Topological properties of Hermitian and non-Hermitian periodic systems (2021)
ABSTRACT: In this work we study some topological properties of Hermitian and non-Hermitian periodic systems with physical importance. For the Hermitian system, we have studied the behavior of 1, 2 and 3 layers of graphene aligned on boron nitride (BN) substrate to analyze how the effective moiré potential and the number of graphene layers affects the Chern number. Our contribution focuses on the calculation of the Chern diagrams of N-layer (N = 1, 2, 3) ABC graphene boron nitride moire superlattices, the respective analysis of the potential function and the rol of the pseudomagnetic moiré vector potential to try to find a theoretical explanation for recent experimental results. It is important to emphasize that our calculations confirm recent results, where the maximum magnitude of the topological invariant (Chern number) coincides with the number of graphene layers. However, the effective moiré potential in the low energy model allows Chern number magnitudes smaller than the number of layers. The Chern diagrams that we calculated have practical importance, because prior to any experimental implementation, the topological properties of the material can be known. This issue is relevant to applications on nano-devices. On the other hand, the non-Hermitian system that we have studied is new type of Su-SchriefferHeeger (SSH) model with complex hoppings, where we propose its correspondence with an electrical circuit model to represent the topological behavior and some quantum properties. Our model can be configured so that the hoppings between sites of the chain are independently parameterized and related to RLC circuit elements, which makes it useful to find and analyze topological properties. Our non-Hermitian circuit model opens the door to new topological material designs based on RLC circuit components.