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

Abstract

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 T_c≈2.0 K is observed at 8.5 GPa. The T_c 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.

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_xBi₂Se₃ and Cu_x(PbSe)₅(Bi₂Se₃)₆ are considered to be candidates for TSCs,^3–6 while Sn_1−xIn_xTe is considered as a candidate for topological crystalline superconductor.^7,8 Under pressure, Bi₂Te₃, Bi₂Se₃, Sb₂Te₃ and Sb₂Se₃ become superconducting, which are also regarded as candidates for TSCs.^9–14 Note that there are debates on whether these candidates are indeed TSCs,^9–17 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 three-dimensional (3D) Dirac semimetal was discovered, with examples of SrMnBi₂, Na₃Bi and Cd₃As₂.^18–29 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 Na₃Bi and Cd₃As₂ was confirmed by the angle-resolved photoemission spectroscopy experiments.^{20–22,24–26} The compound Cd₃As₂ is of particular interests, as it is stable in air, unlike Na₃Bi. 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 Cd₃As₂.^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 Cd₃As₂ by carrier doping,²³ but this has not been realised so far. As pressure is an effective way to induce superconductivity in TIs,^10–15 it will be very interesting to check whether superconductivity can be achieved by applying pressure on Cd₃As₂.

Here we present the resistance measurements on Cd₃As₂ 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 Cd₃As₂ may be a new topological superconductor under high pressure.

Results

Pressure-induced superconductivity

Figure 1a shows the crystal structure of Cd₃As₂.³⁰ The cubic Cd lattice with two vacancies resides in a face-centred cubic As lattice. Figure 1b plots a typical resistivity curve of Cd₃As₂ single crystal at 0 GPa. It is metallic and non-superconducting down to 1.5 K.

Figure 1

Crystal structure and resistivity of Cd₃As₂. (a) The crystal structure of Cd₃As₂. The cubic Cd lattice with two vacancies resides in a face-centred cubic As lattice. (b) A typical resistivity curve of Cd₃As₂ single crystal at 0 GPa.

In Figure 2, the resistance curves for Cd₃As₂ single crystal under various pressures are plotted. From Figure 2a, the temperature dependence of resistance already changes to insulating behaviour (dR/dT<0) 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.

Figure 2

Experimental evidence of pressure-induced superconductivity. The temperature dependence of resistance for Cd₃As₂ single crystal under various pressures. (a,b) The resistance from 1.8 to 300 K. (c,d) Low-temperature resistance showing the superconducting transition. The superconductivity appears at P=8.5 GPa with T_c≈2.0 K. The T_c is defined as on the curve of P=11.7 GPa. 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 3

The upper critical field H_c2 of Cd₃As₂ under 13.5 GPa. (a) The superconducting transition of the Cd₃As₂ single crystal under 13.5 GPa and in magnetic fields applied perpendicular to the (112) plane. (b) Temperature dependence of the upper critical field H_c2. The dashed line is a linear fit to the data, which points to H_c2(0)≈4.29 T.

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 $H_{\mathrm{c}2}^{\mathrm{orb}}\left(0\right)=0.72T_{\mathrm{c}}{\left|\mathrm{d}{H}_{\mathrm{c}2}/\mathrm{d}T\right|}_{T=T_{\mathrm{c}}}=3.71\mathrm{T}$, 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 MgB₂,^35–37 or an unconventional superconducting state as in heavy-fermion compound UBe₁₃.³⁸ Similar linear temperature dependence of H_c2 has recently been observed in pressurised TSC candidates Bi₂Se₃ and Cu_xBi₂Se₃, in natural TSC candidate Au₂Pb and in non-centrosymmetric superconductor YPtBi under ambient and high pressures, which was considered as an indication of unconventional superconducting state.^11,39–41

We notice that no superconductivity was observed up to 13.43 GPa in an earlier pressure study of Cd₃As₂ 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 Cd₃As₂ 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 Cd₃As₂, 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.^9–14 High-pressure powder XRD measurements on Cd₃As₂ 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 I4₁/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 P2₁/c.⁴²

Figure 4

Crystal structure phase transition of Cd₃As₂ under pressure. The powder XRD patterns of Cd₃As₂ under different pressures at room temperature. Below 2.60 GPa, the XRD patterns can be well indexed as the tetragonal phase in space group I4₁/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.

The unusual T_c–p phase diagram

In Figure 5, we plot the temperature versus pressure phase diagram for Cd₃As₂. 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 Bi₂Se₃, 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 Bi₂Se₃, 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 Bi₂Se₃.¹¹ The similarity between Cd₃As₂ and Bi₂Se₃ under pressure is worthy of further investigation.

Figure 5

The phase diagram of Cd₃As₂. Temperature versus pressure phase diagram of Cd₃As₂. 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 Bi₂Se₃.

Discussion

Now we discuss whether the superconducting state of Cd₃As₂ 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 Cd₃As₂. Considering its special topological property, they suggested that Cd₃As₂ under high pressure is a candidate of the TSC.⁴⁴ Furthermore, a recent theoretical work also argued that Cd₃As₂ 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 C₄ reduces to C₂ (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 Cd₃As₂ is needed to give more information about this possible TSC phase.

In summary, we have done resistance measurements on the 3D Dirac semimetal Cd₃As₂ 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 Cd₃As₂ under high pressure provides an interesting candidate for topological superconductor.

Materials and Methods

High-quality Cd₃As₂ single crystals were grown from Cd flux.²⁸ The largest natural surface was determined as (112) plane by XRD. The resistivity in vacuum (0 GPa) was measured on a large sample with dimension of 1.50×0.40 mm² in the (112) plane and 0.15 mm in thickness. The resistance measurement under pressure between 1.1 and 50.9 GPa was performed using diamond anvil cell with solid transmitting medium hexagonal boron nitride.^9,13,14 The sample size is about 80×80 μm² 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.