Topological superconducting phase and Majorana fermions in half-metal/superconductor heterostructures

As a half-metal is spin polarized at its Fermi level by definition, it was conventionally thought to have little proximity effect to an $s$-wave superconductor. Here we show that with interface spin-orbit coupling $p_x+i{p}_y$ superconductivity without spin degeneracy is induced on the half-metal, and we give an estimate of its bulk energy gap. Therefore, a single-band half-metal can give us a topological superconductor with a single chiral Majorana edge state. Our band calculation shows that two atomic layers of VTe or CrO${}_2$ is a single-band half-metal for a wide range ($\sim$0.1 eV) of Fermi energy and thus is a suitable candidate material.

Figure 1

The heterostructure for obtaining $p_x+i{p}_y$ superconductivity. The half-metal layer has a 2D electronic structure with a single Fermi surface without spin degeneracy. It is coupled to the $s$-wave superconductor through hopping. The substrate stabilizes the half-metal crystal structure without affecting qualitatively its electronic structure.

Figure 2

A schematic representation of the HM and SC bands for weak hopping. Two HM bands are due to the artificial doubling of degrees of freedom in the Bogoliubov-de Gennes formalism. In this formalism, the pairing amplitude and gap require hybridization of the “particle” and “hole” bands, which is due to the interface hopping in our model.

Figure 3

Crystal structures of two candidate materials, VTe and CrO${}_2$. The left-hand side shows the zinc-blende crystal structure of bulk VTe. Here, both V and Te forms are body-centered cubic with a lattice constant of $a=0.6271$ nm ($a=0.6202$ nm for zb-CrTe). The right-hand side shows the rutile crystal structure of bulk CrO${}_2$, where $a=0.4421$ nm, $c=0.2916$ nm. The distance between the nearest O and Cr on the same layer is 0.1817 nm.

Figure 4

(a) The band structure of the VTe-ZnTe(111) model. There is no spin degeneracy in these bands; the red (darker gray) and the green (gray) dotted curve shows the spin-up and spin-down bands when SOC is absent. The region shaded in orange (lighter gray) shows the energy range for which we obtain a single Fermi pocket. (b) The single Fermi surface at the energy level 0.0 eV for the ZnTe-VTe(111) model. The green (gray) box shows the first Brillouin zone (BZ). (c) The band structure of the CrO${}_2$ (001) model. (d) The single Fermi surface around the $\Gamma$ point at the energy level 0.01 eV for the CrO${}_2$ (001) model, the green (gray) box showing the first BZ.