Flat bands with higher Chern number in pyrochlore slabs

TL;DR

This paper constructs nearly dispersionless bands with higher Chern numbers in a pyrochlore-inspired lattice model, opening avenues for exploring novel topological and correlated states of matter.

Contribution

It introduces an intuitive method to realize flat bands with arbitrary Chern numbers in a multilayer kagome lattice model inspired by pyrochlore structures.

Findings

Finite regions with flat bands of C=N in parameter space

Explicit wave function expressions for topological bands

Layer and reciprocal space coupling in C=N wave functions

Abstract

A large number of recent works point to the emergence of intriguing analogs of fractional quantum Hall states in lattice models due to effective interactions in nearly flat bands with Chern number C=1. Here, we provide an intuitive and efficient construction of almost dispersionless bands with higher Chern numbers. Inspired by the physics of quantum Hall multilayers and pyrochlore-based transition-metal oxides, we study a tight-binding model describing spin-orbit coupled electrons in N parallel kagome layers connected by apical sites forming N-1 intermediate triangular layers (as in the pyrochlore lattice). For each N, we find finite regions in parameter space giving a virtually flat band with C=N. We analytically express the states within these topological bands in terms of single-layer states and thereby explicitly demonstrate that the C=N wave functions have an appealing structure in which layer index and translations in reciprocal space are intricately coupled. This provides a promising arena for new collective states of matter.