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.

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 23,[39][40][41][42][43][44] .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 Tc 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.indicating the high quality of our samples.The c-axis lattice constant is 6.625 ± 0.005 Å, consistent with the previous reports 37 .The energy dispersive x-ray spectrometry (EDXS) data in Fig. S1 gives the ratio of Zr:Te as 1：2.01.Fig. 1(d) presents the band structure of ZrTe2 calculated along high-symmetry lines in the first Brillouin zone (BZ) [Fig.1(c)].We can observe a band inversion around the Γ point, confirming topological semimetal behaviors.The Fig. 1(e) 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 37 .We further conduct the transversal Hall resistance at 10 K [Fig.1(f)] and the ZrTe2 is dominated by electron-type carriers with the electron concentration ne ~ 2.97 × 10 21 cm -3 at 10 K.  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.Fig. 3(a S1].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 Fig. 3(d), the Raman spectra at ambient pressure contain two characteristic peaks, which are due to the in-plane mode Eg and the out-of-plane mode A1g of the ZrTe2 structure; this is also in agreement with a previous report 46    transition.This is similar to the results observed in β-Bi4I4 47 .The surface states on (001) plane at various pressures are shown in Fig. 6 and Fig. S13.We could observe the split and cross of surface states around  � point with the pressure increasing, while, the surface states around the  � point are more complex as shown in Fig. S9.

TABLE I. The
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 48,49 and Josephson effect 50,51 under high pressure, to explore potential topological superconductivity and Majorana fermions.

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.

FIG. 1 .
FIG. 1.(a) The crystal structure of ZrTe2 (Zr: gray; Te: orange).(b) X-ray diffraction peaks from the ab plane of ZrTe2 single crystal.The inset shows the details of the (002) reflection.(c) The bulk Brillouin zone and its projections onto the conventional cell (001) surface.(d) Calculated band structure of ZrTe2 with spin-orbit coupling (SOC).(e) Temperature dependence of resistivity for ZrTe2.Inset: The evolution of the resistivity at low temperature.(f) Transversal Hall resistance of ZrTe2 single crystal at 10 K.

FIG. 2 .
FIG. 2. Electrical resistivity of ZrTe2 as a function of temperature (a) below and (b) above 13.7 GPa.(c) Temperature-dependent resistivity of ZrTe2 in the vicinity of superconductivity.(d) Temperature dependence of resistivity under different magnetic fields for ZrTe2 at 19.4 GPa.The inset shows the results of Ginzburg-Landau fitting.(e) Hall resistance of ZrTe2 as a function of magnetic field under selected pressures at 10 K. (f) Pressure dependence of Hall coefficient and carrier concentration at 10 K for ZrTe2.Hollow points represent noise effects.

FIG. 3 .
FIG. 3. (a) High pressure XRD patterns of ZrTe2 up to 60.1 GPa at room temperature.The X-ray diffraction wavelength  is 0.6199 Å.(b) Rietveld refinement of XRD pattern at 2.4 GPa.The red solid line and black stars represent the calculated and experimental data, respectively, and the blue solid lines are the residual intensities.The vertical bars are the diffraction peak positions.(c) Pressure dependence of unit-cell volume.(d) Raman spectra of ZrTe2 at ambient pressure (Zr: gray; Te: orange).(e) Pressure dependence of vibration modes frequencies of ZrTe2.
) displays the high-pressure synchrotron XRD patterns of ZrTe2 up to 60.1 GPa.A representative refinement at 2.4 GPa is presented in Fig. 3(b).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 towards 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.Fig. 3(c) 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 [Fig.S14 and Table

FIG. 4 .
FIG. 4. The Fermi surface of ZrTe2 at various pressures.The Brillouin zone path is shown in (a), and different Fermi surfaces are indexed as I, II and III in (b), respectively.

FIG. 5 .
FIG. 5. (a)-(f) The band structures of ZrTe2 at various pressures.The orange, blue, cyan and brown bands are indexed as band I, II, III and IV, respectively.The insets show the details of the band structures.(g)-(i) The partial density of states (PDOS) at various pressures.The black and red solid lines are the PDOS of the d electrons of Zr atoms and the p electrons of Te atoms, respectively.
ℤ 2 invariant of band II under different pressures.observed a gap opening at Γ point [Fig.S11] and the band inversion at L point [Fig.S9], suggesting potential topological properties.We calculated the ℤ 2 invariant of band I and II up to 50 GPa.The detailed results are shown in Table I.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 ℤ 2 invariant around 2 GPa (1→0→1) suggests the topological states

FIG. S3 .
FIG. S3.(a) Hall resistance of ZrTe2 as a function of magnetic field under various pressures at 10 K. (b) Hall resistance of ZrTe2 as a function of magnetic field up to 11.2 GPa with sodium chloride as pressure transmitting medium at 10 K.

FIG. S6 .
FIG. S6. (a)-(f) The Fermi surface of the band II under different pressures.(g) The Brillouin zone path on the kz = 0.25 plane.The band structures at 9 GPa (h) and 18 GPa (i), the arrow points to a saddle point around the Fermi level at 18GPa (i).

Table R1 .
Sample data and structure refinement for ZrTe2 under 5.8 and 14.3 GPa.