Topological superconductivity on a kagome magnet coupled to a Rashba superconductor

Abstract

A quantum anomalous Hall system is predicted to realize topological superconductivity when proximity-coupled to an $s$-wave superconductor. A kagome magnet with chiral magnetic ordering exhibits the quantum anomalous Hall effect; however, superconducting proximity to an ordinary $s$-wave superconductor fails to induce pairing in the strong exchange coupling limit. In this work, we demonstrate that proximity coupling to a Rashba superconductor gives rise to topological superconducting phases characterized by odd Bogoliubov-de Gennes Chern numbers. We confirmed their consistency with the chiral central charge calculated based on the modular commutator. We also show that the magnetic ordering of kagome magnets is affected energetically by the proximity effect.

Figures (9)

• Figure 1: (a) Schematic illustration of the hybrid system considered here. The quantum anomalous Hall system on a kagome lattice (top layer) is proximity-coupled to the Rashba $(s+p)$-wave superconductor (bottom layer). (b) Localized spins (red arrows) on a kagome lattice. Their orientations are specified by $\theta$ and $\phi$. (c) Model parameters appearing in $H$.
• Figure 2: Partition of subsystems $A$, $B$, and $C$ in the bulk $\Lambda$.
• Figure 3: Energy bands of $h_{\text{hop}}$ for the several polar angles $\theta$. Each band is denoted by $\epsilon_{n}$ with $n=1,2,3$. All three bands at $\theta\neq0,\pi/2$ are isolated, and their band Chern numbers $C$ are $-1$, 0, 1 from the bottom, respectively.
• Figure 4: Pair potential projected onto each band. Each row represents a different band ($\Delta_n$ corresponds to $\epsilon_n$ in Fig. \ref{['fig:band']}). From left to right, the polar angle $\theta$ is varied as indicated. The color intensity encodes $\phi$. We scale $\Delta_n(\bm{k})$ by $\Delta_p$ since the effect of the $s$-wave pairing is not included. The gray vertical bars indicate the momenta at which band touchings occur, where $\Delta_n$ is ill-defined. We focus on $0\leq\phi\leq\pi/2$ since we have numerically verified that $|\Delta_n(\bm{k})|$ with $\phi$ and $\pi-\phi$ are identical.
• Figure 5: BdG Chern number $\mathcal{N}$ as a function of the polar angle $\theta$ and (a) the chemical potential $\mu$ or (b) the band filling $\nu$. Black regions represent $|\mathcal{N}|\geq4$. White regions correspond to parameters where quasiparticle energy $E_n(\bm{k})$ becomes negative. This occurs because inversion symmetry is absent in in our system. Other parameters are set to be $\Delta_s/t=\Delta_p/t=0.1$ and $\phi=\pi/2$.