Chern number modification in crossing the boundary between different band structures: Three-band models with cubic symmetry

Abstract

A family of [Formula: see text] Hermitian matrix Hamiltonians defined on the sphere [Formula: see text] and depending on extra control parameters in the presence of a finite subgroup of [Formula: see text] as a symmetry group are studied with eigen-line bundles which are constructed by piecing together locally-defined eigenvectors. The condition for degeneracy in eigenvalues splits in general the space of control parameters into distinct iso-Chern domains on each of which the Chern numbers of the associated eigen-line bundles are constant. A Chern number modification or a delta-Chern occurs when crossing the boundary from one iso-Chern domain to another. The present article provides a formula for the delta-Chern on the model of a two-parameter family of [Formula: see text] Hermitian matrix Hamiltonians with cubic symmetry together with the whole sets of Chern numbers on respective iso-Chern domains.