Quantized Density Response in Insulators

TL;DR

This paper demonstrates that the response of particle density to potential changes in insulators is quantized, linking it to phenomena like the quantum Hall effect and unifying various quantized response phenomena.

Contribution

It introduces the concept of quantized density response in insulators, connecting it to known effects such as adiabatic transport and the gap labeling theorem.

Findings

Density response to potential dilation is quantized in insulators.

Derivative of electron density w.r.t. magnetic field is quantized in quantum Hall systems.

Unifies several phenomena under the notion of quantized density response.

Abstract

The response of particle density to a dilation of a periodic potential in an insulator, with or without a fixed background potential or a magnetic field, is shown to be quantized. A similar phenomenon occurs in a quantum Hall system, where the derivative of the electron density with respect to the magnetic field is quantized in units of $e/h$, the inverse flux quantum. A number of other interesting results may be unified under the notion of quantized density response, including the quantization of adiabatic particle transport, the gap labeling theorem and its generalization in the presence of a magnetic field.