Bulk-Boundary Correspondence for Topological Insulators with Quantized Magneto-Electric Effect

TL;DR

This paper explores the bulk-boundary correspondence in three-dimensional topological insulators with quantized magneto-electric effects, using operator algebraic methods to connect bulk invariants with surface phenomena, including Hall effects and quantum pumping.

Contribution

It introduces a novel application of $K$-theory connecting maps to model and analyze surface phenomena in topological insulators with disorder and irrational magnetic fluxes.

Findings

Distinct surface phenomena linked to different $K$-theory maps.

Modeling of irrational magnetic fluxes and large disorder effects.

Prediction of experimentally observable Hall effects and quantum pumping.

Abstract

We study bulk-boundary correspondences and related surface phenomena stabilized by the second Chern number in three-dimensional insulators driven in adiabatic cycles. Magnetic fields and disorder effects are incorporated in our analysis using operator algebraic methods. We use the connecting maps between the $K$-theories of bulk and boundary algebras as engines for the bulk-boundary correspondences. We discovered that both the exponential and the index connecting maps are relevant for the context considered here as they lead to distinct experimentally observable surface phenomena, such as pumping and transfer of quantum surface Hall states or proximity induced Hall effect. The surface Hall physics of time-reversal symmetric topological insulators is also investigated using the new tools, which can model irrational magnetic fluxes and arbitrary large surface disorder.