Braiding of Majorana corner states in electric circuits and its non-Hermitian generalization

Abstract

We propose to realize Majorana edge and corner states in electric circuits. First, we simulate the Kitaev model by an LC electric circuit and the $p_{x}+ip_{y}$ model by an LC circuit together with operational amplifiers. Zero-energy edge states emerge in the topological phase, which are detectable by measuring impedance. Next, we simulate the Bernevig-Hughes-Zhang model by including an effective magnetic field without breaking the particle-hole symmetry, where zero-energy corner states emerge in the topological phase. It is demonstrated that they are Ising anyons subject to the braiding. Namely we derive $\sigma ^{2}=-1$ for them, where $\sigma $ denotes the single-exchange operation. They may well be called Majorana states. We also study non-Hermitian generalizations of these models by requiring the particle-hole symmetry. It is shown that the braiding holds in certain reciprocal non-Hermitian generalizations.