Enhancement of superconductivity under pressure and the magnetic phase diagram of tantalum disulfide single crystals

In low-dimensional electron systems, charge density waves (CDW) and superconductivity are two of the most fundamental collective quantum phenomena. For all known quasi-two-dimensional superconductors, the origin and exact boundary of the electronic orderings and superconductivity are still attractive problems. Through transport and thermodynamic measurements, we report on the field-temperature phase diagram in 2H-TaS2 single crystals. We show that the superconducting transition temperature (Tc) increases by one order of magnitude from temperatures at 0.98 K up to 9.15 K at 8.7 GPa when the Tc becomes very sharp. Additionally, the effects of 8.7 GPa illustrate a suppression of the CDW ground state, with critically small Fermi surfaces. Below the Tc the lattice of magnetic flux lines melts from a solid-like state to a broad vortex liquid phase region. Our measurements indicate an unconventional s-wave-like picture with two energy gaps evidencing its multi-band nature.


a b
Extended Data Figure 1: Crystal Structure and X-ray single crystal diffraction of 2H-TaS2: X-ray diffraction patterns along c-axis of 2H-TaS2. Note that a red asterisk is the background signal from the vacuum chuck. The insets a presents he small spheres (yellow) represent S atoms. Top view of a single layer 2H-TaS2 superlattice. b Schematic illustration of the unit-cell structure. The bulk 2H structure contains two trilayers per unit cell. the S atom in the layer beneath, but the lateral registry is different: in 2H the S atoms are fully eclipsed. The inset of Extended Data Figure 1a presents top view of a single layer 2H-TaS 2 superlattice, while the inset b illustrates the unit-cell structure of 2H-TaS 2 . The tantalum atoms are surrounded by sulfur atoms following a hexagonal coordination.
In order to examine the composition of 2H-TaS 2 single crystals, an electron probe micro analysis (EPMA) system was used. Bulk analysis of the EPMA shows that TaS 2 has a composition of 1 : 2.0066, which is in excellent agreement with the composition of the investigated system. To determine the crystalline structure of 2H-TaS 2 , we have done X-ray diffraction measurements on our single crystal from the same batch as those measured with transport, magnetization and specific heat using a Bruker D8 VENTURE Single Crystal X-ray Diffractometer, see the Extended Data Figure 1. We find a clear evidence for the purity in our system and the XRD pattern shows sharp distinct peaks.
The temperature dependence of specific heat and magnetization are illustrated in Extended Data Figure 2. A clear maximum of both data at 76 K, typically found in 2H-TaS 2 which is weakly first-order, is an indication of the CDW transition. The CDW transition temperature is in good agreement with transport and earlier reports. A jump in the specific heat at 76 K of 10.14 J/mol K is found (full width at half maximum ≈ 1.2, and 1 K). This transition is sharper than previously on polycrystalline samples [1] and indicates the high quality of our single crystals. On the other hand, below the CDW transition the magnetic susceptibility decreases sharply and continuously. This decrease in the susceptibility can be attributed to the decrease in the density of states on the hole band due to the opening of the CDW gap and additionally there is no long-range magnetic order was ever detected in this material [2].

ELECTRONIC SPECIFIC HEAT
We discuss various gap values obtained in the present simple system for analyzing the T -dependence of our zero-field specific heat data down to 70 mK. The normalized C el /γ n T as a function of the reduced temperature T /T c is presented in Extended Data Figure 3 together with the fits to various models. It is obvious that the superconducting transition at T c is well pronounced, with a sharp jump in C el at T c . We have attempted best fits to the data using three different models: the single-band weak-coupling BCS theory with the s-wave gap ∆ (0) /k B T c = 1.76; a d-wave calculation [3] using ∆ = ∆ (0) cos(2φ); and a two-gap s-wave. The almost linear T -dependence of C el /γ n T indicates that the experimental data cannot be described by the standard BCS-model. Below T c we observed a systematic deviation of both single-gap and d-wave fits from the data showing a higher jump at T c than the s-wave model. Thus, we focus our discussions on the possibility of two superconducting energy gaps using the generalized α-model explaining the specific heat behavior in a multi-band superconductor [4]. Although the two-gap model contains two distinct gaps, the specific heat value is calculated as the sum of contributions, each one following the BCS-type T -dependence, ∆(0) = γ 1 ∆ s (0) + γ 2 ∆ l (0) [4]. The thermodynamic properties are obtained as the sum of the contributions from the individual bands, i.e., α s = ∆ s /k B T c and α l = ∆ l /k B T c . The estimated ∆ s (0)/k B T c for the small gap is 1.2±0.1, while the large gap ∆ l (0)/k B T c is found to be 2.05±0.1 and the calculated data are illustrated by the solid line. The error bars represent the width of the corresponding range of gap amplitudes obtained in the fits for both values of ∆ s (0)/k B T c and ∆ l (0)/k B T c . The relative weight of each contribution illustrates that γ 2 /γ n = 0.68 is larger than γ 1 /γ n = 0.32. This indicates that the major gap develops around the FS sheet that exhibits the largest density of states. The ratio of the two gaps ∆ s (0)/∆ l (0) ≈ 0.58 is comparable to the NbSe 2 case [5]. It has been theoretically demonstrated that it is a multiband superconductor if the ratio of two isotropic s-wave gaps ∆ 1 (0)/∆ 2 (0) > 0.5 [6] as in our case, further confirming the multi-band nature in 2H-TaS 2 .

BAND STRUCTURE AND ELECTRONIC DOS
The obtained band structure for 2H-TaS 2 is displayed in Extended Data Figure 4a. The Fermi surface is shown in Extended Data Figure 4b and the projected density of states for Ta-d orbitals and S-p orbitals on a per-atom basis in Extended Data Figure 4c. For the band structure, it is obvious that two bands cross the Fermi level in the energy range from -1 eV to 2 eV and contribute to the conductivity. These two bands give rise to Fermi surface as depicted in b, which further suggests the multi-gap nature in our system. Correspondingly in the projected density of states shown in c, we find that the states near the Fermi level are mostly derived from d xy , d z 2 and d x 2 −y 2 orbitals of tantalum and p orbitals of sulfur have also a contribution to the states. The metal d and p contributions are estimated to be 0.531 states/eV and 0.074 states/eV, respectively. Interestingly, the width and the peaks of the projected density of states are almost coincidentally same, which is due to the formation of the strong Ta-S covalent bonds. This strong covalent effect as well as the superconductivity instability nature of the Fermi surface of a transition metal suggests that the electrons involved in pairing in bands are primarily derived from d states, hybridized with p states.
In summary, based on both experimental and theoretical studies, we believe that the multi-gap scenario is more favorable than the anisotropic s-wave model in describing the gap structure of 2H-TaS 2 .