Coexistence of pressure-induced superconductivity and topological surface states in elementary substance Sb

Topological superconductors are expected to host non-Abelian Majorana zero mode which is of fundamental importance for topological quantum computing. However, the discovered topological superconductor candidates are still rare. Here, we systematically studied the topological semimetal antimony Sb through first-principles calculations, and found that a moderate pressure could induce the superconductivity coexisting with topological surface states. The superconducting critical transition temperature ($T_c$) reaches $\sim 0.3\mathrm{K}$ under $\sim 8\mathrm{GPa}$ and the topological surface states can be well preserved. The $T_c$ can be much enhanced to $\sim 2\mathrm{K}$ through further electron doping. Elementary substance antimony may provide a simple material platform to detect the Majorana boundary states and develop the topological quantum computation.

Figure 1

Crystal and electronic structure. (a) The crystal structure of antimony Sb. (b) The bulk band structures of Sb. There is a hole pocket around $T$ point and an electron pocket at $L$ point. (c) Projected surface band structures of the (111) surface. There is a single Dirac-type surface state at $\overline{\mathrm{\Gamma }}$ point, crossing the Fermi level. (d) The Fermi surface of bulk and surface bands. The green arrows indicate the spin texture of surface states.

Figure 2

Effects on phonon and electronic structures of external pressures. (a) The phonon dispersions of Sb under different pressures (0, 6, 7, and 8 GPa). The pressure distinctly shifts the phonon dispersions. (b) The corresponding phonon DOS under different pressures (0, 6, 7, and 8 GPa). (c) The bulk and surface states of Sb under different pressures. The bulk bands become more metallic and the Dirac-type surface states are well preserved.

Figure 3

Pressure-induced superconductivity. (a) The evolution of the total energy under the external pressures. There is a discontinuous change around 8 GPa which indicates the structure phase transition. (b) The superconducting transition temperature $T_c$ and DOS at the Fermi level under the external pressures. (c), (d) The Eliashberg spectral function ${\alpha }^{2}F\left(w\right)$ and integrated electron-phonon coupling parameter $\lambda \left(w\right)$ of Sb at 7 and 8 GPa, respectively.

Figure 4

Chemical doping enhanced superconductivity. (a) The evolution of the superconducting transition temperature $T_c$ with the chemical doping at 8 GPa. (b) The bulk bands and DOS at 8 GPa. The red dashed line represents the Fermi level and the orange region represents the chemical doping range. (c) Fermi surfaces at different chemical potentials (I, II, III, IV).