Electronic circuit analogs of non-hermitian topological edge states - Trung, Ha Quang (2018)
In this pro ject, we devise a technique to simulate tight-binding lattices of infinite size with circuitry. Each atom in the lattice is mo delled by a parallel LC resonator; the hoppings between atoms are modelled by a capacitor that connects the pairs of nodes. We devise a setup that introduces a tunable momentum parameter, enabling the simulation of infinitely large lattices. In the first half of the paper. we shows how this technique works by applying it to specific examples in one and two dimensions - to a 1D tight-binding chain and graphene with zigzag edge, respectively. The dispersion relation is successfully reproduced in these two examples. In the second half of the paper, we propose a two-dimensional non-Hermitian tight-binding model that reduces to a previously studied continuum Hamiltonian and that exhibits topological edge states. This tight binding model can also be simulated with circuits using the same procedure outline in the previous sections. It is left for future work to construct the corresponding non-Hermitian circuitry lattice to find experimental evidences for the predicted edge states.