Understanding the onset of negative electronic compressibility in one- and two-band 2D electron gases: Application to LaAlO$_3$/SrTiO$_3$

TL;DR

This paper models the onset of negative electronic compressibility in 2D electron gases, highlighting how multi-band effects and inter-band coupling influence critical carrier densities, with application to LaAlO$_3$/SrTiO$_3$ interfaces.

Contribution

It introduces a simple homogeneous multi-band model to analyze NEC in 2DEGs and applies it to LAO/STO, providing a new method to identify multi-band systems from bulk properties.

Findings

Population of a second band affects critical carrier density.

Inter-band coupling significantly influences NEC onset.

LAO/STO likely hosts a two-band 2DEG.

Abstract

We investigate the effects of two electronic bands at the negative electronic compressibility (NEC) in a two-dimensional electron gas (2DEG). We use a simple homogeneous model with Coulombic interactions and first-order multi-band coupling to examine the role of effective mass and relative permittivity in relation to the critical carrier density, where compressibility turns negative. We demonstrate that the population of a second band, along with the presence of inter-band coupling, can dramatically change the cross-over carrier density. Given the difficulty in determining and confirming multi-band electronic systems, this model provides a potential method for identifying multi-band electronic systems using precise bulk electronic properties measurements. To help illustrate this method, we apply our results to the observed NEC in the 2D electron gas at the interface of LaAlO$_3$/SrTiO$_3$ (LAO/STO) and determine that, for the known parameters of LAO/STO, the system is likely a realization of a two-band 2D electron gas. Furthermore, we provide general limits on the inter-band coupling with respect to the electronic band population.