Ground states of $\mathrm{A}{\mathrm{u}}_2\mathrm{Pb}$ and pressure-enhanced superconductivity

$\mathrm{A}{\mathrm{u}}_2\mathrm{Pb}$ is a candidate of natural topological superconductors that has attracted much attention in the last few years. Combining ab initio calculations with machine-learning accelerated crystal structure searches, we have found two ground states of $\mathrm{A}{\mathrm{u}}_2\mathrm{Pb}$: $Pca{2}_1$ phase at ambient pressure and $I\overline{4}2d$ phase at high pressure. The $Pca{2}_1$ phase is energetically more favorable than the known Pbcn structure and can be a candidate for x-ray diffraction refinement; our calculations suggest that high-pressure $I\overline{4}2d$ is a conventional superconductor. By the high-pressure electric resistance measurements, we observed evidence of a $T_c$ enhancement. $T_c$ reaches a maximum value of around 4 K at 5 GPa, then decreases with further compression. The superconductivity can remain unchanged after pressure releasing, in line with our theoretical predictions. These results show that $\mathrm{A}{\mathrm{u}}_2\mathrm{Pb}$ exhibits abundant behaviors under varied pressure and temperature, which can help to understand how to adjust its electronic properties by pressure.

Figure 1

(a) Crystal structures of $\mathrm{A}{\mathrm{u}}_2\mathrm{Pb}$: the high-temperature phase $Fd\overline{3}m$; known low-temperature phase Pbcn; the predicted structures $Pca{2}_1$ and $I\overline{4}2d$. They have similar frameworks, but belong to different versions of the cubic Laves structure. The golden and gray balls represent Au and Pb atoms, respectively. (b) The pressure-dependent enthalpy difference relative to $Fd\overline{3}m$ using GGA-PBE. (c) The enthalpy difference among Pbcn, $Pca{2}_1$, and $I\overline{4}2d$ from 0 to 5 GPa using GGA-PBE. The enthalpy difference calculation is rechecked by (d) SCAN meta-GGA.

Figure 2

The phonon curves of the (a) $Pca{2}_1$ and (b) Pbcn structures calculated at 0 GPa. There is no imaginary frequency for $Pca{2}_1$, while Pbcn has imaginary phonon modes. (c) The simulation XRD pattern of $Pca{2}_1$ and Pbcn compared with the experiment results. The experimental data are from Ref. [35]. The $Pca{2}_1$ simulation curves match well with the experiment curves, suggesting that the previous experiment [35] is possible to explain by the predicted $Pca{2}_1$ structure.

Figure 3

(a) Calculated phonon dispersion curves, phonon density of states (PHDOS), Eliashberg EPC spectral function ${\alpha }^{2}F\left(\omega \right)$, and electron-phonon integral $\lambda \left(\omega \right)$ of $I\overline{4}2d$ at 5 GPa. (b) The calculated pressure dependence of $T_c$ for $I\overline{4}2d$ from 0 to 20 GPa with different ${\mu }^{*}$. (c) The resistivity of $\mathrm{A}{\mathrm{u}}_2\mathrm{Pb}$ for various pressures as a function of temperature from 5 to 30 GPa in run 1. The inset shows the detailed $\rho$-T curves from 2 to 8 K. (d) The resistivity as a function of temperature for $\mathrm{A}{\mathrm{u}}_2\mathrm{Pb}$ applied with different magnetic field at 6.5 GPa in run 2. $T_c$ is suppressed with the increasing magnetic field. The inset compares the normalized critical field $h^{*}$ (blue squares) to the $s$-wave superconductor model (black line).

Figure 4

Superconducting phase diagram of $\mathrm{A}{\mathrm{u}}_2\mathrm{Pb}$ with the $I\overline{4}2d$ structure. The blue region corresponds to the superconducting phase and the orange region corresponds to the normal state. The black squares represent the measured values of $T_c$ in the pressure-increasing process of run 1; the red circles are those in the pressure-releasing process of run 1; the purple pentagram represents the $T_c$ under 0 T in run 2 and the blue triangles represent the calculated values of $T_c$ with ${\mu }^{*}=0.13$.