Invisible flat bands on a topological chiral edge

TL;DR

This paper demonstrates the universal existence of invisible flat bands at topological interfaces in 2D Chern insulators, revealing their connection to chiral edge modes and interactions through theoretical proof and numerical simulations.

Contribution

It provides a theoretical proof of invisible flat bands at topological interfaces and verifies their presence and interaction effects in a Hubbard model using real-space dynamical mean-field theory.

Findings

Invisible flat bands exist ubiquitously at topological interfaces.

Interactions split chiral modes into branches connected by invisible flat bands.

Numerical results confirm the theoretical predictions in a Hubbard model.

Abstract

We prove that invisible bands associated with zeros of the single-particle Green's function exist ubiquitously at topological interfaces of 2D Chern insulators, dual to the chiral edge/domain-wall modes. We verify this statement in a repulsive Hubbard model with a topological flat band, using real-space dynamical mean-field theory to study the domain walls of its ferromagnetic ground state. Moreover, our numerical results show that the chiral modes are split into branches due to the interaction, and that the branches are connected by invisible flat bands. Our work provides deeper insight into interacting topological systems.