# Propagating edge states in strained honeycomb lattices

## TL;DR

This paper studies helical edge states in strained honeycomb lattices, deriving a criterion for their existence, verifying it numerically, and showing how edge shape engineering can control their propagation.

## Contribution

It provides a general criterion for propagating edge states in strained honeycomb lattices and demonstrates control of these states via edge shape manipulation.

## Key findings

- Edge states exist under specific chiral symmetry conditions.
- Edge shape engineering can control edge state propagation.
- Next-nearest-neighbour hoppings affect edge state sensitivity.

## Abstract

We investigate the helically-propagating edge states associated with pseudo-Landau levels in strained honeycomb lattices. We exploit chiral symmetry to derive a general criterion for the existence of these propagating edge states in the presence of only nearest-neighbour hoppings and we verify our criterion using numerical simulations of both uni-axially and trigonally strained honeycomb lattices. We show that the propagation of the helical edge state can be controlled by engineering the shape of the edges. Sensitivity to chiral-symmetry-breaking next-nearest-neighbour hoppings is assessed. Our result opens up an avenue toward the precise control of edge modes through manipulation of the edge shape.