Superconductivity in noncentrosymmetric $\mathrm{A}{\mathrm{g}}_2\mathrm{P}{\mathrm{d}}_3\mathrm{S}$

We have successfully synthesized the single crystal of $\mathrm{A}{\mathrm{g}}_2\mathrm{P}{\mathrm{d}}_3\mathrm{S}$, which exhibits superconductivity with the transition temperature of $T_{\mathrm{c}}=2.25\mathrm{K}$. $\mathrm{A}{\mathrm{g}}_2\mathrm{P}{\mathrm{d}}_3\mathrm{S}$ crystallizes in the space group $P{4}_{1}32$ with the filled $\beta -\mathrm{Mn}$ structure, which has no inversion symmetry. The value of the Ginzburg-Landau parameter ${\kappa }_{\mathrm{GL}}$ indicates that $\mathrm{A}{\mathrm{g}}_2\mathrm{P}{\mathrm{d}}_3\mathrm{S}$ is a type-II superconductor. $\mathrm{\Delta }C\left(T_{\mathrm{c}}\right)/{\gamma }_{\mathrm{n}}{T}_{\mathrm{c}}=1.50$ and $2\mathrm{\Delta }/k_B{T}_{\mathrm{c}}=3.48$ from the heat-capacity analyses indicate that $\mathrm{A}{\mathrm{g}}_2\mathrm{P}{\mathrm{d}}_3\mathrm{S}$ is a weak-coupling Bardeen-Cooper-Schrieffer (BCS) superconductor with an isotropic superconducting gap. On the other hand, the violation of the Werthamer-Helfand-Hohenberg curve in the $H-T$ phase diagram implies $\mathrm{A}{\mathrm{g}}_2\mathrm{P}{\mathrm{d}}_3\mathrm{S}$ is not a typical BCS superconductor.

Figure 1

(a) Crystal structure of $\mathrm{A}{\mathrm{g}}_2\mathrm{P}{\mathrm{d}}_3\mathrm{S}$. Each shaded polyhedron represents a $\mathrm{P}{\mathrm{d}}_6\mathrm{S}$ octahedron, in which sulfur is located at the center. The interstitial space in the Ag network is filled by corner-sharing $\mathrm{P}{\mathrm{d}}_6\mathrm{S}$ octahedra. (b) Crystal structure of the ${\mathrm{A}}_2{\mathrm{B}}_3 \beta -\mathrm{Mn}$ structure. The solid line represents a cubic unit cell.

Figure 2

(a) Temperature dependence of the resistivity of $\mathrm{A}{\mathrm{g}}_2\mathrm{P}{\mathrm{d}}_3\mathrm{S}$ up to 300 K under magnetic fields ${\mu }_{0}H=0$ and 1 T, and (b) resistivity between 0.5 and 3 K under various magnetic fields. The inset of (a) illustrates the definition of the transition temperature $T_{\mathrm{c}}$ and shows a magnified version of the region around the transition temperature. The arrow indicates the $T_{\mathrm{c}}$ estimated from the onset resistivity.

Figure 3

(a) Temperature dependence of the magnetic susceptibility in $\mathrm{A}{\mathrm{g}}_2\mathrm{P}{\mathrm{d}}_3\mathrm{S}$. The data for zero-field-cooled (ZFC) and field-cooled (FC) processes were plotted. (b) Magnetization vs magnetic field ($M-H$) curve for $\mathrm{A}{\mathrm{g}}_2\mathrm{P}{\mathrm{d}}_3\mathrm{S}$. The inset of (b) shows the $M-H$ curve in the low-magnetic-field region. The arrow indicates the lower critical field $H_{\mathrm{c}1}$ defined as the deviation field, which represents the deviation from the linear behavior of magnetization.

Figure 4

(a) Temperature dependence of the total heat capacity under magnetic fields ${\mu }_{0}H=0$ and 1 T in the $C_{\mathrm{total}}/T$ vs $T^2$ plot. The solid line indicates the result of fitting to the conventional equation $C/T=\gamma +\beta T^2$. (b) Temperature dependence of the electron part of the heat capacity, $C_{\mathrm{el}}$, divided by the temperature at zero field. The $T_{\mathrm{c}}$ value is determined by requiring conservation of the entropy balance around the heat capacity jump. (c) Electronic heat capacity in the $C_{\mathrm{el}}$ vs. $T$ plot at zero field. The solid line shows the result of fitting to $C_{\mathrm{el}}={\gamma }_{0}T+a^{*}\exp \{-\mathrm{\Delta }\left(0\right)/k_{\mathrm{B}}T\}$. (d) Electronic heat capacity divided by temperature under several magnetic fields: ${\mu }_{0}H=0,0.01,0.05,0.1,0.2,0.3$, and 1 T.

Figure 5

Calculated DOS of $\mathrm{A}{\mathrm{g}}_2\mathrm{P}{\mathrm{d}}_3\mathrm{S}$ with spin-orbit interaction. The total and partial DOS for each atom is illustrated. The broken line at $E=0$ indicates the Fermi energy.

Figure 6

$H-T$ phase diagram of $\mathrm{A}{\mathrm{g}}_2\mathrm{P}{\mathrm{d}}_3\mathrm{S}$ deduced from the temperature dependence of the resistivity and heat capacity. The solid and open circles indicate the $T_{\mathrm{c}}$ values from onset and zero resistivity, respectively. The solid triangles show the $T_{\mathrm{c}}$ values from the heat capacity. The solid and dashed lines are respectively the linear fit and the WHH fit to the data around the low-magnetic-field region of the diagram.