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# Concurrence of superconductivity and structure transition in Weyl semimetal TaP under pressure

• npj Quantum Materialsvolume 2, Article number: 66 (2017)
• doi:10.1038/s41535-017-0066-z
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## Abstract

Weyl semimetal defines a material with three-dimensional Dirac cones, which appear in pair due to the breaking of spatial inversion or time reversal symmetry. Superconductivity is the state of quantum condensation of paired electrons. Turning a Weyl semimetal into superconducting state is very important in having some unprecedented discoveries. In this work, by doing resistive measurements on a recently recognized Weyl semimetal TaP under pressures up to about 100 GPa, we show the concurrence of superconductivity and a structure transition at about 70 GPa. It is found that the superconductivity becomes more pronounced when decreasing pressure and retains when the pressure is completely released. High-pressure x-ray diffraction measurements also confirm the structure phase transition from I41 md to P-6m2 at about 70 GPa. More importantly, ab-initial calculations reveal that the P-6m2 phase is a new Weyl semimetal phase and has only one set of Weyl points at the same energy level. Our discovery of superconductivity in TaP by high pressure will stimulate investigations on superconductivity and Majorana fermions in Weyl semimetals.

## Introduction

Superconductivity and topological quantum state are two important fields of frontier research in nowadays condensed matter physics.1,2,3 Superconductivity is the state of quantum condensation of paired electrons. A Weyl semimetal defines a kind of materials with three-dimensional Dirac cones, which appear in pair with opposite spin chirality due to the breaking of spatial inversion or time reversal symmetry. The relevant electronic bands of a Weyl semimetal may cross or pass through nearby the so-called Weyl nodes with different chirality and the low-energy excitations near these points disperse linearly in the momentum space. It naturally contains the long sought novel quasiparticle excitations, namely the Weyl fermions.4,5 When the Weyl semimetal falls into superconducting state, it is possible to observe some exotic excitations, such as the Majorana fermions.6,7 Therefore, turning a Weyl semimetal into superconducting state is very important in having some unprecedented discoveries.

Recently, TaAs and TaP were predicted to be Weyl semimetals,8,9 which is followed immediately by experimental proofs.10,11,12,13,14 The Weyl semimetal normally exhibits a giant and sometime negative magnetoresistance (MR) due to the semimetal behavior and the opposite spin chirality of the paired Weyl nodes.15,16,17,18 It is very interesting and highly desired to realize bulk superconductivity in such Weyl semimetals.19 Previously, Wang et al. observed superconducting-like anomaly in the point contact tunneling spectrum on TaAs.20 The recent measurements under high pressure on Weyl semimetals NbAs and TaAs have revealed some interesting physics,21,22 but did not show the trace of superconductivity. While transition metal dichalcogenides materials, MoTe2 and WTe2, were found to show superconductivity under high pressure and both of them were considered to be the type-II Weyl semimetal.19,23,24,25,26,27,28,29,30,31,32,33,34,35 In this paper, we report, for the first time, the discovery of bulk superconductivity accompanied by a structure phase transition in Weyl semimetal TaP by applying high pressure. More importantly, first-principles calculations confirm that the P-6m2 phase with superconductivity induced by high pressure has the Weyl semimetal feature, but is distinct from the ambient phase.

## Results

### Resistivity and MR under different pressures

In Fig. 1, we show the temperature-dependent resistance R(T) of a TaP single crystal under different pressures up to 92 GPa. The pristine sample is a TaP single crystal with high quality, as characterized by x-ray diffraction (XRD), residual resistivity ratio (RRR≈31), and giant MR (about 30,000% at 8 T) with clear quantum oscillations. The large value of RRR implies low density of impurities or disorders in the sample at ambient pressure. The related data are presented in Supplementary Figs. 1 and 2, and Supplementary Note 3. Figure 1a, b display the raw data of resistance under pressures from 0.4 to 14.6 GPa (referred as low-pressure region) and from 19.2 to 92 GPa (high-pressure region), respectively. The resistivity measurements under high pressure are given in section “Methods” and Supplementary Note 4. The resistance globally gets enhanced with applied pressure starting from ambient pressure, and reaches a maximum value at about 19.2 GPa. Then the resistance decreases monotonically as the pressure continues to increase. Three-dimensional contour plot of resistance with temperature and pressure is shown in Fig. 1c. The ridge like surface graphically shows the variation of resistance with temperature and pressure. Six typical R(T) curves with pressures of 0.4, 5.0, 8.5, 19.2, 46.3 and 80.0 GPa are representatively highlighted in the contour plot. We will see later that this complex evolution of resistivity is closely related to the crossing of Fermi energy through the paired Weyl points.

Figure 2a shows the change of resistance at 5 and 300 K under different pressures. Figure 2b presents the MR at different pressures. One can see that now the MR at 0.4 GPa and 8 T is about 275%, which is much smaller than that measured on the pristine sample at ambient pressure. This may be induced by two reasons: (1) the direction of applied magnetic field is different from the one in the case of measurement at ambient pressure; (2) the non-uniform stress under a pressure. We calculated electronic resistance of the I41 md structure and the DOS near Fermi level using DFT and the semi-classic Boltzmann transport theory, as shown in Fig. 2d. In TaP or TaAs families, the Weyl points can be divided into two types according to their positions in reciprocal space: W1 (k z = 0) and W2 (k z ≠ 0), these two types of Weyl points locate at different energies.8,9 At ambient pressure, the energy of W1 is 50 meV under the Fermi level and that of W2 is about 15 meV above Fermi level, as shown in Fig. 2e. We focus on the energy of W2 at different pressures, which may have more significant influence on the density of states near the Fermi level and thus the electrical conductivity than W1. The energy of W2 relative to Fermi level changes significantly with pressure by our calculations. The detailed calculation results are given in Supplementary Note 1 and Supplementary Table 1. W2 is above the Fermi level at low pressures, and becomes below the Fermi level when a pressure at around 20 GPa is applied. Thus, when the pressure is increased to about 20 GPa, the finite DOS corresponding to this Weyl point is getting smaller, leading to the increase of the global resistivity. When the pressure is larger than about 20 GPa, the reversal process dominates. The W2 point becomes below the Fermi energy and the DOS becomes larger leading to the dropping down of the global resistance. This picture also gets support from the behavior of MR measurement. A giant MR shows up at a low pressure, which was considered as a result of the contribution of the electron and hole pockets in the material. More in detail, from the semi-classical two-band model, the MR can be calculated as follows:

$MR= Δ ρ ρ 0 = ρ B - ρ 0 ρ 0 = σ e σ h μ h - μ e 2 B 2 σ h + σ e 2 + μ h σ e + μ e σ h 2 B 2$

where $ρ 0$ is the resistivity at zero field, $σ i = n i e 2 τ i ∕ m i$(i = h, e) is the conductivity (being always positive) at the hole and electron derived band, respectively. And $μ i = e i τ i ∕ m i$(i = h,e) is the mobility of each band with a negative (positive) sign for the electron (hole) band. At ambient pressure, the Fermi energy is in between W1 and W2 (close to W2), we have an electron and hole contribution for conductivity from the Weyl nodes of W1 and W2, respectively, therefore we have a sizable MR. With compression, the chemical potential gets higher and becomes closer to W2. The electron-pocket Fermi surfaces around W1 become larger while the hole-pocket Fermi surfaces around W2 become smaller. Therefore, it is natural that the MR decreases when increasing pressure. Superconductivity has been induced in some materials with giant MR23,24,36,37,38 when pressure is applied. In the following, we will show that superconducting behavior has also been detected in TaP with further increasing pressure.

### Superconductivity induced by high pressure

Since superconductivity survives when the pressure is released, we thus did a new round of pressurizing experiment and then measure resistivity at ambient pressure. We chose a new TaP sample and ramp the pressure up to 100 GPa, keep it for 24 h (in order to have a uniform phase under high pressure) at room temperature and then release the pressure to ambient. Afterwards, we measure the resistivity down to 0.3 K, and we successfully confirm the superconducting transition. Since the sample is too small with an irregular shape after exfoliated from the high-pressure cell, we can only make two electric contacts on the sample. The residual resistance here is due to the contacting resistance. Moreover, since the sample is too small, with a full volume of superconductivity and under an external magnetic field of 10 Oe, the total magnetization is only about 10−7 emu, which is just at the marginal of measurement sensitivity. The readers are referred to Supplementary Note 2 and Supplementary Fig. 3 for details. In addition, the transitions under different magnetic fields are also determined yielding the upper critical field µ 0 H c2(T) at the pressure released state.

### XRD under high pressure

In order to understand the pressure-induced superconductivity in TaP single crystals, we further perform High-pressure-XRD (HP-XRD) experiments up to 101.66 GPa, as detailed in Supplementary Note 5. The HP-XRD results are shown in Fig. 4a. The diffraction peaks gradually move to higher angles indicating that the lattice parameters become smaller. The data are also collected when the sample is decompressed to ambient pressure, as shown in the top of Fig. 4a. It seems that the data at 101.66 GPa have almost the same diffraction pattern with that after the pressure is released to ambient one, the only difference is that the peaks globally shift due to the external pressure. Upon increasing pressure, some peaks, for example those indexed by (103) and (105) become weakened and gradually vanish above about 53.94 and 71.08 GPa, respectively. However, some other peaks show a systematic shift and weaken, but which do not disappear, for example (004) and (020). These evolutions are indicated by red dashed lines in Fig. 4a. Figure 4b shows the intensity evolution of these four peaks mentioned above. Shown in Fig. 4c is the emergence of the peak (021) at 71.08 GPa and beyond, which is indexed to the P-6m2 structure. These results give the evidence that there is indeed a structure phase transition around 70 GPa. This pressure is consistent with the one for the emergence of superconductivity, so we believe that the superconductivity is closely related to the structure P-6m2 of TaP. By using the high-pressure structure P-6m2, which is illustrated on the right-hand side of Fig. 4d, the XRD data with pressure released can be fitted very well, as shown in Fig. 4e. Interestingly, in ref. 22 the authors also find that TaAs transforms to P-6m2 structure at 14 GPa and the structure can be reserved to ambient pressure. This stabilization of high-pressure phase in TaP is exactly the same as TaAs, but in TaAs no superconductivity was discovered above 1.8 K with the structure of P-6m2. We must mention that the data at 101.66 GPa can still be fitted with this structure, with some peaks broadened and deviated a little bit. This deviation may be due to the pressure inhomogeneity within the sample as the applied pressure is rather high. Due to the almost coincident pressure for both the emergence of superconductivity and the new structure P-6m2 at about 70 GPa, we thus can naturally conclude that superconductivity arises from TaP with the P-6m2 structure.

## Discussion

Next we study the electronic structures and surface states of this new P-6m2 TaP. The ab initial calculations are detailed in section “Method” and Supplementary Note 6. Our calculations show that TaP P-6m2 phase is a new topological Weyl semimetal, similar to TaAs high-pressure phase22 P-6m2. The band structures around the Weyl point of the P-6m2 phase at 70 GPa are shown in Fig. 5a, which exhibits linear energy dispersion near the Weyl point. According to our calculation, there are six pairs of Weyl points near the K point, as shown in Fig. 5b. All the Weyl points can be related to each other by mirror and C 3 rotation symmetry, so that there is only one set of Weyl points in this system and they are at the same energy. The surface state of P termination (100) surface are calculated based on the Wannier orbitals and surface Green’s functions.40 There are two kinds of projected Weyl points in Fig. 5c, WD (two Weyl points of same chirality projected to the same position) and WS (single Weyl point projected). Figure 5d, e show that detail surface states near WS and WD. As for WD, there are two Fermi arcs connected to this projected point. For WS, there is only one Fermi arc connected WS and another WS across the first Brillouin zone boundary. These interesting theoretical results indicate clearly that the TaP P-6m2 phase has still the Weyl semimetal feature, which is quite different to the ambient I41 md phase.

Superconductivity is discovered by resistivity measurement in TaP when the pressure exceeds about 70 GPa. HP-XRD also reveals a structure phase transition from I41 md to P-6m2 at a similar pressure, which is related to the emergence of superconductivity. This high-pressure phase and superconductivity can be retained when the pressure is released. It would be interesting to know what leads to the superconductivity and which band plays the dominant role of Cooper pairing. Ab initial calculations on TaP with the high pressure converted P-6m2 structure indicate that it is a new Weyl semimetal with the typical surface Fermi arc state. Unfortunately, angle resolved photo-emission spectroscopy (ARPES) cannot be done under pressure for this state in order to check the surface Fermi arc. It is widely expected that the order parameter of superconductivity by electrons with the spin chirality due to the Weyl semimetal feature should have complex compositions, for example, some component with triplet pairing is inevitable. Thus, it is highly desired to investigate the superconducting gap structure of this novel superconducting phase. Superconductivity discovered directly from pressurized Weyl semimetal TaP will stimulate further efforts in investigating superconductivity in topological materials and paving a possible path to the ultimate discovery of topological superconductors.

## Methods

TaP single crystals were synthesized by chemical vapor transport method.16 The sample at ambient pressure has high quality with a nice fitting to the x-ray XRD pattern and clear exhibition of large MR. High-pressure resistance measurements with repeating cycles were conducted via the four-probe method in a screw pressure-type diamond anvil cell. HP-XRD measurements were carried out with angle-dispersive diffraction mode at the beamline 16BM-D, High-Pressure Collaborative Access Team (HPCAT), Advanced Photon Source, Argonne National Laboratory.

### Data availability

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

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## Acknowledgements

We appreciate useful discussions with Yong Chen at Purdue University and Liang Fu at MIT. This work was supported by the Ministry of Science and Technology of China (Grant Nos. 2016YFA0300400, 2015CB921202, and 2016YFA0401804), the National Natural Science Foundation of China (NSFC) with the projects: 11534005, 11190023, 11374143, U1530402, U1532267, 51372112, 11574133, 11574323, U1632275, NSF Jiangsu province (No. BK20150012), the Special Program for Applied Research on Super Computation of the NSFC–Guangdong Joint Fund (the second phase), HPCC of Nanjing University and “Tianhe-2” at NSCC-Guangzhou. The HP-XRD experiments were conducted at HPCAT, which is supported by DOE-NNSA under Award No. DE-NA0001974 and DOE-BES under Award No. DE-FG02-99ER45775, with partial instrumentation funding by NSF. APS is supported by DOE-BES, under Contract No. DE-AC02-06CH11357.

## Author information

### Author notes

1. Yufeng Li, Yonghui Zhou, Zhaopeng Guo and Fei Han contributed equally to this work.

### Affiliations

1. #### National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, 210093, Nanjing, China

• Yufeng Li
• , Zhaopeng Guo
• , Pengchao Lu
• , Jie Xing
• , Guan Du
• , Xiyu Zhu
• , Huan Yang
• , Jian Sun
•  & Hai-Hu Wen
2. #### High Magnetic Field Laboratory, Chinese Academy of Sciences, 230031, Hefei, China

• Yonghui Zhou
• , Xuliang Chen
• , Xuefei Wang
• , Chao An
• , Ying Zhou
• , Zhaorong Yang
•  & Yuheng Zhang
3. #### Center for High Pressure Science and Technology Advanced Research (HPSTAR), 201203, Shanghai, China

• Fei Han
• , Wenge Yang
•  & Ho-Kwang Mao
4. #### High Pressure Synergetic Consortium (HPSynC), Geophysical Laboratory, Carnegie Institution, Argonne, IL, 60439, USA

• Fei Han
•  & Wenge Yang
5. #### Center for the Study of Matter at Extreme Conditions, Department of Mechanical and Materials Engineering, Florida International University, Miami, FL, 33199, USA

• Fei Han
•  & Wenge Yang
6. #### Collaborative Innovation Center of Advanced Microstructures, Nanjing University, 210093, Nanjing, China

• Xiyu Zhu
• , Huan Yang
• , Jian Sun
• , Zhaorong Yang
• , Yuheng Zhang
•  & Hai-Hu Wen
7. #### Geophysical Laboratory, Carnegie Institution, Washington, 20015, USA

• Ho-Kwang Mao

### Contributions

The samples were grown by Y.F.L. and X.Y.Z. The high-pressure resistivity measurements were conducted by Y.H.Z., X.L.C., X.F.W., C.A., Y.Z., and Z.R.Y. The low temperature with He3 was measured by J.X., Y.F.L., G.D., and H.Y. HP-XRD measurements were done by F.H., W.G.Y., and H.-K.M The structure analysis was done by Y.F.L. and F.H. The DFT calculations were done by Z.P.G., P.C.L., and J.S. H.-H.W. coordinated the whole work. H.-H.W., Y.F.L. and J.S. wrote the manuscript, which is supplemented by others. All authors have discussed the results and the interpretations.

### Competing interests

The authors declare no competing financial interests.

### Corresponding authors

Correspondence to Jian Sun or Zhaorong Yang or Wenge Yang or Hai-Hu Wen.