Stability of sub-dimensional localization to electronic interactions

TL;DR

This paper demonstrates that sub-dimensional localization in 2D electron systems remains stable despite electronic interactions, predicting its occurrence in moire materials with anisotropic conductivity and emergent conservation laws.

Contribution

It establishes the robustness of sub-dimensional localization against interactions and predicts its manifestation in moire materials with anisotropic transport properties.

Findings

Sub-dimensional localization persists with electronic interactions.

Electrons form incommensurate charge density waves enabling longitudinal conduction.

Transverse conductivity remains suppressed due to charge dipole conservation.

Abstract

Sub-dimensional localization, also known as directional localization, arises when 2d electrons are subject to a periodic potential and incommensurate magnetic field which cause them to become exponentially localized along one crystal axis, while remaining extended in the orthogonal direction. We establish that sub-dimensional localization is robust to the presence of electronic interactions, which are known to generically destabilize single-particle localization. Consequently we predict that sub-dimensional localization may occur in moire materials, where it is manifest as a total absence of conductivity in the localized (transverse) direction, with finite conductivity in the extended (longitudinal) direction. We find the electrons form longitudinal charge density waves which are incommensurate with the moire potential, allowing them to slide and hence conduct in the longitudinal direction. The conductivity remains prohibited in the transverse direction due an emergent charge dipole moment conservation law.