Shifted Landau levels in curved graphene sheets

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.

References in corpus (20)

• The electronic properties of graphene
• Graphene: Status and Prospects
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• The structure of suspended graphene sheets
• Electronic transport in two dimensional graphene
• Intrinsic ripples in graphene
• Infrared spectroscopy of Landau levels in graphene
• Observation of Landau levels of Dirac fermions in graphite
• Cyclotron Resonance study of the electron and hole velocity in graphene monolayers
• Space dependent Fermi velocity in strained graphene
• Charge inhomogeneities due to smooth ripples in graphene sheets
• Lattice Boltzmann Equation for Quantum Mechanics
• Generalizing the Fermi velocity of strained graphene from uniform to nonuniform strain
• Quantum Lattice Boltzmann is a quantum walk
• Generalized Lorentz-Dirac Equation for a Strongly-Coupled Gauge Theory
• Quantum Field Theory on Curved Backgrounds
• Reversal of thermoelectric current in tubular nanowires
• Basic quantum mechanics for three Dirac equations in a curved spacetime
• Optical conductivity of curved graphene
• Thermoelectric current in topological insulator nanowires with impurities

Cited by in corpus (8)

• Confining massless Dirac particles in two-dimensional curved space
• Curvature-induced quantum spin-Hall effect on a Möbius strip
• Pseudospectral computational methods for the time-dependent Dirac equation in static curved spaces
• Effective magnetic field induced by inhomogeneous Fermi velocity in strained honeycomb structures
• Landau levels in curved space realized in strained graphene
• Numerical quasi-conformal transformations for electron dynamics on strained graphene surfaces
• Quantized alternate current on curved graphene
• Landau levels in wrinkled and rippled graphene sheets