Precise Fermi level engineering in a topological Weyl semimetal via fast ion implantation

The precise controllability of the Fermi level and carrier doping in a solid-state material holds paramount significance in condensed matter physics and materials science. In microelectronics such as high-electron-mobility transistors, the ability to fine-tune the Fermi level is crucial to control the operation thresholds and high-frequency responses.^1–3 In strongly correlated systems such as high-temperature cuprate superconductors, achieving optimal hole doping is essential for enhancing the superconducting critical temperature.^4–6 As for energy harvesting applications such as thermoelectrics, a well-adjusted Fermi level strikes a delicate balance between electrical conductivity and thermopower, which leads to an optimized power factor.^7–10 A particularly noteworthy utilization for Fermi level fine-tuning lies in topological materials, where only a precisely positioned Fermi level can unveil the topological properties. For instance, in topological insulators, dissipationless electronic states such as quantum anomalous Hall states can only manifest when the Fermi level is located precisely within the small surface bandgap. This can only be achieved through a strategic blend of chemical doping^11–13 and electrostatic gating in thin heterostructures.^14–17 For topological Weyl semimetals (WSM), exotic phenomena such as large charge-to-spin interconversion,^18,19 strong higher-order photoresponse,^20,21 anomalous Nernst effect,^22,23 and quantized thermoelectric Hall effect^24,25 emerge due to a divergent Berry curvature, which can only happen when the Fermi level is tuned to be exactly at the Weyl nodes.

However, unlike in lower dimensional materials, where the Fermi level can be continuously fine-tuned through a variety of accessible techniques such as electrostatic and ionic gating, achieving this level of control in three-dimensional (3D) bulk materials has presented a long-standing challenge. Chemical doping can only be performed during the synthesis and offers limited precision, which does not meet the stringent requirement for topological semimetals. The electronic states in topological semimetals, such as from the Weyl and Dirac bands, have a linear dispersion with zero density-of-states at the topological singularities, making the Fermi level location extremely sensitive to the carrier concentration.^26,27 Therefore, there is an urgent need to attain enhanced fine-tunability of topological semimetals for more practical energy and information applications.

In this work, we use high-energy, accelerator-based hydrogen implantation to achieve ultra-fine carrier doping in WSM of tantalum phosphide (TaP).²⁴ Although hydrogenation and low-energy ion implantation have been used to tune materials properties,^28–33 there are a few key distinct features presented in the current setup. Foremost, the fine controllability of the advanced accelerator technique enables an ultra-fine tuning of the Fermi level down to the milli electron volt (meV) regime, far beyond the previous approaches. In addition, the high energy beam also enables the doping of a bulk crystal beyond a thin film with tens of nanometers thickness.^30,31,34 Moreover, thanks to the rapid development of the accelerator technology with high precision control of the accelerator beam energy and flux of ions, we were able to achieve a priori doping planning through a combination of density functional theory (DFT) and Monte Carlo calculations, which eventually shows quantitative agreement with actual experiments. This sets up an example for ultrafine doping planning experiments. High-resolution transmission electron microscopy (HRTEM), particularly scanning transmission electron microscopy with high-angle annular dark-field (STEM-HAADF) imaging, shows the presentation of high-quality crystal preservation under irradiation with stacking faults within the depth of about 200 nm. It is well known that in high T_c superconductors, heavy-ion irradiation typically leads to stacking faults near amorphized ion tracks.^35,36 However, in our case with hydrogen implantation, the low stopping power preserves the structural integrity of TaP without generating visible amorphous tracks, voids, or defects. Despite the observation of stacking faults within a 200 nm depth from the sample surface, likely induced by the kinetic energy of H⁻ ion bombardment causing rigid lattice shifts, electric transport and carrier mobility remain intact. On the other hand, the temperature to reach the charge neutral point is nearly doubled. Notably, inversion symmetry is not restored, which is crucial for Weyl node formation, potentially explaining the preservation of Weyl nodes under irradiation.

The doping experiment uses the Tandem accelerator located at the Center for Science and Technology with Accelerators and Radiation (CSTAR). The schematic used in our experiment is shown in Fig. 1(a). This type of accelerator consists of two successive linear accelerators with the same power supply. A cesium sputtering source is used as the ion source to generate negative ions from most of the elements with low vapor pressure (excluding noble gases). This source works by cesium sputtering a solid target, which produces negative ions that are then subjected to electron exchange with neutral cesium. Negative ions are initially introduced into the first stage (blue arrow), where they are accelerated toward the positive high-voltage (HV) terminal. Subsequently, depending on the experimental preferences, nitrogen gas can be injected into the HV terminal to strip some of the electrons from the ions, which transforms them into positive ions. As a result, the Tandem accelerator enables a remarkable capability to dope tens of different elements in the period table of elements. We have chosen negative hydrogen as the dopant, which offers several advantages in materials science due to its small atomic size, i.e., it does not significantly alter the structure of pristine materials.³⁷ Electrochemical hydrogenation can also be used for electron doping of semiconductors with good doping regime controllability, but not with high-precision doping level control.³⁸ In addition, hydrogen can exhibit a range of exotic properties as a dopant that makes it particularly interesting for research and applications, including metal-to-insulator transitions,³⁹ magnetostriction,⁴⁰ enhanced superconductivity,⁴¹ and paraelectric-to-ferroelectric phase transitions.⁴² 

The earlier study²⁴ highlights TaP as a remarkable topological Weyl semimetal with an inversion symmetry-breaking crystal structure [Fig. 1(b)]. It exhibits a non-saturating thermopower, a giant magnetoresistance, and a quantized thermoelectric Hall effect. Shubnikov–de Haas (SdH) oscillations are observed in the background-subtracted MR (ΔMR) data at temperatures below 25 K. The Fourier transform of ΔMR showed four pockets, with two small carrier pockets, one with a low-frequency F_α = 4 T and the other with F_β = 18 T, indicating the presence of two Weyl nodes' levels (W1, and W2) relative to Fermi level [Fig. 1(c)].²⁴ Introducing H⁻ ions through irradiation is expected to shift the Fermi level, perturb the existing Weyl nodes, and introduce new band crossings, as illustrated in the schematic diagram in Fig. 1(d).

To quantitatively link the hydrogen implantation profile to the shift of the Fermi level in TaP, we build a simple model, which shows that the required doping dosage is on the order of 10¹⁹ cm⁻³ in order to shift the Fermi level to one of the Weyl nodes (details in Sec. SI A). We also support this theoretical model with DFT^43,44 calculations from Quantum ESPRESSO^45,46 package, which gives the same order of dosage requirements (details in Sec. SI B).

To understand the defect structures and characteristics, we employ Quantum ESPRESSO and Vienna ab initio simulation package (VASP),^47,48 which provide quantitative information on H defects' characteristics inside TaP as well as qualitative insight into the energy redistribution of Weyl node energy levels upon H doping. With standard supercell method, we specify the most probable interstitial sites for H defects to be at (0, 0, 1/6) distance from every Ta conventional unit cell [also shown in Fig. S7(a)]. Our calculation also determines the zero-point formation Gibbs free energy of an interstitial H defect in TaP to be 0.226 eV. After that, a nudge elastic band (NEB)⁴⁹ method is performed to determine both H defects' migration pathways and their respective migration barrier. The calculations show the lowest migration barrier of 1.45 eV, and the anisotropy of defect diffusion, which favors the (0,0,1) direction by sixfold (details in Sec. SI C).

We also perform band structure calculation of H-doped TaP, providing direct computational evidence on the preservation of Weyl nodes upon doping. The energy of the Weyl nodes with respect to the Fermi level (E_f) is shown in Fig. 2(a) for TaP and Fig. 2(b) for the doped TaP system (one H in Ta₁₆P₁₆). Here, the horizontal axis is the index of the Weyl nodes. The Weyl nodes are ranked according to their energy so the index itself does not carry additional reciprocal space information. Notably, the doped TaP system exhibits Weyl nodes that are distributed somewhat continuously. One of the Weyl nodes near the Fermi level in Fig. 2(b) was selected, and the unfolded band structure of a short path that passes through the node's position is shown in Fig. 2(c) (pristine TaP) and Fig. 2(d) (H-doped TaP). Comparing these results, our DFT calculations indicate that the doping actually shifts the Fermi level, perturbs band structure, and introduces additional band crossings (of which, some can be Weyl nodes) as hypothesized. However, it is important to note that this DFT calculation is for one H in Ta₁₆P₁₆ corresponding to 10²¹ cm⁻³ doping concentration, which is two orders of magnitude higher than intended. Furthermore, in an actual experiment, it is impossible to periodically dope H at the same interstitial site for every supercell. Because of these, we should expect our experiment to be affected by the Fermi level shift, broadening, and appearance of minor peaks not corresponding to the perturbed W1 and W2.

To calculate the implanted ion energy, penetration depth within the crystal, and damage to the target material, the stopping and range of ions in matter software (SRIM/TRIM)⁵⁰ was employed. The detailed calculations are presented in Sec. SI E. Single crystals of TaP were irradiated with 20 keV H⁻ ions with varying durations to achieve the desired doping concentration. The summary of different samples with their respective dose of irradiation and time duration is presented in Table I.

To see the effect of ion implantation on the possible change of the crystal structures, particularly excluding the effect from radiation damage, we have performed HRTEM, including STEM-HAADF measurements on the S_3m sample in both non-irradiated regime away from ion implantation direction (Fig. 3) and irradiated regimes (Fig. 4). As shown from STEM-HAADF images [Fig. 4(a)], hydrogen implantation only has minimal radiation disturbance to the TaP crystal compared to the pristine regime [Fig. 3(a)], with moderate stacking fault created at the shallow region up to 200 nm [Fig. 3(b)]. We observed no significant extended defects such as voids or precipitates, nor did we find evidence of radiation-induced segregation or amorphization. Notably, even with the formation of stacking faults, inversion symmetry is not being restored (Fig. 4). Since the inversion symmetry breaking is the prerequisite for the formation of Weyl nodes, the lack of inversion in the stacking fault regime may explain why Weyl nodes are largely preserved under irradiation (shown in Fig. 5). More HRTEM images are shown in Sec. SI G. The preservation of crystallinity is further supported by synchrotron x-ray diffraction with very minor peak broadening (Sec. SI F).

The irradiated samples S_3m and S_20m exhibit a significantly high magnetoresistance (MR) on the order of 10⁴% and accompanied by SdH oscillations at temperatures below 15 K [see Figs. 5(a) and 5(f), respectively]. In contrast, the S_2h sample does not display such oscillations even up to B = 9T (details in Sec. SI I). It is important to note that the analysis of carrier pockets based on quantum oscillations can be influenced by the choice of the background for MR. Therefore, we calculated the background-subtracted MR (ΔMR) using different background subtraction methods (details in Sec. SI I).

Figures 5(b) and 5(g) illustrate the ΔMR obtained with a polynomial-fitted background subtraction method, while Figs. 5(g) and 5(h) show the corresponding fast Fourier transform (FFT) results for S_3m and S_20m, respectively. These FFT plots reveal a noticeably lower oscillation frequency, as well as the appearance of minor peaks compared to the pristine TaP.²⁴ Furthermore, Figs. 5(d) and 5(i) present the results of the Landau level (LL) fan diagram analysis, which indicates the presence of more oscillations with lower frequencies. This finding supports and validates our DFT calculations concerning the preservation of Weyl nodes in proximity to the Fermi surface compared to pristine TaP. The oscillation frequencies have been repeatedly extracted using various background subtraction methods, and scatter plotted together to show agreement between methods [see Figs. 5(e) and 5(j)]. Our analysis indicates the shift in relative energy of Fermi level from 5 meV below W1 for pristine TaP, to 3.8 meV below W1 for S_3m, and to 3.2 meV above W1 for S_20m (details in Sec. SI A).

To find the effect of irradiation on the carrier concentration and the mobility Fig. 6, the longitudinal and transverse conductivity data were fitted with a two-band model. The details of the data extraction from these measurements are discussed in Sec. SI H. The compensation temperature increased to 160 and 155 K for S_3m and S_20m, respectively, whereas it is 110 K for pristine TaP.²⁴  Figure 7 shows the normalized carrier concentration n_T extracted from the simple extended Kohler's rule. The consistent temperature-dependent trend observed in our analysis, in accordance with the fitted two-band model, serves as compelling evidence for the accuracy and validity of our findings (see Sec. SI J for detailed calculation).

In summary, we have addressed a novel method for ultrafine Fermi level tuning in the prototype bulk WSM TaP using high-energy hydrogen implantation facilitated by accelerator-based techniques. HRTEM and XRD show the high-quality crystals after ion implantation. The transport measurements demonstrate a successful increment in the charge neutral point temperature through precise tuning of the Fermi level in proximity to the Weyl nodes. These experimental results are achievable by the guidance of DFT calculations. The approach presented in this study represents a highly controllable and universally applicable technique for fine-tuning the Fermi level and quantum orderings in bulk quantum materials. By enabling precise control over the Fermi level in bulk crystals, the work could open up new possibilities for exploring and manipulating the unique properties of topological WSM and other quantum materials. This advancement holds significant promise for the development of future quantum technologies and applications.