Supercell Wannier Functions and Emergent Kondo Lattices in Topological Bands

TL;DR

This paper introduces a novel approach to understanding Mott insulators in topological bands using supercell Wannier functions, revealing emergent Kondo lattices and new topological Mott states stabilized by strong interactions.

Contribution

It develops a partial Wannier basis for topological bands, constructing supercell Wannier orbitals that describe emergent Kondo lattices and topological Mott insulators with broken translation symmetry.

Findings

Strong interactions stabilize topological Mott insulators.

Supercell Wannier functions reveal emergent Kondo lattice structures.

Competing phases include fractional Chern insulators.

Abstract

Conventional theories for Mott insulators involve well-localized electronic orbitals. This picture fails in the presence of topological obstructions in Chern bands which prevent the formation of exponentially localized orbitals and are instead often viewed by analogy to Landau levels. Here, we show that strong interactions in fractionally-filled topological bands realize a class of Mott insulating states on emergent topological Kondo lattices. These can be naturally described by a partial Wannier basis of N-1 exponentially-localized orbitals for an N-band manifold with net non-zero Chern number. Choosing a gauge which breaks translation symmetry, we construct a supercell basis which segregates an isolated topological band into well-localized supercell Wannier orbitals that can host the local moments of a Mott insulating state, as well as an itinerant power-law-localized orbital that retains the topological obstruction. Together, they constitute a spontaneous Kondo lattice. We study fractionally-filled interacting quantum spin Hall bands in the Bernevig-Hughes-Zhang model as well as twisted bilayers of MoTe2 at -1/3 filling. We demonstrate that strong short-ranged Coulomb interactions can stabilize a new class of topological Mott insulating states with broken translation symmetry and antiferromagnetic order, which compete with fractional Chern insulating states. Our results predict a new scenario for time-reversal-symmetric interacting topological bands in solids, beyond conventional Landau level paradigms for the fractional quantum Hall effect.