-band system, S(T) is given by

where e is the electron charge, $kB$ is the Boltzmann constant, $TF$ is the Fermi temperature, which is related to the Fermi energy $εF$ and the density of states $N(εF)$ as $N(εF)$ = $3n/2εF$ = $3n/kBTF$⁠, and n is the carrier concentration. (The positive sign is for hole, and the negative sign is for electron.)^56,57 In a multiband system, it gives the upper limit of the $TF$ of the dominant band. The derived value of S/T from 5 to 20 K is ∼0.292(3) μV/K² for ZrTe₃. It changes to ∼0.252(5) and 0.156(3) μV/K² for ZrTe_2.99Se_0.01 and ZrTe_2.96Se_0.04, respectively. We obtain the $TF$ ∼ $1.69(3)×103$ and $2.72(5)×103$ K for ZrTe_2.99Se_0.01 and ZrTe_2.96Se_0.04, respectively. The ratio of $Tc/TF$ characterizes the correlation strength in bulk superconductors. For instance, $Tc/TF$ is close to 0.1 in Fe_1+yTe_1−xSe_x, pointing to the importance of electronic correlation;⁵⁰ while it is ∼0.02 in BCS superconductor LuNi₂B₂C. The value of $Tc/TF$ is 0.0020(1) for ZrTe_2.99Se_0.01 and 0.0016(1) for ZrTe_2.96Se_0.04, respectively. Hence, electronic correlation probed by the b-axis thermal transport in ZrTe_2.96Se_0.04 is not strong and is highly sensitive to volume changes since unit cell contraction typically brings band broadening.^58,59 On the other hand, this points to highly anisotropic correlations since the Kadowaki-Woods scaling A_a/$γ2$ is comparable to Sr₂RuO₄.¹⁵ 

Temperature dependence of specific heat $Cp$(T) in zero field for ZrTe_2.96Se_0.04 is depicted in Fig. 3(b). After subtraction of the phonon part by a polynomial fit, the electronic term C_e(T) of ZrTe_2.96Se_0.04 shows a clear jump at $Tc$ [the inset in Fig. 3(b)], in agreement with the resistivity and thermopower data. The observed C/T increases below 10 K and just above T_c takes the value of γ ∼3.4 mJ/mol $·$ K² for ZrTe_2.96Se_0.04. This is larger than those of bulk superconducting ZrTe₃ and (Ni,Cu)_0.05 ZrTe₃ (2.1 ∼2.7 mJ/mol $·$ K²).^32–34 The electronic specific heat jump at T_c, i.e., ΔC_e/$γTc≈$ 0.22, is smaller than the weak coupling value of 1.43 for the electron-phonon mediated BCS superconductors.⁶⁰ As we know, the electronic specific heat can also be expressed as

Combining Eqs. (1) and (2) yields: $S/T=±γ/ne$⁠, where the units are V/K for S, J/K²$·$ m³ for γ, and m⁻³ for n. This relation was shown to hold in the T = 0 limit for a lot of materials, including heavy fermion metals, organic conductors, and cuprates.⁴⁹ Then we can estimate a dimensionless quantity

where $NA$ is the Avogadro number. The value of q gives the number of carriers per formula unit, which is ∼4.4.1(1) for ZrTe_2.96Se_0.04 and the estimated carrier density per volume $n≈9.8(1)×1020$ cm⁻³. Then the Fermi momentum $kF=(3π2n)1/3≈3.07(1)$ nm⁻¹, and the effective mass $m*$⁠, derived from $kBTF=ℏ2kF2/2m*$⁠, is 1.53(1) m_e for ZrTe_2.96Se_0.04.

Figures 4(a) and 4(b) show the XPS spectra of ZrTe₃, Zr_0.95Hf_0.05Te₃, and ZrTe_2.96Se_0.04. For the analysis of Te 3d peaks [Fig. 4(a)], doublets with the spin–orbit splitting separation (⁠$≈$10.4 eV), which are located at 573.0 eV (3$d5/2$⁠) and 583.4 eV (3$d3/2$⁠), 572.1 eV (3$d5/2$⁠) and 582.5 eV (3$d3/2$⁠), and 573.9 eV (3$d5/2$⁠) and 584.2 eV (3$d5/2$⁠) were deconvoluted and assigned to the Zr–Te bonds (Te atoms at the corners), Zr–Te bonds (Te atoms in neighboring chains), and Te–Te bonds after the background subtraction, respectively.⁴³ We also observe peaks at 576.3 eV (3$d5/2$⁠) and 586.7 eV (3$d3/2$⁠) that are contributed by the Te–O band from the small concentration of residual oxidized Te at the surface.^61,62 Zr–Te bonds at the ZrTe₆ prism corners are contributed by all Te atoms, i.e., by Te1, Te2, and Te3 atomic positions whereas Te–Te bonds in chains are contributed by Te2 and Te3 atoms only [Fig. 1(a)]. In the Zr 3d spectra [Fig. 4(b)], two sets of doublets are observed with spin–orbit splitting separation (⁠$≈$2.4 eV) located at 180 eV (3$d5/2$⁠) and 182.4 eV (3$d3/2$⁠), and 183.0 eV (3$d5/2$⁠) and 185.4 eV (3$d3/2$⁠) after background subtraction, respectively. Such observation is quite similar to the XPS analysis of ZrTe₃ and HfTe₃, in which mixed-valence states of metal atoms were assumed.^41,43 Therefore, we also consider that Zr⁴⁺ (doublets located at the high-energy part) and Zr²⁺ (doublets located at the low-energy part) might coexist. The atomic concentration ratio of Zr²⁺/Zr⁴⁺ is lower in ZrTe_2.96Se_0.04 (8.8%) when compared to Zr_0.95Hf_0.05Te₃ (13.5%) and ZrTe₃ (25.1%). The positions of characteristics Raman peaks for all investigated crystals around 215 and 155 cm^–1 are shown in [Fig. 4(c)]. Peak positions, the relative peak intensity, and the absence of Raman peaks at lower wave numbers for pure ZrTe₃ are consistent with previous observations on freshly exfoliated ZrTe₃.⁶³ The wide Raman peak at lower wave numbers is wider in Zr_0.95Hf_0.05Te₃. In addition, we observe a small red shift in ZrTe_2.96Se_0.04 to lower wave numbers (∼145 cm^–1). Both observed peaks correspond to A_g phonon modes, which involve atomic movements in the ac plane.²⁷ The wide Raman mode at low wave numbers is strongly coupled to continuum of electronic excitation and is a fingerprint of the electron-phonon interaction, involving longitudinal deformation of Te2-Te3 chains in its eigenvector.²⁷ 

When compared to ZrTe₃ [Fig. 4(a)], the relative intensity of the peak at 573.9 eV binding energy associated with Te2-Te3 is somewhat decreased for the Se-doped sample. The reduced intensity at 573.9 eV could indicate some Te2-Te3 bonds breaking, or the Te2-Te3 bonds relaxing that leads Te 3d binding energy decrease to the energy range around 573 eV, where it cannot be distinguished with the major Te-Zr bond at the prism corner. In either case, a small part of the Te2-Te3 lattice chain in the a-axis direction is randomly relaxed or distorted due to random substitution of dopant Se atoms. Since the CDW originates in the Fermi surface pocket of the Te2-Te3 orbital character, the CDW suppression mechanism by Se doping is associated with a randomly disordered Te2-Te3 lattice chain in the a-axis direction. Due to Te2-Te3 bond relaxation, the Raman active Ag mode vibration in the ac plane becomes easier, which is consistent with the 10 cm^–1 Raman red shift at 215 cm^–1 [Fig. 4(e)].

When compared to ZrTe₃, in the Hf-doped crystal Te2-Te3 lattice chain in the a-axis direction, most Te2-Te3 bonds are relaxed as the intensity of Te2-Te3 bonds almost vanished. In addition, the relative intensity of Zr–Te bonds (Te in neighboring chains) is somewhat reduced due to the substitution of Zr by Hf. The entire Te2-Te3 chain relaxation does not affect its periodicity; hence, it preserves CDW. Moreover, since longitudinal deformations of the Te2-Te3 chain exhibit strong interactions with the conduction electrons,²⁷ the electron-phonon coupling becomes easier, consistent with the rise in $TCDW$⁠. Though the longitudinal deformations of the Te2-Te3 chain also increase the electron-phonon coupling in the Se-doped sample, random disorder in the Te2-Te3 lattice affects the nesting condition.⁶⁴ A wider Raman peak at low wave numbers is likely due to disorder at the Zr atomic position with Hf substitution. Though the Te–Zr bonds at the prism corners are the same since their Te 3d binding energy are unchanged at 573 eV [Fig. 4(a)], the spatial distribution of Te around Zr is not spatially uniform. This creates an unequal charge orbital environment and consequently inhomogeneous Zr valence.

In summary, our study showed that electronic correlations in superconducting ZrTe_2.96Se_0.04 viewed by thermal transport along the b-axis of the unit cell are not strong and are governed by the unit cell contraction as more Se is added in the lattice. Hf substitution on the Zr site in ZrTe₃ increases $TCDW$⁠, whereas it is rapidly suppressed with Se substitution on the Te site due to disorder in Te2-Te3 atomic chains whose orbitals form bands with the nesting condition at the Fermi surface. The mixed valence disparity of Zr in ZrTe₃, Zr²⁺, and Zr⁴⁺ is reduced in doped crystals, but superconductivity with a large increase in T_c emerges only if the CDW is suppressed. Since even modest correlations induce considerable scattering anisotropy in ZrTe_2.96Se_0.04,¹⁵ and since ZrTe₃ is considered for interconnects in next generation room-temperature nanoscale semiconductor technology due to its size-independent low resistivity, high breakdown current density that increases with size reduction,^65–67 future nanoscale devices that would exploit anisotropic properties of ZrTe₃-doped crystals are also of considerable interest.

This work at BNL was supported by the Office of Basic Energy Sciences, Materials Sciences and Engineering Division, U.S. Department of Energy (DOE) under Contract No. DE-SC0012704. This research used the 8-ID beamline of the NSLS II and resources of the Center for Functional Nanomaterials (CFN), which is a U.S. Department of Energy Office of Science User Facility, at Brookhaven National Laboratory under Contract No. DE-SC0012704.