Superconductivity in HfTe5 across weak to strong topological insulator transition induced via pressures

Recently, theoretical studies show that layered HfTe5 is at the boundary of weak & strong topological insulator (TI) and might crossover to a Dirac semimetal state by changing lattice parameters. The topological properties of 3D stacked HfTe5 are expected hence to be sensitive to pressures tuning. Here, we report pressure induced phase evolution in both electronic & crystal structures for HfTe5 with a culmination of pressure induced superconductivity. Our experiments indicated that the temperature for anomaly resistance peak (Tp) due to Lifshitz transition decreases first before climbs up to a maximum with pressure while the Tp minimum corresponds to the transition from a weak TI to strong TI. The HfTe5 crystal becomes superconductive above ~5.5 GPa where the Tp reaches maximum. The highest superconducting transition temperature (Tc) around 5 K was achieved at 20 GPa. Crystal structure studies indicate that HfTe5 transforms from a Cmcm phase across a monoclinic C2/m phase then to a P-1 phase with increasing pressure. Based on transport, structure studies a comprehensive phase diagram of HfTe5 is constructed as function of pressure. The work provides valuable experimental insights into the evolution on how to proceed from a weak TI precursor across a strong TI to superconductors.

single crystals 28 . Our preliminary study on HfTe 5 shows very different quantum physical behaviors at ambient pressure in spite of the two compounds possess the same crystal structure 28 . These interesting results make HfTe 5 a potential material for the study of the novel topological quantum phenomenon and topological phase transitions as function of pressures.
High pressure is a neat but powerful method [29][30][31][32][33][34][35] to tune the electronic and crystal structures of emergent quantum matters with advantages of without introducing disorder or impurity that are always inherent to chemical doping. In this work, we report the discovery of pressure induced superconductivity in HfTe 5 single crystals. Transport experiments indicate consecutive transitions induced by pressure from semiconductor to metal before superconductivity appears at a critical pressure of ~5.5 GPa. A systematic phase diagram on crystal and electronic properties of HfTe 5 as a function of pressure is constructed. Figure 1 shows the evolution of ac plane resistance as a function of temperature of HfTe 5 single crystals at various pressures. At 1.3 GPa, the resistance displays a typical semiconductor like behavior above 40 K. As temperature continues to decrease, the resistance increases much slowly. When pressure increases up to 2.1 GPa, the resistance shows a hump near 49 K, and then decreases with temperature, accompanied by an upturn below 11 K. The behaviors of the abnormal resistance appearing at 40 K and 49 K are intimately tied to the band structure evolution with temperatures, which are similar to those observed at ambient pressure 19,20,28 . The temperature with peak resistance (Tp) increases to 84 K at 4.0 GPa, accompanied by the broadening of the hump and the decrease of the peak resistance. Up to 5.5 GPa, in addition to the increases of Tp to 136 K, a small drop of resistance is observed at low temperature which signifies the occurrence of superconducting.

Results and Discussion
Both HfTe 5 and ZrTe 5 display a resistive abnormal hump. The Tp in HfTe 5 crystal decreases with pressure up to 1.7 GPa but those of ZrTe 5 is on the opposite 36 . This results in the reduced Tp of HfTe 5 under low pressure than that at ambient pressure (65 K) as seen in the insert of Fig. 1(a). Our experiment indicates that Tp changed systematically with pressure, showing the anomaly resistance peak moves to low temperature first before reverses to high temperature then followed by disappearance. That is in opposite to the effect of pressure on ZrTe 5 26 .
Due to weak interlayer coupling strength, both ZrTe 5 and HfTe 5 locate at the vicinity between weak and strong TI 23 , as confirmed by ARPES experiments on bulk ZrTe 5 27 . The identification of a temperature induced Lifshitz transition directly accounts to the origin of the transport property anomalies in ZrTe 5 27 . ARPES revealed two branches of bands near the Г point of ZrTe 5 : the upper branch (UB) above the Fermi level corresponds to electron like conduction band, and the lower branch (LB) band corresponds to the hole like valence band. There is a clear Lifshitz transition that occurs across 135 K where the Fermi surface topology transforms from an electron like pocket at low temperature to a hole like pocket at high temperature. This Lifshitz transition corresponds to the band structure where the energy gap center just crosses the Fermi level 27 . Assuming the same scenario to HfTe 5 , while the bands shift with increasing temperature, high pressure will reduce its energy gap, resulting into lower temperature where Fermi level crosses the gap center. In other word, the temperature of the resistance hump decreases with pressure first. With further increasing pressure, the enhanced interlayer coupling will transform the state from a weak TI to a strong TI thus Tp increases via the pressure. In Weng's work 23 , they show that the stacked 3D ZrTe 5 compound is located at the vicinity of a transition between strong and weak TI. Only the 2% change of lattice parameter will cause this transition. This can be realized through compression for HfTe 5 as shown in Fig. 2. With the pressure increased, the topological state gradually crossed the boundary of weak and strong TI. This is in consistent with the anomaly shift of Tp via pressure shown in Fig. 1.
Further increasing pressure, the maximum of resistance is totally suppressed and the overall resistance shows a metallic transport behavior. A superconducting transition with signature of resistance drop at around 2.7 K was observed at 5.5 GPa, as shown in Fig. 1(b). The transition temperatures (Tc) was defined based on the differential of resistance over temperature (dR/dT) 29 . With pressure increasing to 6.6 GPa, Tc grows rapidly with resistance drop getting more pronounced and the zero resistance starting to be fully realized. The superconductivity transitions at pressures up to 35 GPa are shown in Fig. 1(b). In the whole pressure range, the highest Tc is achieved at about 5 K, while Tc descends slightly above 20 GPa.
To assure the drop observed in Fig. 1(b) is indeed a superconducting transition, we further measured the resistance versus temperature at variant applied magnetic field(H). The evolutions of Tc at 18 GPa as a function of magnetic field are performed, as shown in Fig. 3, with insets showing the change of Tc with H. It is obvious that Tc shifts toward lower temperature with magnetic field, indicating the transition is superconductivity in nature. According to the Werthamer-Helfand-Hohenberg (WHH) formula 30  To determine the carrier density we conducted Hall Effect measurements with a magnetic field H perpendicular to ac plane of HfTe 5 single crystal using Van der Pauw method. Carrier density increases almost three orders of magnitude with pressure up to 9.8 GPa, as shown in Fig. 4. It is visual that carrier density increases much faster above 5 GPa than that at lower pressure, which coincides with occurrence of superconductivity. In other world, the variations of Tc with pressure are closely related to the change of carrier density or mobility. The carrier is found to be n-type like in the whole range of pressure which might be the results of two carriers competing.
We performed crystal structure studies based on first-principle calculations on HfTe 5 at pressure up to 40 GPa. The enthalpies of the newly predicted stable phases, calculated at the high level of accuracy, are plotted as a function of pressure as shown in Fig. 5. The ambient pressure Cmcm structure is the most stable phase up to 5 GPa, followed by a phase transition to a monoclinic C2/m structure, which corresponds to the appearance of the superconductivity at 5.5 GPa in the transport measurements. Beyond 12 GPa, triclinic P-1 structure becomes the most stable phase at least up to 40 GPa. The crystal structures of C2/m and P-1 are shown in the inset of Fig. 5, respectively. In considerations of transport experiments, the occurrence of superconductivity is possibly related to the transition from Cmcm to monoclinic C2/m. The orthorhombic Cmcm phase is a layered structure with the interlayer distance of 6.9 Å at 5 GPa. Upon compression, the new phase of monoclinic C2/m phase is also of layered structure but with reduced interlayer distance to 3.4 Å at 6 GPa. The interlayer distance along the stacking direction decreases due to the volume shrink. The second high pressure phase with triclinic P-1 symmetry is a compacted cubic like structure.
To further study the structure stability and the predicted new phases, we conducted in situ high-pressure synchrotron X-ray diffraction measurement on the HfTe 5 powder sample as shown in Figure S3. New peaks marked with star appeared at 4.69 GPa that indicated a phase transition in well consistent with the theoretical We further studied the electronic structure of HfTe 5 via first-principle calculations by taking into account spin orbital coupling (SOC). Figure S2 shows that HfTe 5 is a weak topological insulator at ambient, but transforms to a metal with complicated Fermi surface at high pressures as revealed by the electronic structures at 10 GPa and 20 GPa, respectively.
Referring to the results of electrical transport and predicted structure at high pressures, the phase diagram of HfTe 5 as function of pressures is built as shown in Fig. 6. HfTe 5 remains the ambient structure below 5.5 GPa with Cmcm symmetry but changes from weak topological character to strong topological character at around 1 GPa. The abnormal peak temperature Tp of resistance forms a minimum valley due to the weak TI to strong TI transition. The Tp reaches highest value ~136 K at 5.5 GPa, while superconductivity occurs. The superconductivity is stable in the pressure range at least up to 35 GPa, with the highest Tc ~ 5 K at 20 GPa.

Conclusion
In summary superconductivity is discovered following the pressure driven transition from a weak Tl to a strong Tl in HfTe 5 single crystal.

Methods
Sample synthesis and characterization. Single crystals of HfTe 5 were grown by chemical vapor transport. Stoichiometric amounts of Hf (powder, 3 N, Zr nominal 3%) and Te (powder, 5 N) were sealed in a quartz ampoule with iodine (7 mg/mL). Quartz ampoule was placed in a two-zone furnace for almost one month with typical temperature gradient from 500 °C to 400 °C applied. HfTe 5 single crystals present long ribbon shape 28 . The crystal structure of HfTe 5 has been determined by powder X-ray diffraction experiments 22 , which is orthorhombic with space group of Cmcm as shown in Figure S1. Trigonal prismatic chains of HfTe 3 run along a axis, and  High-pressure transport measurements. The transport properties of HfTe 5 single crystals at high pressure are measured using the standard four-probe method by diamond anvil cell (DAC) made of nonmagnetic BeCu alloy as described in refs 29 and 31-35. Pressure was generated by a pair of diamonds with 500 μ m culet. A T301 stainless steel gasket, pre-indented from 250 μ m to 30 μ m thickness, was drilled a center hole with 250 μ m in diameter. The gasket was then covered by cubic BN insulator layer to protect electrode from short circuit to gasket. A center hole with a diameter of 100 μ m was further drilled at the insulating layer to serve as sample chamber. The HfTe 5 single crystal with a dimension of 80 μ m * 80 μ m * 10 μ m was loaded into sample chamber with soft NaCl fine powder as pressure transmitting medium. Slim gold wires of 18 mm in diameter are used as electrodes. Pressure was calibrated by ruby fluorescence shift method for all the experiments. The DAC was placed inside a MagLab system to perform the electric transport experiments 35 . To ensure equilibrium, the temperature was automatically controlled by the MagLab system with slow temperature change rate. A thermometer located around the sample in the diamond anvil cell was used to monitor sample temperature.
High-pressure synchrotron XRD experiments. The high pressure X-ray diffraction experiments are conducted with a symmetric DAC. The similar procedures to transport measurements are adopted. The X-ray diffraction experiments at high pressure with synchrotron source are performed at HPCAT of Advanced Photon Source in Argonne National Laboratory with a wavelength of 0.4246 Å using a symmetric Mao Bell diamond anvil cell at room temperature. The XRD patterns are collected with a MAR 3450 image plate detector and integrated from the images by using the FIT2d software.
High-pressure structure evolution and electronic band calculation. The structure search simulations are performed through the CALYPSO method, which is specially designed for global structural minimization unbiased by any known structural information. The first principles calculations have been carried out by using the projector augmented wave (PAW) method implemented in Vienna ab initio simulation package (VASP). The lattice parameters determined by X-ray diffraction are adopted in our calculations. Generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof type is used. The k-point sampling grids are set to 14 * 14 * 8, 11 * 11 * 7 and 11 * 7 * 3 for the self-consistent calculations of HfTe 5 in 0 GPa, 10 GPa and 20 GPa, respectively. The cut-off energy for the plane wave expansion is chosen as 500 eV. Spin-orbit coupling (SOC) is taken into account self-consistently.
Note added: During the submission, we became aware the work reported by Y. Qi et al. 34 . Both works are uploaded to arXiv within three days (arXiv: 1602.08616 & arXiv: 1603.00514).