Coevolution of Superconductivity With Structure and Hall Coefficient in Pressurized NaSn 2 As 2

A new class of van der Waals-type layered materials, A Sn 2 Pn 2 (A = Li, Na, Sr, Eu; Pn = As, P, Sb), has attracted much attention in the field of condensed matter physics because they have interesting physical properties and various ground states, as well as potential applications. Here, we are the first to report the close connection among the superconducting transition temperature T c, crystal structure and Hall coefficient in pressurized NaSn 2 As 2 single crystal. We found that the superconducting NaSn 2 As 2 displays two pressure-induced crystal structure phase transitions, first from an ambient-pressure rhombohedral (R) phase to a monoclinic (M) phase starting at ∼ 12 GPa (P C1), and then to a simple cubic (C) phase starting at ∼ 33 GPa (P C2). In these phases, the T c value and carrier concentration change correspondingly. Our results suggest that the observed three superconducting states are related to the change of structural phase and the variation of carrier concentrations.

The new class of van der Waals-type layered materials A Sn 2 Pn 2 (A = Li, Na, Sr, Eu; Pn = As, P, Sb) exhibits special physical properties and different ground states, such as low thermal conductivity (Lee et al., 2015; Lin et al., 2017), topological state (Rong et al., 2017; Gui et al., 2019), magnetically topological insulating state (Gibson et al., 2015; Li et al., 2019) and superconducting state (Goto et al., 2017; Cheng et al., 2018; Goto et al., 2018; Ishihara et al., 2018; Yuwen et al., 2019; Zhao et al., 2021), etc. Since A Sn 2 Pn 2 has a layered structure, similar to cuprate and iron-based superconductors (Bednorz and Muller, 1986; Wu et al., 1987; Hsu et al., 2008; Kamihara et al., 2008; Guo et al., 2010; Wang et al., 2011; Chu et al., 2015; Arguilla et al., 2016; Hu, 2016; Goto et al., 2018; He et al., 2019; Proust and Taillefer, 2019), it is expected that the materials may present superconductivity or emerge exotic phenomena through chemical doping or applied pressure. Earlier studies on Na 1+x Sn 2-x As 2 and Na 1-x Sn 2 P 2 found that the superconductivity can be truly developed by Na doping on the Sn site or self-doping by Na vacancy defects (Goto et al., 2018; Yuwen et al., 2019), indicating that the superconductivity of these materials is sensitive to the tuning parameters.

Pressure is an effective method to tune crystal and electronic structure without changing chemistry. Which can be used as a probe to test whether there is a link between the crystal structure and superconductivity in van der Waals-type layered materials. In this paper, we are the first to report the connection among the crystal structure, Hall coefficient (R H) and T c in the superconducting NaSn 2 As 2, through the complementary measurements of in-situ high-pressure X-ray diffraction (XRD), electric resistance, ac susceptibility and Hall coefficient.

The high-quality single crystal samples were synthesized by solid-state reaction methods, as reported elsewhere (Lin et al., 2017). High pressure was generated by a Diamond anvil cell (DAC) with two opposing anvils sitting on the Be-Cu supporting plates. In the high-pressure measurements, diamond anvils with 300 μm flats were employed to create pressure, and NaCl powder was adopted as pressure transmitting medium. High pressure resistance and Hall coefficient measurements were carried out using four-probe technique and Van der Paw method (van der Pauw, 1958), respectively. High-pressure alternating-current (ac) susceptibility measurements were performed by using the home-made primary/secondary-compensated coils around the diamond anvil (Debessai et al., 2008; Sun et al., 2012). High pressure x-ray diffraction (XRD) measurements were carried out at beamline 4W2 at Beijing Synchrotron Radiation Facility and at beamline 15U at the Shanghai Synchrotron Radiation Facility, respectively. The polycrystalline samples prepared for the x-ray diffraction measurements were obtained by grinding single-crystal samples. The pressure in all experiments was determined by the ruby fluorescence method (Mao et al., 1986).

We first performed in-situ high pressure XRD measurements. Figure 1A shows the XRD diffraction patterns collected at different pressures up to ∼ 50 GPa. It is found that all patterns below 9.9 GPa can be indexed well by the rhombohedral (R) phase with space group R 3 ¯ m (Figure 1B), as what was observed at ambient pressure (Lin et al., 2017). However, new peaks appear when pressure is increased up to 11.6 GPa, indicating that application of pressure induces the structure change. The analysis on the XRD patterns for this high-pressure phase reveals that the sample partially transforms into the monoclinic (M) phase (C2/m) (Figure 1C). The two coexisted phases (R and M) persist up to ∼ 30 GPa before another obvious change of the XRD patterns at ∼ 33 GPa (Figure 1D), where the presence of a new sets of diffraction peaks suggests that pressure drives a new phase transition. We found that the new phase can be indexed to a simple cubic phase (Figure 1E). The refinements of the XRD results allow us to obtain the pressure dependence of lattice parameters and corresponding volume for the R, M and C phases (Figures 1F,G).

NaSn 2 As 2 crystalizes in rhombohedral (R) unit cell at ambient pressure, similar to that of Bi 2 Te 3 or Bi 2 Te 2 Se (Kushwaha et al., 2016). Theoretical calculations indicate that Bi 2 Te 3 undergoes structural phase transitions under pressure, from R phase to M phase, and eventually to C phase due to that the C phase has a lower enthalpy (Zhu et al., 2011). Our high pressure XRD measurements reveal that NaSn 2 As 2 shows the similar high-pressure behavior as Bi 2 Te 3, occurring the transitions of R -to- M -to- C phase upon increasing pressure. The same phase evolution observed in our compressed NaSn 2 As 2 sample allows us to propose that these two materials may share the same mechanism of driving the phase transition.

To investigate the pressure effects on the transport properties of NaSn 2 As 2 in these different phases, we carried out in-situ high pressure resistance measurements for the sample. Figures 2A–C show the electrical resistance as a function of temperature under different pressures up to 52.2 GPa for the sample #1. Below 12 GPa, a tiny kink is observed at around 200 K, which has also been found by Pugliese et al. (2019). We propose that this anomaly may be associated with an instability of the CDW order. Since the ambient-pressure superconducting transition of NaSn 2 As 2 is about 1.3°K (Goto et al., 2017; Cheng et al., 2018; Ishihara et al., 2018), which is lower than the base temperature (1.5 K) of the cryostat employed for this run, no resistance drop is observed. However, we find that the normal resistance value versus temperature is reduced with increasing pressure up to 12.7 GPa, then it is enhanced with further compression, we propose that the observed phenomenon should be attributed to the partial R-M phase transition (Figures 2A,B).

Noticeably, a resistance drop is found at ∼2.1 K at 22.6 GPa (as shown in the inset of Figure 2B) and it shifts to higher temperature with further compression. A zero-resistance state is observed at 1.5 K at 28.7 GPa and above, indicative of an emergence of a superconducting transition (inset of Figure 2B and Figure 2C). The transition temperature (T c) is enhanced upon increasing pressure and remains almost unchanged at pressure higher than ∼ 36 GPa (Figure 2C). To understand the full evolution process of T c with pressure at lower temperature for NaSn 2 As 2, we performed high-pressure resistance measurements for the sample #2 in another cryostat that can cool the sample down to ∼ 0.3 K (Figure 2D). We observed a superconducting transition at 1.4 K at the lowest pressure of 0.4 GPa, adopted in this study, close to the T c obtained at ambient pressure (Goto et al., 2017; Cheng et al., 2018; Ishihara et al., 2018). With increasing pressure, T c decreases down to ∼ 0.3 K at ∼ 13 GPa and then increases with further compression up to 19.4 GPa (Figure 2D).

To support the observed resistance drops in pressurized NaSn 2 As 2 are attributed to superconducting transitions, we performed resistance measurements under different magnetic fields for the sample subjected to 28.7 and 40.1 GPa (Figure 3A and Figure 3B). It is found that the resistance drops shift to lower temperature with increasing magnetic field (Figure 3A and Figure 3B). We also performed alternating-current (ac) susceptibility measurements on the sample in the pressure range of 2.8–46.2 GPa and found the diamagnetism (Figure 3C). The evolution of T c with pressure obtained from the ac susceptibility measurement is consistent with that measured by the resistance. These results confirm that the pressure-induced resistance drop originates from the superconducting transition. We extract midpoint T c as a function of magnetic field and estimate the value of the upper critical magnetic field (H c2) at zero temperature by Werthamer-Helfand-Honhenberg (WHH) formula (H c2 WHH (0) = -0.693 T C (dH c2 /dT) T=Tc.) (Werthamer et al., 1966). The H c2 value is ∼ 1.2 T at 28.7 GPa and ∼ 2.1 T at 40.1 GPa (Figure 3D), which are much higher than the value of ∼ 0.25 T obtained at ambient pressure (Goto et al., 2017). These results indicate that the three superconducting phases are different in nature.

We summarized the pressure dependence of superconducting transition temperature T c and structure information in Figure 4A. To compare T c (P) detected from resistance and ac susceptibility measurements in a unified way, we used zero-resistance T c in the phase diagram. It is seen that T c of the ambient-pressure superconducting phase decreases continuously with increasing pressure up to P C1 (∼ 12 GPa), where the R phase partially transforms to the M phase. Meanwhile, the T c increases with further compression up to ∼ 31 GPa. By applying higher pressure, the simple cubic phase appears and coexists with the M phase, in which T c rises in this pressure range. When pressure is higher than 36 GPa, the structure transforms into a pure single cubic phase and the corresponding T c remains almost unchanged. These results show that the T c are strongly influenced by the structural phase transition. To further understand the change of superconducting transition temperature in pressurized NaSn 2 As 2, we performed high-pressure Hall coefficient measurements on the sample by sweeping the magnetic field perpendicular to the ab plane up to 2 T at 10 K. The pressure dependence of Hall coefficient (R H) is illustrated in Figure 4B. It is found that R H is positive in the R phase, reflecting the dominance of hole carriers (the carriers in the studied material are composed of hole and electron carriers). Meanwhile, the value of R H is enhanced with elevating pressure and reaches a maximum at ∼ P C1, implying that the role of the hole carrier is reduced with increasing pressure and it may be responsible for the monotonic decline of T c in this pressure range. In the pressure range of a coexistence of R and M phase (12–31 GPa), R H is still positive but decreases dramatically with increasing pressure, suggesting that the role of hole carriers is weakened by applying pressure. It suggests that the structural phase transition enhances the contribution of electron carriers which seems to be in favor of superconductivity. It is worth noting that the tendency of the change in T c (P) is contrary to that in R H (P) in the superconducting phase with the dominance of hole carriers (Figures 4A,B), implying that the component of the carriers plays a vital role in determining T c of this material. At pressure about 33 GPa (P C2), R H goes through zero, suggesting that both holes and electrons are likely present and making compensating contributions. At P > P C2, the cubic phase appears and R H changes its sign from positive to negative, demonstrating that the M -to- C phase transition gives rise to a drastic change in the character of the first Brillouin zone, which impacts directly on the T c value, and the cubic superconducting phase with the domination of electron carriers holds highest T c (∼ 4.1°K). Noted that NaSn 2 As 2 exhibit opposite conduction polarities along in-plane and cross-plane directions due to the unique Fermi surface geometry (He et al., 2019). The Hall coefficient shown in this study is obtained from the in-plane measurement, how the cross-plane Hall coefficient changes with pressure deserves further investigations in the future.

In conclusion, we have investigated high-pressure coevolution of superconductivity with structure and transport properties for NaSn 2 As 2, one of the van der Waals-type layered materials, through in-situ measurements of XRD, resistance, ac susceptibility and Hall coefficient. We found a close correlation of superconductivity with crystal structure and Hall coefficient. Based on the evolution from the ambient-pressure superconducting phase of NaSn 2 As 2, we find that pressure induces two dramatic changes of superconductivity that are associated with the R - M phase at the critical pressure of 12 GPa (P C1) and M - C phase transition at another critical pressure of ∼ 33 GPa (P C2), respectively. Hall coefficient measurements find that the tendency of the change in T c (P) of the rhombohedral and monoclinic superconducting phases is opposite to that in R H (P), suggesting that hole carriers are dominant in these SC phases, At P C2, the Hall coefficient change the sign from positive to negative, meanwhile the sample undergoes a structure phase transition from the M phase to the C phase. The T c value of the cubic phase is higher than that of the rhombohedral and monoclinic superconducting phases. The connection among the superconductivity, structural phase transition and R H revealed by our high-pressure study is expected to shed new insight on the underlying superconducting mechanism of the tin-pnictide-based superconductors and provide a route to explore new superconductors with potential applications.