Non-linear sigma model with particle-hole asymmetry for the disordered two-dimensional electron gas

TL;DR

This paper develops an extended non-linear sigma model that incorporates particle-hole asymmetry, enabling the study of thermoelectric transport in disordered two-dimensional interacting electron systems.

Contribution

It introduces a minimal extension of the Keldysh non-linear sigma model to include particle-hole asymmetry for 2D systems, facilitating analysis of thermoelectric effects.

Findings

Derived a new sigma model for 2D systems with particle-hole asymmetry.

Analyzed the heat density-density correlation function structure.

Calculated interaction corrections to the static part of the correlation function.

Abstract

The non-linear sigma model is a well-established theoretical tool for studies of transport and thermodynamics in disordered electronic systems. The conventional sigma model approach for interacting systems does not account for particle-hole asymmetry. It is therefore not suited for studying quantities that are sensitive to this effect such as the thermoelectric transport coefficient. Here, we derive a minimal extension of the Keldysh non-linear sigma model tailored for two-dimensional interacting systems. We argue that this model can be used to systematically study the combined effect of interactions and disorder on thermoelectric transport. As a first step in this direction, we use the model to analyze the structure of the heat density-density correlation function and calculate interaction corrections to its static part. The calculation of interaction corrections to the dynamical part of the correlation function and the thermodynamic transport coefficient is left for future work.