# Second-order topological phases protected by chiral symmetry

## TL;DR

This paper explores second-order topological phases protected by chiral symmetry, proposing new models for topological insulators and semimetals with hinge states, and analyzing phase transitions in these systems.

## Contribution

It introduces a theoretical framework for second-order topological phases protected by chiral symmetry and proposes models for topological semimetals and insulators with hinge states.

## Key findings

- Proposes a model for 2D second-order topological insulators with chiral symmetry.
- Introduces a 3D second-order topological semimetal with flat hinge bands.
- Shows that broken chiral symmetry can lead to chiral hinge states in 3D phases.

## Abstract

We study second-order topological insulators and semimetals characterized by chiral symmetry. We investigate topological phase transitions of a model for construction of the two-dimensional second-order topological insulators protected only by chiral symmetry. By the theory of the phase transitions, we propose a second-order topological semimetal and insulators with flat hinge bands in chiral-symmetric three-dimensional systems. The three-dimensional second-order topological phases can be obtained from the stacked two-dimensional second-order topological insulators with chiral symmetry. Moreover, we show that broken chiral symmetry in the three-dimensional second-order topological phase allows a second-order topological insulator with chiral hinge states. We also demonstrate the second-order topological phases by using a lattice model.