# Electric circuit simulations of $n$th-Chern insulators in $2n$-dimensional space and their non-Hermitian generalizations for arbitral $n$

## TL;DR

This paper demonstrates how electric circuits can simulate topological $n$-th Chern insulators in $2n$-dimensional space, including non-Hermitian cases, by measuring admittance spectra to observe boundary states.

## Contribution

It introduces a method to simulate arbitrary $n$-th Chern insulators in $2n$-dimensional space using electric circuits with operational amplifiers, extending to non-Hermitian systems.

## Key findings

- Simulation of $n$-th Chern insulators via electric circuits.
- Observation of boundary states through admittance spectra.
- Quantization of non-Hermitian $n$-th Chern number persists with complex Dirac masses.

## Abstract

We show that topological phases of the Dirac system in arbitral even dimensional space are simulated by $LC$ electric circuits with operational amplifiers. The lattice Hamiltonian for the hypercubic lattice in $2n$ dimensional space is characterized by the $n$-th Chern number. The boundary state is described by the Weyl theory in $2n-1$ dimensional space. They are well observed by measuring the admittance spectrum. They are different from the disentangled $n$-th Chern insulators previously reported, where the $n$-th Chern number is a product of the first Chern numbers. The results are extended to non-Hermitian systems with complex Dirac masses. The non-Hermitian $n$-th Chern number remains to be quantized for the complex Dirac mass.