Ground State thermodynamic and response properties of electron gas in a strong magnetic and electric field: Exact analytical solutions for a conventional semiconductor and for Graphene

TL;DR

This paper provides exact analytical solutions for the ground state energy and response properties of a 2D electron gas in strong magnetic and electric fields, revealing fractional and irrational Hall conductivities in semiconductors and graphene.

Contribution

It offers the first exact analytical analysis of ground state and response properties of electron gases under strong electromagnetic fields in both conventional semiconductors and graphene.

Findings

Fractional Hall conductivity in semiconductors due to strong electric fields.

Complex, possibly irrational, Hall values in graphene.

Analytical expressions for magnetization and polarization in strong fields.

Abstract

Consequences of an exceedingly strong electric field (E field) on the ground state energetics and transport properties of a 2D spinless electron gas in a perpendicular magnetic field (a Quantum Hall Effect (QHE) configuration) are investigated to all orders in the fields. For a conventional semiconductor, we find fractional values of the Hall conductivity and some magnetoelectric coefficients for certain values of E and B fields that do not result from interactions or impurities, but are a pure consequence of a strong enough in-plane E field. We also determine analytically the ground state energy, and response properties such as magnetization and polarization as functions of the electromagnetic field in the strong E field limit. In the case of Graphene, we obtain more complex behaviors leading to the possibility of irrational Hall values. The results are also qualitatively discussed in connection to various mechanisms for the QHE-breakdown.