Electric circuits for non-Hermitian Chern insulators

We analyze the non-Hermitian Haldane model where the spin-orbit interaction is made non-Hermitian. The Dirac mass becomes complex. We propose to realize it by an $LC$ circuit with operational amplifiers. A topological phase transition is found to occur at a critical point where the real part of the bulk spectrum is closed. The Chern number changes its value when the real part of the mass becomes zero. In the topological phase of a nanoribbon, two non-Hermitian chiral edges emerge connecting well separated conduction and valence bands. The emergence of the chiral edge states is signaled by a strong enhancement in impedance. Remarkably it is possible to observe either the left-going or right-going chiral edge by measuring the one-point impedance. Furthermore, it is also possible to distinguish them by the phase of the two-point impedance. Namely, the phase of the impedance acquires a dynamical degree of freedom in the non-Hermitian system.