Bulk-interface correspondence from quantum distance in flat band systems

TL;DR

This paper reveals that quantum distance, a geometric property of wave functions, can predict boundary modes in flat band systems, extending the bulk-boundary correspondence beyond topology.

Contribution

It introduces quantum distance as a new geometric quantity that hosts a bulk-interface correspondence in flat band systems, even when topological invariants are trivial.

Findings

Nonzero maximum quantum distance guarantees boundary modes.

Quantum distance predicts dispersion relation of interface modes.

Flat bands with quantum distance exhibit boundary modes despite trivial topology.

Abstract

The bulk-boundary correspondence is an integral feature of topological analysis and the existence of boundary or interface modes offers direct insight into the topological structure of the Bloch wave function. While only the topology of the wave function has been considered relevant to boundary modes, we demonstrate that another geometric quantity, the so-called quantum distance, can also host a bulk-interface correspondence. We consider a generic class of two-dimensional flat band systems, where the flat band has a parabolic band-crossing with another dispersive band. While such flat bands are known to be topologically trivial, we show that the nonzero maximum quantum distance between the eigenstates of the flat band around the touching point guarantees the existence of boundary modes at the interfaces between two domains with different chemical potentials or different maximum quantum distance. Moreover, the maximum quantum distance can predict even the explicit form of the dispersion relation and decay length of the interface modes.