Chiral-Flux-Phase-Based Topological Superconductivity in Kagome Systems with Mixed Edge Chiralities

Abstract

Recent studies have attracted intense attention on the quasi-2D kagome superconductors $A{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$ ($A=\mathrm{K}$, Rb, and Cs) where the unexpected chiral flux phase (CFP) associates with the spontaneous time-reversal symmetry breaking in charge density wave states. Here, commencing from the 2-by-2 charge density wave phases, we bridge the gap between topological superconductivity and time-reversal asymmetric CFP in kagome systems. Several chiral topological superconductor (TSC) states featuring distinct Chern numbers emerge for an $s$-wave or a $d$-wave superconducting pairing symmetry. Importantly, these CFP-based TSC phases possess unique gapless edge modes with mixed chiralities (i.e., both positive and negative chiralities), but with the net chiralities consistent with the Bogoliubov--de Gennes Chern numbers. We further study the transport properties of a two-terminal junction, using Chern insulator or normal metal leads via atomic Green's function method with Landauer-B\"uttiker formalism. In both cases, the normal electron tunneling and the crossed Andreev reflection oscillate as the chemical potential changes, but together contribute to plateau transmissions (1 and $\frac{3}{2}$, respectively) that exhibit robustness against disorder. These behaviors can be regarded as the signature of a TSC hosting edge states with mixed chiralities.