Pressure-induced superconductivity in the three-dimensional topological Dirac semimetal Cd3As2

The recently discovered Dirac and Weyl semimetals are new members of topological materials. Starting from them, topological superconductivity may be achieved, e.g., by carrier doping or applying pressure. Here we report high-pressure resistance and X-ray diffraction study of the three-dimensional topological Dirac semimetal Cd3As2. Superconductivity with Tc≈2.0 K is observed at 8.5 GPa. The Tc keeps increasing to about 4.0 K at 21.3 GPa, then shows a nearly constant pressure dependence up to the highest pressure 50.9 GPa. The X-ray diffraction measurements reveal a structure phase transition around 3.5 GPa. Our observation of superconductivity in pressurised topological Dirac semimetal Cd3As2 provides a new candidate for topological superconductor, as argued in a recent point contact study and a theoretical work. Cd3As2 is shown to become a topological superconductor candidate under pressure. Topological superconductors are typically obtained by modifying the surface electronic structure of topological insulators. Doping and pressure have been demonstrated as two ways to achieve this. However, pressure has yet to be explored as a route to topological superconductivity in the recently discovered three-dimensional (3D) Dirac semimetals, the Fermi surface of which exhibits 3D Dirac points. The electrical resistance of Cd3As2 single crystals have now been investigated under pressure: superconductivity initiates at around 8.5 GPa, and increases to 4 K at approximately 21 GPa. A structural phase transition is additionally evidenced from x-ray diffraction data at roughly 3.5 GPa. This study demonstrates that pressure could be a feasible route to achieve topological superconductivity in 3D topological Dirac semimetals.


INTRODUCTION
In recent few years, the search for topological superconductors (TSCs) has been a hot topic in condensed matter physics. 1,2 The TSCs have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. 1 This is in close analogy to the topological insulators (TIs), which have a full insulating gap in the bulk and gapless edge or surface states. 1 The TSC is of great importance, as it is not only a new kind of exotic superconductor but also one source of Majorana ferimons for future applications in quantum computations. 1,2 Experimentally, the simplest way to get a candidate for TSC is to convert a TI into superconductor, by tuning the parameters such as doping or pressure. For example, by doping, Cu x Bi 2 Se 3 and Cu x (PbSe) 5 (Bi 2 Se 3 ) 6 are considered to be candidates for TSCs, [3][4][5][6] while Sn 1 − x In x Te is considered as a candidate for topological crystalline superconductor. 7,8 Under pressure, Bi 2 Te 3 , Bi 2 Se 3 , Sb 2 Te 3 and Sb 2 Se 3 become superconducting, which are also regarded as candidates for TSCs. [9][10][11][12][13][14] Note that there are debates on whether these candidates are indeed TSCs, [9][10][11][12][13][14][15][16][17] therefore further experimental works are needed to definitely identify a TSC and manipulate the Majorana fermions on its surface.
More recently, a new kind of topological material, the threedimensional (3D) Dirac semimetal was discovered, with examples of SrMnBi 2 , Na 3 Bi and Cd 3 As 2 . [18][19][20][21][22][23][24][25][26][27][28][29] As a 3D analogue to graphene, the Fermi surface of the 3D Dirac semimetal only consists of 3D Dirac points with linear energy dispersion in any momentum direction. 19,23 The exotic Fermi surface of Na 3 Bi and Cd 3 As 2 was confirmed by the angle-resolved photoemission spectroscopy experiments. [20][21][22][24][25][26] The compound Cd 3 As 2 is of particular interests, as it is stable in air, unlike Na 3 Bi. On the basis of quantum transport measurement, a non-trivial π Berry's phase is obtained, which provides bulk evidence for the existence of 3D Dirac semimetal phase in Cd 3 As 2 . 28,29 By symmetry breaking, this 3D Dirac semimetal may be driven to a topological insulator or Weyl semimetal. 23 More interestingly, it was predicted that topological superconductivity may be achieved in Cd 3 As 2 by carrier doping, 23 but this has not been realised so far. As pressure is an effective way to induce superconductivity in TIs, [10][11][12][13][14][15] it will be very interesting to check whether superconductivity can be achieved by applying pressure on Cd 3 As 2 .
Here we present the resistance measurements on Cd 3 As 2 single crystals under pressure up to 50.9 GPa. After an initial increase with pressure, the low-temperature resistance starts to decreases with pressure above 6.4 GPa. Superconductivity appears at 8.5 GPa with T c ≈2.0 K, and the T c increases to about 4.0 K at 21.3 GPa, then persists to the highest pressure 50.9 GPa. A structure phase transition around 3.5 GPa is also observed by X-ray diffraction (XRD) measurements. These results suggest that Cd 3 As 2 may be a new topological superconductor under high pressure. Figure 1a shows the crystal structure of Cd 3 As 2 . 30 The cubic Cd lattice with two vacancies resides in a face-centred cubic As lattice. Figure 1b plots a typical resistivity curve of Cd 3 As 2 single crystal at 0 GPa. It is metallic and non-superconducting down to 1.5 K.

Pressure-induced superconductivity
In Figure 2, the resistance curves for Cd 3 As 2 single crystal under various pressures are plotted. From Figure 2a, the temperature dependence of resistance already changes to insulating behaviour (dR/dTo0) at 1.1 GPa. With increasing pressure, it becomes more and more insulating until 6.4 GPa. However, upon further increasing pressure, the resistance at low temperature decreases with pressure. In Figure 2b, it becomes more and more metallic up to 32.7 GPa. Figure 2c,d) show the low-temperature part of the resistance curves above 8.5 GPa. A drop of resistance is observed below 2.0 K at 8.5 GPa, which is like a superconducting transition.
At 11.7 GPa, the resistance drops to zero, and the transition temperature T c = 3.3 K is defined at the cross of the two straight lines. The T c increases to about 4.0 K at 21.3 GPa, then persists to the highest pressure 50.9 GPa.
To make sure the resistance drop in Figure 2 is a superconducting transition, we measure the low-temperature resistance under 13.5 GPa in magnetic fields applied perpendicular to the (112) plane, as shown in Figure 3a. The resistance drop is gradually suppressed to lower temperature with increasing field, which demonstrates that it is indeed a superconducting transition. Note that such a superconductivity we observed here is very unlikely due to contamination of pure As, as its highest T c under pressures is much lower, and the pressure dependence of T c is quite different. 31 Figure 3b plots the temperature dependence of H c2 . Although limited by the temperature range we measured, one can see an apparently linear temperature dependence of H c2 . With a linear fit to the data, H c2 (0)≈4.29 T is roughly estimated. This value is higher than the orbital limiting field H orb c2 0 ð Þ ¼ 0:72T c dH c2 =dT j j T¼Tc ¼ 3:71 T, according to Werthamer-Helfand-Hohenberg formula. 32 It is much lower than the Pauli limiting field H P (0) = 1.84T c = 7.89 T, 33,34 suggesting an absence of Pauli pair breaking. The linear temperature dependence of H c2 in Figure 3b is actually very interesting. It may come from a two-band Fermi surface topology as in MgB 2 , [35][36][37] or an unconventional superconducting state as in heavy-fermion compound UBe 13 . 38 Similar linear temperature dependence of H c2 has recently been observed in pressurised TSC candidates Bi 2 Se 3 and Cu x Bi 2 Se 3 , in natural TSC candidate Au 2 Pb and in noncentrosymmetric superconductor YPtBi under ambient and high pressures, which was considered as an indication of unconventional superconducting state. 11,[39][40][41] We notice that no superconductivity was observed up to 13.43 GPa in an earlier pressure study of Cd 3 As 2 single crystal. 42 The reason may be that their sample is slightly different from ours, and pressure higher than 13.43 GPa is needed to induce superconductivity. Interestingly, we also notice two recent point contact studies on Cd 3 As 2 polycrystal and single crystal, respectively. 43,44 In both studies, indication of superconductivity was found around the point contact region on the surface, with T c comparable to ours. In particular, no superconductivity is observed by the 'soft' point contact technique, therefore it was suggested that the superconductivity observed around the point contact region under the 'hard' tip might be induced by the local pressure. 44 In this sense, our bulk resistance measurements under hydrostatic pressure confirm pressure-induced superconductivity in Cd 3 As 2 , although the local pressure under the 'hard' tip is more like uniaxial stress.
Pressure-induced crystal structure phase transition Before discussing whether the pressure-induced superconductivity is topological or not, it is important to know whether it is accompanied by a structure phase transition, as observed in pressurised TIs. [9][10][11][12][13][14] High-pressure powder XRD measurements on Cd 3 As 2 were performed up to 17.80 GPa. In Figure 4, the XRD patterns below 2.60 GPa can be well indexed as the tetragonal phase in space group I4 1 /acd. 30 All the peaks are slightly shifted to higher angle with increasing pressure, due to the shrink of the lattice. However, when the pressure increases to 4.67 GPa and above, a set of new peaks emerges, which is clearly different from that of low-pressure tetragonal phase. This abrupt change indicates that a new crystal structure phase appears, and we roughly determine the transition pressure around 3.5 GPa. Similar high-pressure XRD patterns have been observed in an earlier work, and the new high-pressure phase was determined as monoclinic in space group P2 1 /c. 42 The unusual T c -p phase diagram In Figure 5, we plot the temperature versus pressure phase diagram for Cd 3 As 2 . As the resistance was only measured down to 1.8 K, we cannot judge whether the superconductivity emerges at the same time as the structural transition near 3.5 GPa, or inside the high-pressure phase. Nevertheless, after increasing from 1.8 to about 4.0 K, there is apparently a region of constant T c from 21.3 to 50.9 GPa. Such a phase diagram is very similar to that of 3D TI Bi 2 Se 3 , which also shows a nearly constant T c from 30 to 50 GPa after an initial increase of T c starting from 12 GPa. 11 A constant T c over such a large pressure range is highly anomalous, as Kirshenbaum et al. 11 already pointed out. For Bi 2 Se 3 , two mechanisms with contrasting pressure-dependant T c may be balanced to produce a pressure-invariant T c over a wide range of pressure. 11 It was argued that the unique pressure evolution of T c and the anomalous linear temperature dependence of H c2 are two evidences for unconventional superconductivity in Bi 2 Se 3 . 11 The Figure 1. Crystal structure and resistivity of Cd 3 As 2 . (a) The crystal structure of Cd 3 As 2 . The cubic Cd lattice with two vacancies resides in a face-centred cubic As lattice. (b) A typical resistivity curve of Cd 3 As 2 single crystal at 0 GPa. similarity between Cd 3 As 2 and Bi 2 Se 3 under pressure is worthy of further investigation.

DISCUSSION
Now we discuss whether the superconducting state of Cd 3 As 2 under high pressure is topological or not. In ref. 44, the observation of zero bias conductance peak and double conductance peaks under 'hard' tip reveal p-wave like unconventional superconductivity in Cd 3 As 2 . Considering its special topological property, they suggested that Cd 3 As 2 under high pressure is a candidate of the TSC. 44 Furthermore, a recent theoretical work also argued that Cd 3 As 2 likely realises a TSC with bulk point nodes and a surface Majorana fermion quartet. 45 Under high pressure, the symmetry-lowering effect may stabilise the TSC phase by increasing the condensation energy, as the point nodes in the TSC phase are gapped when C 4 reduces to C 2 (the structure phase transition from tetragonal to monoclinic). 45 These two works suggest that the superconductivity we observe under hydrostatic pressure is topological, although detailed band structure calculation for the high-pressure phase of Cd 3 As 2 is needed to give more information about this possible TSC phase.
In summary, we have done resistance measurements on the 3D Dirac semimetal Cd 3 As 2 single crystals under pressures up to 50.9 GPa. It is found that superconductivity with T c ≈2.0 K emerges at 8.5 GPa. The T c increases to 4.0 K at 21.3 GPa, then it shows an anomalous constant pressure dependence up to the highest pressure measured. High-pressure powder XRD measurements reveal a structure phase transition around 3.5 GPa. Our observation of superconductivity in Cd 3 As 2 under high pressure provides an interesting candidate for topological superconductor.

MATERIALS AND METHODS
High-quality Cd 3 As 2 single crystals were grown from Cd flux. 28 The largest natural surface was determined as (112)  Pressure-induced superconductivity in Dirac semimetal Cd 3 As 2 L He et al hexagonal boron nitride. 9,13,14 The sample size is about 80 × 80 μm 2 in the (112) plane, with the thickness of ∼ 10 μm. The pressure was determined by ruby fluorescence method at room temperature before and after each cooling down. The high-pressure powder XRD measurements with synchrotron radiation were performed at the HPCAT of Advanced Photon Source of Argonne National Lab (Lemont, IL, USA) using a symmetric Mao Bell diamond anvil cell at room temperature. The X-ray wavelength is 0.434 Å.    Figure 4. Crystal structure phase transition of Cd 3 As 2 under pressure. The powder XRD patterns of Cd 3 As 2 under different pressures at room temperature. Below 2.60 GPa, the XRD patterns can be well indexed as the tetragonal phase in space group I4 1 /acd (shown by short black lines). A set of new peaks emerges when increasing pressure to 4.67 GPa and above, which shows a structure phase transition from tetragonal to monoclinic phase.  Figure 5. The phase diagram of Cd 3 As 2 . Temperature versus pressure phase diagram of Cd 3 As 2 . A structure phase transition occurs between 2.60 and 4.67 GPa. After increasing from 1.8 to about 4.0 K, there is apparently a region of constant T c from 21.3 to 50.9 GPa. Such a phase diagram is similar to that of the 3D topological insulator Bi 2 Se 3 .