Charge conservation protected topological phases

TL;DR

This paper explores how charge conservation influences topological phases, showing that in certain dimensions, topological insulators can be adiabatically connected to trivial states if superconducting terms are permitted, revealing a nuanced relationship between symmetry and topology.

Contribution

It demonstrates that charge conservation can be bypassed in topological phase transitions through superconducting terms, connecting different topological phases without closing the energy gap.

Findings

Topological insulators in 2D and 3D can be connected to trivial states via superconducting terms.

In 4D, different topological phases with charge conservation are adiabatically connected when symmetry is temporarily broken.

In 1D, non-symmetry-protected topological phases require breaking U(1) charge conservation.

Abstract

We discuss the relation between particle number conservation and topological phases. In four spatial dimensions, we find that systems belonging to different topological phases in the presence of a U(1) charge conservation can be connected adiabatically, i.e., without closing the gap, upon intermediately breaking this local symmetry by a superconducting term. The time reversal preserving topological insulator states in 2D and 3D which can be obtained from the 4D parent state by dimensional reduction inherit this protection by charge conservation. Hence, all topological insulators can be adiabatically connected to a trivial insulating state without breaking time reversal symmetry, provided an intermediate superconducting term is allowed during the adiabatic deformation. Conversely, in one spatial dimension, non-symmetry-protected topological phases occur only in systems that break U(1) charge conservation. These results can intuitively be understood by considering a natural embedding of the classifying spaces of charge conserving Hamiltonians into the corresponding Bogoliubov de Gennes classes.