Landau Levels in Uniaxially Strained Graphene: A Geometrical Approach

TL;DR

This paper presents a geometrical approach to analyze Landau levels in uniaxially strained graphene, revealing that strain causes contraction of LL spectra and accounting for Dirac cone tilting effects.

Contribution

It introduces a novel geometrical method based on Sturm-Liouville theory to compute LLs in strained graphene, incorporating DFT-fitted parameters and Dirac cone tilting effects.

Findings

Uniaxial strain contracts Landau levels spectra in graphene.

The method accounts for Dirac cone tilting due to strain.

Strain effects differ along armchair and zig-zag directions.

Abstract

The effect of strain on the Landau levels (LLs) spectra in graphene is studied, using an effective Dirac-like Hamiltonian which includes the distortion in the Dirac cones, anisotropy and spatial-dependence of the Fermi velocity induced by the lattice change through a renormalized linear momentum. We propose a geometrical approach to obtain the electron's wave-function and the LLs in graphene from the Sturm-Liouville theory, using the minimal substitution method. The coefficients of the renormalized linear momentum are fitted to the energy bands, which are obtained from a Density Functional Theory (DFT) calculation. In particular, we evaluate the case of Dirac cones with an ellipsoidal transversal section resulting from uniaxially strained graphene along armchair (AC) and zig-zag (ZZ) directions. We found that uniaxial strain in graphene induces a contraction of the LLs spectra for both strain directions. Also, is evaluated the contribution of the tilting of Dirac cone axis resulting from the uniaxial deformations to the contraction of the LLs spectra.