Electron polarizability of crystalline solids in quantizing magnetic fields and topological gap numbers

TL;DR

This paper develops a theory for the static electron polarizability in crystals under quantizing magnetic fields, linking it to topological quantum numbers and Hall effects, with potential experimental implications.

Contribution

It introduces a novel theoretical framework connecting electron polarizability to topological gap numbers in magnetic fields, highlighting the role of Hall currents.

Findings

Polarizability is strongly influenced by Hall currents.

Topological quantum numbers are linked to polarizability and Hall conductivity.

Results suggest possible experimental detection of topological gap numbers.

Abstract

A theory of the static electron polarizability of crystals whose energy spectrum is modified by quantizing magnetic fields is presented. It is argued that The polarizability is strongly affected by non-dissipative Hall currents induced by the presence of crossed electric and magnetic fields: these can even change its sign. Results are illustrated in detail for a two dimensional square lattice. The polarizability and the Hall conductivity are respectively linked to the two topological quantum numbers entering the so--called Diophantine equation. These numbers could in principle be detected in actual experiments.