# Chern insulators for electromagnetic waves in electrical circuit networks

## TL;DR

This paper demonstrates how electrical circuit networks of capacitors and inductors can realize Chern insulator phases for electromagnetic waves, exhibiting topologically protected edge modes and tunable bulk gaps.

## Contribution

It introduces simple circuit architectures that emulate Chern insulators for electromagnetic waves, including a practical implementation of Hall resistor elements for symmetry breaking.

## Key findings

- Networks exhibit topologically protected chiral edge modes.
- Bulk gap is tunable over a range of frequencies.
- Implementation of Hall resistors enables time-reversal symmetry breaking.

## Abstract

Periodic networks composed of capacitors and inductors have been demonstrated to possess topological properties with respect to incident electromagnetic waves. Here, we develop an analogy between the mathematical description of waves propagating in such networks and models of Majorana fermions hopping on a lattice. Using this analogy we propose simple electrical network architectures that realize Chern insulating phases for electromagnetic waves. Such Chern insulating networks have a bulk gap for a range of signal frequencies that is easily tunable and exhibit topologically protected chiral edge modes that traverse the gap and are robust to perturbations. The requisite time reversal symmetry breaking is achieved by including a class of weakly dissipative Hall resistor elements whose physical implementation we describe in detail.