# Topological bulk states and their currents

## TL;DR

This paper demonstrates that two-dimensional Chern insulators can support localized bulk states that produce topologically protected bulk currents, even below the energy gap, providing new ways to probe topological phases.

## Contribution

It reveals the existence of bulk states in Chern insulators that generate resilient bulk currents under local potential gradients, expanding understanding of topological phenomena.

## Key findings

- Bulk states produce transverse bulk currents.
- Bulk currents are topologically protected.
- Bulk currents occur below the energy gap.

## Abstract

We provide evidence that, alongside topologically protected edge states, two-dimensional Chern insulators also support localised bulk states deep in their valance and conduction bands. These states manifest when local potential gradients are applied to the bulk, while all parts of the system remain adiabatically connected to the same phase. In turn, the bulk states produce bulk current transverse to the strain. This occurs even when the potential is always below the energy gap, where one expects only edge currents to appear. Bulk currents are topologically protected and behave like edge currents under external influence, such as temperature or local disorder. Detecting topologically resilient bulk currents offers a direct means to probe the localised bulk states.