# Interaction-Driven Topological Switch in a $P$-Band Honeycomb Lattice

## TL;DR

This paper investigates how interactions in a $p$-band honeycomb lattice induce a transition from a quantum anomalous Hall insulator to a Dirac semimetal and finally to a second-order topological insulator with corner states.

## Contribution

It reveals a novel interaction-driven topological switch between first-order and second-order topological phases in a $p$-band honeycomb lattice.

## Key findings

- Weak interactions induce a quantum anomalous Hall phase with chiral edge modes.
- Increasing interactions lead to a Dirac semimetal with emergent Dirac points.
- Strong interactions result in a dimerized insulator with corner states.

## Abstract

The non-interacting band structure of spinless fermions in a two-dimensional ($d=2$) $p$-band honeycomb lattice exhibits two quadratic band touching points (QBTPs), which lie at the Fermi levels of filling $\nu=1/4$ and its particle-hole conjugated filling $\nu=3/4$. A weak Hubbard interaction $U$ spontaneously breaks the time-reversal symmetry and removes the QBTP, rendering the system into a quantum anomalous Hall insulator (QAHI). The first-order topological nature of QAHI is characterized by a nontrivial Chern number and supports ($d-1$)-dimensional chiral edge modes. With increasing the interaction $U$, the system is driven into a Dirac semimetal by breaking the crystal symmetry through a discontinuous quantum phase transition. The emergent Dirac points each with Berry flux $\pi$ are generated in pairs, originating from the $2\pi$ Berry flux of QBTP. A sufficiently large $U$ ultimately drives the system into a dimerized insulator (DI) by simultaneously annihilating the Dirac points at the Brillouin zone boundary. The second-order topological nature of DI is characterized by the quantized polarizations and supports ($d-2$)-dimensional corner states. Our study provides a unique setting for exploring the topological switch between the first-order and second-order topological insulators.