Hall conductance of two-band systems in a quantized field

TL;DR

This paper extends the concept of Hall conductance to two-band systems interacting with quantized fields, providing a quantum-field-aware framework applicable to topological insulators.

Contribution

It introduces a novel definition of Hall conductance considering the quantum nature of external fields, advancing the understanding of topological systems under quantum field interactions.

Findings

Quantum Hall conductance differs from classical predictions when considering quantized fields.

Application to topological insulators reveals new insights into their response properties.

Comparison shows the quantum-field-based conductance aligns with traditional results in classical limits.

Abstract

Kubo formula gives a linear response of a quantum system to external fields, which are classical and weak with respect to the energy of the system. In this work, we take the quantum nature of the external field into account, and define a Hall conductance to characterize the linear response of a two-band system to the quantized field. The theory is then applied to topological insulators. Comparisons with the traditional Hall conductance are presented and discussed.