Surface chiral superconductivity in odd-parity nematic superconductors with magnetic impurities

We study odd-parity nematic superconductivity in doped topological insulators in the presence of surface magnetic impurities. The peculiar surface subgap spectrum, characterized by a Majorana flat band, nodal cones, and the surface states of the parent topological insulator, gives rise to overall ferromagnetic RKKY interactions between the surface impurities. An additional coupling between the impurities and a preemptive chiral order parameter promote a surface time-reversal symmetry breaking solution at the surface of the system. We discuss the relevant scenarios and suggest to engineer surface chiral superconductivity by properly choosing magnetic adatoms with highly anisotropic exchange coupling.

Figure 1

(a) Schematics of the setup considered: a bulk odd-parity nematic superconductor with surface magnetic disorder and chiral surface solution. (b) Directional dependence of the RKKY interaction experienced by magnetic impurities.

Figure 2

Surface spectrum of the system obtained with a tight-binding model for a slab of 200 bilayers [55]. (a) and (b) The nematic phase along the $k_x$ and $k_y$, respectively. The color code represents the charge (red electrons, blue holes). (c) and (d) The nematic phase with surface chiral solution and finite magnetization $\langle S_y\rangle$ only on one surface, along the $k_x$ and $k_y$, respectively.

Figure 3

(a) Phase diagram for the onset of a surface TRSB phase. The separatrix $g_c=2\sqrt{\eta }$, marked in black, divides the diagram in a nematic phase for $g<g_c$ and a TRSB phase for $g>g_c$. (b) Phase $\phi$ and (c) amplitude $\psi$ versus the transverse direction $z$ for $\eta =0.09$: empty dots refer to the exact numerics and continuous lines in (b) to Eq. (13). (d) Surface phase ${\phi }_0$ versus coupling for boundary conditions Eqs. (9) and (10).