Strain-induced Landau Levels in arbitrary dimensions with an exact spectrum

TL;DR

This paper introduces a family of strained bipartite tight-binding models in any dimension that exactly produce pseudo-Landau levels, extending previous approximate models in graphene to higher dimensions with analytical proof.

Contribution

The authors analytically prove that their models in arbitrary dimensions have spectra consisting solely of degenerate pseudo-Landau levels, generalizing strain-induced Landau levels beyond two dimensions.

Findings

Entire spectrum consists of degenerate pseudo-Landau levels

Generalization of strain-induced Landau levels to arbitrary dimensions

Analytical proof of spectrum structure in the models

Abstract

Certain non-uniform strain applied to graphene flakes has been shown to induce pseudo-Landau levels in the single-particle spectrum, which can be rationalized in terms of a pseudo-magnetic field for electrons near the Dirac points. However, this Landau level structure is in general approximate and restricted to low energies. Here we introduce a family of strained bipartite tight-binding models in arbitrary spatial dimension d and analytically prove that their entire spectrum consists of perfectly degenerate pseudo-Landau levels. This construction generalizes the case of triaxial strain on graphene's honeycomb lattice to arbitrary d; in d=3 our model corresponds to tetraxial strain on the diamond lattice. We discuss general aspects of pseudo-Landau levels in arbitrary d.