# Landau levels in wrinkled and rippled graphene sheets

## TL;DR

This paper investigates how curvature in graphene sheets affects Landau levels and resistivity, revealing that deformation shifts energy levels and influences electrical properties, using a quantum lattice Boltzmann approach.

## Contribution

It introduces a method to analyze Landau levels in complex curved graphene geometries and quantifies the impact of deformation on electronic properties.

## Key findings

- Landau levels shift lower with increased average deformation.
- Energy levels follow a square root dependence on quantum number.
- Resistivity varies linearly with average space curvature.

## Abstract

We study the discrete energy spectrum of curved graphene sheets in the presence of a magnetic field. The shifting of the Landau levels is determined for complex and realistic geometries of curved graphene sheets. The energy levels follow a similar square root dependence on the energy quantum number as for rippled and flat graphene sheets. The Landau levels are shifted towards lower energies proportionally to the average deformation and the effect is larger compared to a simple uni-axially rippled geometry. Furthermore, the resistivity of wrinkled graphene sheets is calculated for different average space curvatures and shown to obey a linear relation. The study is carried out with a quantum lattice Boltzmann method, solving the Dirac equation on curved manifolds.