Shifted Landau levels in curved graphene sheets

TL;DR

This study investigates how curvature in graphene sheets affects Landau levels, revealing a shift towards lower energies proportional to deformation, and introduces a new numerical method for analyzing quantum states in curved graphene.

Contribution

It presents the first detailed analysis of Landau levels in curved graphene and develops a novel quantum lattice Boltzmann method for solving the Dirac equation on curved surfaces.

Findings

Landau levels in curved graphene follow the same sqrt dependence as flat sheets.

Landau levels are shifted to lower energies proportional to deformation.

The new numerical method effectively models quantum states in strained graphene.

Abstract

We study the Landau levels in curved graphene sheets by measuring the discrete energy spectrum in the presence of a magnetic field. We observe that in rippled graphene sheets, the Landau energy levels satisfy the same square root dependence on the energy quantum number as in flat sheets, $E_n \sim \sqrt{n}$. Though, we find that the Landau levels in curved sheets are shifted towards lower energies by an amount proportional to the average spatial deformation of the sheet. Our findings are relevant for the quantum Hall effect in curved graphene sheets, which is directly related to Landau quantization. For the purpose of this study, we develop a new numerical method, based on the quantum lattice Boltzmann method, to solve the Dirac equation on curved manifolds, describing the low-energetic states in strained graphene sheets.