Dense superconducting phases of copper-bismuth at high pressure

Although copper and bismuth do not form any compounds at ambient conditions, two intermetallics, $\mathrm{CuBi}$ and ${\mathrm{Cu}}_{11}{\mathrm{Bi}}_7$, were recently synthesized at high pressures. Here we report on the discovery of additional copper-bismuth phases at elevated pressures with high densities from ab initio calculations. In particular, a ${\mathrm{Cu}}_2\mathrm{Bi}$ compound is found to be thermodynamically stable at pressures above 59 GPa, crystallizing in the cubic Laves structure. In strong contrast to ${\mathrm{Cu}}_{11}{\mathrm{Bi}}_7$ and CuBi, cubic ${\mathrm{Cu}}_2\mathrm{Bi}$ does not exhibit any voids or channels. Since the bismuth lone pairs in cubic ${\mathrm{Cu}}_2\mathrm{Bi}$ are stereochemically inactive, the constituent elements can be closely packed and a high density of 10.52 g/${\mathrm{cm}}^3$ at 0 GPa is achieved. The moderate electron-phonon coupling of $\lambda =0.68$ leads to a superconducting temperature of 2 K, which exceeds the values observed both in ${\mathrm{Cu}}_{11}{\mathrm{Bi}}_7$ and CuBi, as well as in elemental Cu and Bi.

Figure 1

The crystal structure of cubic ${\mathrm{Cu}}_2\mathrm{Bi}$ from three different perspectives is shown in panels (a)–(c). Purple (large) and blue (small) spheres denote the Bi and Cu atoms, respectively. The isosurfaces of the ELF are shown at values of 0.9 (red), 0.8 (yellow), 0.7 (green), and 0.6 (blue).

Figure 2

The electronic band structure, color coded according to the projection on the Cu and Bi atoms in red and blue, respectively. In the right panel, the total density of states is shown as the shaded area, and the contributions of the Cu $d$ states, Bi $p$ states, and Bi $s$ states are indicated by the red, blue, and orange lines.

Figure 3

(a) The stability range of the different Cu-Bi compounds are shown as a function of pressure. The dashed line representing the CuBi phase indicates that it is only stable at elevated temperatures. (b) The convex hull of stability at 100 GPa (red) and at 300 GPa (blue). Thermodynamically stable phases are denoted by black circles.

Figure 4

The phonon band structure is shown along a path in the Brillouin zone. The color coding represents the factional mode contribution of the Cu and Bi atoms to the phonon eigenmodes in red and blue, respectively.

Figure 5

The electron-phonon coupling properties are shown in the top panel as a function of the phonon frequency $\omega$, where ${\alpha }^{2}F\left(\omega \right)$ denotes the Eliashberg spectral function, while $\lambda \left(\omega \right)$ is the electron-phonon coupling strength. In the bottom panel the total phonon density of states (PHDOS) is shown with the shaded area, whereas the partial density of states of the Cu and the Bi atoms are shown in red and blue, respectively.