Electron Accumulation Layer in Ultrastrong Magnetic Field

TL;DR

This paper develops a theoretical phase diagram for electron accumulation layers in semiconductors under ultra-strong magnetic fields, revealing phases like metallic, quantum limit, and Wigner crystal states, with implications for experimental detection.

Contribution

It introduces a comprehensive theory of the extreme quantum limit phase in electron accumulation layers, including phase diagrams and quantum capacitance calculations for various materials.

Findings

Identification of a metallic EQL phase in the phase diagram.

Calculation of electron density and potential profiles in the EQL phase.

Proposal of quantum capacitance as an experimental probe for phase identification.

Abstract

When a three-dimensional electron gas is subjected to a very strong magnetic field, it can reach a quasi-one-dimensional state in which all electrons occupy the lowest Landau level. This state is referred to as the extreme quantum limit (EQL) and has been studied in the physics of pulsars and bulk semiconductors. Here we present a theory of the EQL phase in electron accumulation layers created by an external electric field $E$ at the surface of a semiconductor with a large Bohr radius such as InSb, PbTe, SrTiO$_3$ (STO), and particularly in the LaAlO$_3$/SrTiO$_3$ (LAO/STO) heterostructure. The phase diagram of the electron gas in the plane of the magnetic field strength and the electron surface concentration is found for different orientations of the magnetic field. We find that in addition to the quasi-classical metallic phase (M), there is a metallic EQL phase, as well as an insulating Wigner crystal state (WC). Within the EQL phase, the Thomas-Fermi approximation is used to find the electron density and the electrostatic potential profiles of the accumulation layer. Additionally, the quantum capacitance for each phase is calculated as a tool for experimental study of these phase diagrams.