Pressure‐Induced Superconductivity and Topological Quantum Phase Transitions in the Topological Semimetal ZrTe2

Abstract

Topological transition metal dichalcogenides (TMDCs) have attracted much attention due to their potential applications in spintronics and quantum computations. In this work, the structural and electronic properties of topological TMDCs candidate ZrTe₂ are systematically investigated under high pressure. A pressure‐induced Lifshitz transition is evidenced by the change of charge carrier type as well as the Fermi surface. Superconductivity is observed at around 8.3 GPa without structural phase transition. A typical dome‐shape phase diagram is obtained with the maximum T_c of 5.6 K for ZrTe₂. Furthermore, the theoretical calculations suggest the presence of multiple pressure‐induced topological quantum phase transitions, which coexists with emergence of superconductivity. The results demonstrate that ZrTe₂ with nontrivial topology of electronic states displays new ground states upon compression.

Introduction

In the past decades, the layered transition metal dichalcogenides (TMDCs: MX₂, M = Mo, W, Ta, Zr, Hf, etc., and X = S, Se, or Te) have attracted tremendous attention owing to their rich physics and potential device applications.^[] The diversity of electronic properties of TMDCs includes the charge density wave (CDW),^[] the magnetism,^[] and the superconductivity (SC).^[] Recent studies have shown that TMDCs exhibit nontrivial topology,^[] making the study of these materials even more intriguing. In particular, superconductivity was observed successfully in TMDCs, either in stoichiometric compounds at ambient or under high pressure, or by doping/intercalation individual layers.^[] Therefore, TMDC family provides an exotic platform to study the relation between topologically non-trivial state and superconductivity and even exploration of topological superconductivity (TSC).^[]

Among TMDCs, ZrTe₂ has been relatively little investigated; however, it is predicted to possess non-trivial band topology recently. Although theoretical calculations indicated that ZrTe₂ is a topological crystalline insulator protected by crystalline symmetry,^[] however, angle-resolved photoemission spectroscopy (ARPES) studies have revealed that ZrTe₂ is a topological semimetal with approximately equal electron and hole carrier densities.^[] Tian et al. performed nuclear magnetic resonance (NMR) experiments and supported ZrTe₂ as a quasi-2D Dirac semimetal with a nodal line between Г and A.^[] Negative magnetoresistivity has been observed in both thin films, single crystals and nanoplates prepared by mechanical exfoliation,^[] further indicating its topological semimetal features. More interestingly, bulk superconductivity was observed by intercalating Cu or Ni in the van der Waals gap, indicating a possible candidate for TSC.^[]

The application of pressure can effectively tune the crystal structures and the corresponding electronic states in a valid and systematic fashion, and its related studies on MX₂, indeed, have given rise to many novel physical phenomena.^[] To date, the high-pressure properties of ZrTe₂ have not been well explored. Here, we systematically explore the structure and electronic properties of topological TMDC ZrTe₂ single crystal under high pressure. Room-temperature synchrotron x-ray diffraction and Raman scattering measurements reveal the stability of the hexagonal CdI₂-type structure up to 49.3 GPa. We demonstrate a pressure-induced Lifshitz transition revealed by the sign change of the charge carrier type and the Fermi surface. A superconducting transition is observed in ZrTe₂ at around 8.3 GPa and T_c reaches the maximum of 5.6 K around 19.4 GPa. Through the first-principles calculations, we find that the application of pressure alters the electronic properties and leads to multiple topological quantum phase transitions in ZrTe₂.

Results and Discussion

At ambient pressure, ZrTe₂ adopts a hexagonal CdI₂-type structure with space group P-3m1 (No. 164) as shown in Figure . The synthesized ZrTe₂ sample is characterized by the XRD experiments. The XRD pattern of ZrTe₂ single crystal is shown in Figure . The (00l) plane is a natural cleavage facet of as-grown single crystals. The full width at half maximum (FWHM) of (002) peak is only 0.04◦ (inset of Figure ), indicating the high quality of our samples. The c-axis lattice constant is 6.625 ± 0.005 Å, consistent with the previous reports.^[] The energy dispersive x-ray spectrometry (EDXS) data in Figure (Supporting Information) gives the ratio of Zr:Te as 1:2.01. Figure  presents the band structure of ZrTe₂ calculated along high-symmetry lines in the first Brillouin zone (BZ, Figure ). We can observe a band inversion around the Γ point, confirming topological semimetal behaviors. Figure  exhibits the temperature dependence of resistivity for ZrTe₂ crystal. A metallic behavior is observed with decreasing temperature followed by the resistive upturn below ≈6 K. The resistivity behavior shown here is in line with the previously reported data, which may derive from weak Kondo effect.^[] We further conduct the transversal Hall resistance at 10 K (Figure ) and the ZrTe₂ is dominated by electron-type carriers with the electron concentration n_e ≈ 2.97 × 10²¹ cm⁻³ at 10 K.

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Under high pressure, we measure the temperature dependence of resistivity ρ(T) for ZrTe₂ crystals. As depicted in Figure , ZrTe₂ keeps metallic behavior up to 60.1 GPa, while the normal state of resistivity exhibits a non-monotonic evolution with increasing pressure. Increasing the pressure initially induces continuous enhancement of the overall magnitude of ρ with a maximum occurring at 13.7 GPa. Upon further increasing the pressure, the resistivity starts to decrease gradually. As pressure increases up to 8.3 GPa, a sharp drop of resistivity in ZrTe₂ is observed at the lowest temperature (experimental T_min = 1.8 K), indicating the emergence of superconductivity, and zero resistivity is obtained when the pressure enhances to 11.6 GPa. The critical temperature T_c reaches the maximum T_c of 5.6 K around 19.4 GPa and then decreases with pressure, as plotted in Figure  (T_c is referred to T_c^onset defined as the temperature at 90% of the residual resistivity in this paper). The measurements on different samples of ZrTe₂ from two independent runs provide reproducible and consistent results, confirming the superconductivity transition under pressure (Figure , Supporting Information). To gain insights into the superconducting transition, we applied the magnetic field for ZrTe₂ subjected to 19.4 GPa. As shown in Figure , T_c is gradually suppressed with the enhancement of magnetic fields and the superconductivity extinguishes under the magnetic field µ₀H = 7 T. We tried to use the Ginzburge–Landau formula to fit the data (inset of Figure ). The estimation of µ₀H_c2 at 0 K is ≈ 6.1 T, and the Ginzburg–Landau coherence length ξ_GL(0) is 7.3 nm. High-pressure Hall resistivity measurements were further carried out to extract the evolution of charge carriers in the pressurized ZrTe₂. Figure  and Figure (Supporting Information) show the Hall resistivity curves R_xy(H) measured at 10 K under various pressures. At low pressure region, the R_xy(H) curve exhibits a negative slope, indicating an electron-dominated feature of the electrical transport. This is in agreement with the carriers type at ambient pressure. When the pressure is above 27.7 GPa, the Hall resistance slope becomes positive, suggesting the dominance of hole-type carriers. In the first run of Hall measurements, R_xy is affected by the noise between 6.7 and 27.7 GPa due to the competition between two types of carriers caused by pressure gradient. We repeated the high-pressure Hall measurements with sodium chloride as pressure transmitting medium. Compared to previous Hall measurements, we reduced the noise influence, as shown in Figure (Supporting Information). The slope of R_xy changes from negative to positive at 11.2 GPa, and the sign change of the R_xy(H) demonstrates the change of charge carrier type, which indicates the change of the Fermi surface topology. This variation could be viewed as a signature of the Lifshitz transition.^[] Pressure dependence of Hall coefficient and carrier concentration at 10 K are summarized in Figure .

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To examine the thermodynamic stability of the ZrTe₂ phase and whether the pressure-induced SC is associated with structural phase transition, we performed in situ high-pressure powder XRD measurements at room temperature. Figure  displays the high-pressure synchrotron XRD patterns of ZrTe₂ up to 60.1 GPa. A representative refinement at 2.4 GPa is presented in Figure . All the diffraction peaks can be indexed well to ambient structure (space group P-3m1, No. 164) based on Rietveld refinement with General Structure Analysis System (GSAS) software package. All the XRD peaks continuously shift toward higher angles without new peaks appearing when the pressure increases up to 49.3 GPa, indicating the absence of structural phase transition in the pressurized ZrTe₂. Above 49.3 GPa, the signal intensity of the main peak deviates from the symmetry of P-3m1. We expect to study this structural transitions in the future. Figure  shows the pressure (P) dependence of volume (V). Upon compression from 1.5 to 49.3 GPa, the overall volume decreases by 29% without volume collapse. In addition, We have performed single-crystal XRD under 5.8 and 14.3 GPa (Figure and Table , Supporting Information). The results of single crystal XRD demonstrate that ZrTe₂ retains P-3m1 up to 14.3 GPa. The stability of ZrTe₂ was also confirmed by in situ Raman spectroscopy measurements. As shown in Figure , the Raman spectra at ambient pressure contain two characteristic peaks, which are due to the in-plane mode E_g and the out-of-plane mode A_1g of the ZrTe₂ structure; this is also in agreement with a previous report.^[] The frequencies of both vibrational modes move gradually without discontinuities as pressure increases (Figure , Supporting Information) indicating the robustness of structure in the whole studied pressure range at room temperature. Interestingly, E_g mode displays the opposite trend and shows redshift behavior when the pressure is raised. This pressure-induced phonon softening is probably associated with emergence of superconductivity in the pressurized ZrTe₂.

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To further understand the transport behavior of ZrTe₂ under high pressure, we first conducted the Fermi surface calculations at various pressures (Figure ). The Fermi surfaces are indexed as I, II, and III in Figure . The decomposed Fermi surfaces are plotted in Figures (Supporting Information), and the Fermi surface IV is enclosed by the Fermi surface III. The Fermi surface I forms a connection around 2 GPa (Figure ). The pocket enlarges with the pressure and closes around 12 GPa (Figure ). The Fermi surface II transforms from shuttle shape to David-star shape at 18 GPa (Figure , Supporting Information). The hexagon (Figure , Supporting Information) in Fermi surface III becomes a David-star at 12 GPa (Figure , Supporting Information), and an opening emerges at A point under 18 GPa (Figure , Supporting Information). The Fermi surface IV emerges around 5 GPa (Figure , Supporting Information) and vanishes about 12 GPa (Figure , Supporting Information). The evolution of the Fermi surface under high pressure could be the signature of the Lifshitz transitions, and the reshape of Fermi surface I, III, and IV at 12 GPa is in line with the normal state anomalies in our resistivity measurements.

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Next, we calculated the band structures of ZrTe₂ at various pressures and the details are shown in Figure . The band indexes I, II, III, and IV are in line with the Fermi surfaces. The band I crosses the Fermi energy along Γ-M at 2 GPa (Figure ), causing the connection in Figure , and the pocket enclosing at L point (Figure ) can be identified to a p-type conversion of band I (Figure ). As for the David-star in the Fermi surface II, the band structures on the k_z = 0.25 plane (Figure , Supporting Information) indicate a saddle point around the Fermi energy under 18 GPa (Figure , Supporting Information). The reshape of the Fermi surface III (Figure , Supporting Information) is owing to the saddle point along Γ-M (Figure ), and the opening at 18 GPa is due to the p-type crossing at the Fermi energy around A point (Figure ). The emerging and vanishing of Fermi surface IV originates from the variation of band IV around Γ point from 5 to 12 GPa (Figure ). Thus, band structures calculation provides details for the Lifshitz transitions of Fermi surface topology, and the p-type conversion at A (Figure , Supporting Information) and L (Figure , Supporting Information) points is in line with the charge carrier type transition under high pressure.

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Moreover, we calculated the orbital contribution around A, Γ, and L points (Figures –, Supporting Information). Around the Fermi energy, the main distribution is from the p electrons of Te atoms, such as the band I at L point (Figure , Supporting Information), band III at A point (Figure , Supporting Information) and band IV at Γ point (Figure , Supporting Information). Accordingly, we calculated the partial density of states (PDOS) at various pressures (Figure ). The PDOS is more diverged under high pressure, and a peak emerges on the Fermi energy around 9 GPa. This peak is from the Te-p electrons and could contribute to the pressure-induced superconductivity. Besides, we calculated the charge density between the inter-layer and intra-layer Te atoms under high pressure (Figure , Supporting Information). Compared with intra-layer Te atoms, more electrons are distributed between inter-layer Te atoms. This is empirically true since the inter-layer distance is easier to compress in layered TMDCs. Such novel bonds explain the DOS peak of Te-p electrons around the Fermi energy, which could be favorable for the superconducting transition through electron-phonon coupling. Hence, our results demonstrated that the anisotropic compression behaviors in ZrTe₂ cause the redistribution of Te-p electrons. It leads to the reshape of the band structures and the Fermi surface topology, which is in agreement with the transport anomalies of normal state and the carriers type conversion under high pressure. The anisotropic compression causes the bonding and PDOS elevation around Fermi energy of Te-p electrons as well, which is in consistent with the pressure-induced superconductivity in our experiments.

Meanwhile, we observed a gap opening at Γ point (Figure , Supporting Information) and the band inversion at L point (Figure , Supporting Information), suggesting potential topological properties. We calculated the $${\mathbb{Z}}_2$$ invariant of band I and II up to 50 GPa. The detailed results are shown in Table . The band I keeps topologically trivial within the pressure range. For band II, it transforms from topologically non-trivial state at 30 GPa to trivial state at 50 GPa, and the variation of $${\mathbb{Z}}_2$$ invariant around 2 GPa (1→0→1) suggests the topological states transition. This is similar to the results observed in β-Bi₄I₄.^[] The surface states on (001) plane at various pressures are shown in Figure and Figure (Supporting Information). We could observe the split and cross of surface states around $$\bar{M}$$ point with the pressure increasing, while, the surface states around the $$\bar{\Gamma }$$ point are more complex as shown in Figure (Supporting Information). Therefore, the topological properties of ZrTe₂ could be modulated by high pressure. More importantly, our results shown here demonstrate the coexistence of non-trivial topology and superconductivity in ZrTe₂ upon compression. Our study will stimulate further studies, such as the quantum oscillations^[] and Josephson effect^[] under high pressure, to explore potential topological superconductivity and Majorana fermions.

Table 1 The $${\mathbb{Z}}_2$$ invariant of band II under different pressures.

Pressure [GPa]	Time reversal invariant planes	$${\mathbb{Z}}_2$$ index (υ0;υ1υ2υ3)
	kx = 0.0	ky = 0.5	ky = 0.0	ky = 0.5	kz = 0.0	kz = 0.5
0	0.0	0.0	0.0	0.0	1.0	0.0	(1;000)
2	1.0	0.0	1.0	0.0	1.0	1.0	(0;001)
5	0.0	0.0	0.0	0.0	0.0	1.0	(1;001)
7	1.0	0.0	1.0	0.0	0.0	1.0	(1;001)
9	1.0	0.0	1.0	0.0	0.0	1.0	(1;001)
12	1.0	0.0	1.0	0.0	0.0	1.0	(1;001)
18	0.0	0.0	0.0	0.0	0.0	1.0	(1;001)
24	0.0	0.0	0.0	0.0	0.0	1.0	(1;001)
30	0.0	0.0	0.0	0.0	0.0	1.0	(1;001)
50	0.0	0.0	0.0	0.0	0.0	0.0	(0;000)

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Based on the above resistivity, XRD, and theoretical calculation, the T-P phase diagram is summarized in Figure . These results demonstrate that high pressure dramatically alters both topological and transport properties of ZrTe₂. Its crystal sustains a hexagonal CdI₂-type structure under high pressures up to 49.3 GPa, while applied pressure induces multiple topological quantum phase transitions in ZrTe₂. More interestingly, superconductivity emerges around 8.3 GPa and T_c reaches maximum of 5.6 K around 19.4 GPa, showing a typical dome-like evolution. The combined theoretical calculations and in situ high-pressure measurements demonstrate the topologically non-trivial state is accompanied by the appearance of superconductivity, making ZrTe₂ possible platform to study topological superconductivity.

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Conclusion

In summary, we discovered pressure-induced superconductivity in topological TMDC ZrTe₂ by combining experimental and theoretical investigations. High pressure dramatically alters the electronic state, and a pressure-induced Lifshitz transition is evidenced by the change of charge carrier type as well as the Fermi surface. Superconductivity is observed in ZrTe₂ at large pressure region with a dome-shape evolution. Theoretical calculations indicated that ZrTe₂ experiences multiple pressure-induced topological quantum phase transitions, which coexists with superconductivity. Our results demonstrate that ZrTe₂ with a nontrivial topology of electronic states display new ground states upon compression and have potential applications in next-generation spintronic devices.

Experimental Section

Crystal Growth and Sample Characterization

High-quality single crystals of ZrTe₂ were grown by using chemical vapor transport method. High-purity starting materials (total amount of 0.5 g) of Zr powder and Te powder were loaded in a quartz tube with the ratio of Zr:Te = 1:2, and I₂ with the concentration of 4 mg mL⁻¹ was added as a transport agent. The tube was sealed after it was evacuated to a vacuum of 2 × 10⁻⁴ Pa, which was then put into a two-zone tube furnace. The temperatures were set to be 1173 and 1073 K for the hot-side (source) and cold-side (crystal), respectively. After a week, the furnace was cooled to room temperature with the power supply switched off. In order to obtain crystals with high quality, surface cleaning was performed for all starting materials to remove the oxide layers formed in air.^[] The crystalline phase of ZrTe₂ was checked by the single-crystalline x-ray diffraction (XRD, Cu K_α, λ = 1.54184 Å). The chemical composition value of ZrTe₂ was given by energy-dispersive x-ray spectra (EDX).

High Pressure Electrical Transport Measurements

The electrical transport measurements were carried out by the van der Pauw four-probe method using a nonmagnetic Be-Cu alloy diamond-anvil cell (DAC) with 200 µm culets.^[] Thickness of the pre-indented Be-Cu gasket was 30 µm and a hole with diameter of about 140 µm was drilled using a pulse laser. The mixture of cubic boron nitride (c-BN) powder and epoxy was loaded into the hole, and then compressed to insulate the platinum electrodes with the Be-Cu gasket. A plate-like single crystal was loaded into the sample chamber. Pressure was calibrated by the ruby luminescence method.^[] Electrical transport measurements were performed in a commercial Physical Property Measurement System (PPMS, Quantum Design Inc.).

High-Pressure Structure Measurements

In situ high-pressure x-ray diffraction (XRD) experiments were performed on ZrTe₂ powder sample at the BL15U1 beamline of Shanghai Synchrotron Radiation Facility (wavelength λ = 0.6199 Å). A symmetrical DAC with 200 µm culets was used with rhenium gasket. The XRD images were integrated and analyzed using the FIT2D software.^[] The diffraction patterns were refined by the General Structure Analysis System (GSAS) and the graphical user interface EXPGUI.^[] High-pressure in situ Raman spectroscopy investigation on ZrTe₂ was carried out on a Raman spectrometer (Renishaw in Via, U.K.) with a laser excitation wavelength of 532 nm as well as a low-wavenumber filter. Symmetric DAC with anvil culet sizes of 300 µm and mineral oil was used as pressure transmitting medium. Pressure was also calibrated by the ruby luminescence method and silicon oil was used as the pressure transmitting medium (PTM).

Theoretical Calculation

In the present first-principles calculations, the Vienna Ab-initio Simulation Package (VASP) was employed based on the density functional theory.^[] The exchange-correlation functional was treated by the generalized gradient approximation (GGA) and parameterized by the Perdew, Burkey, and Ernzerhof functional.^[] Projector-augmented wave (PAW)^[] approach was used to describe the core electrons and their effects on valence orbitals. To conduct the van der Waals correction, the zero-damping DFT-D3 functional was employed^] and the spin-orbit coupling (SOC) was taken into account in all the calculations. The plane-wave kinetic-energy cutoff was set to 500 eV, and the Brillouin zone was sampled with the special k-mesh generated by the Monkhorst-Pack scheme with a k-point spacing of 2π × 0.02 Å⁻¹. The convergence tolerance was 10⁻⁶ eV for total energy and all forces were converged to be < 0.003 eV Å⁻¹. Tight-binding models were constructed based on maximally localized Wannier functions (MLWFs) using WANNIER90 code.^[] The topological electronic structures were studied by the WANNIERTOOLS package.^[]

Acknowledgements

S.Z., J.W., and P.Z. contributed equally to this work. This work was supported by the National Natural Science Foundation of China (Grant No. 12004252, U1932217, 52272265, 11974246, 92065109), the National Key R&D Program of China (Grant Nos. 2018YFA0704300, 2020YFA0308800, 2022YFA1403401), Shanghai Science and Technology Plan (Grant No. 21DZ2260400), and the Beijing Natural Science Foundation (Grant Nos. Z190006, Z210006). The calculations were carried out at the HPC Platform of ShanghaiTech University Library and Information Services. The authors thank the support from Analytical Instrumentation Center (# SPST-AIC10112914), SPST, ShanghaiTech University. The authors thank the staffs from BL15U1 at Shanghai Synchrotron Radiation Facility for assistance during data collection.

Conflict of Interest

The authors declare no conflict of interest.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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