Landau Levels and Quantum Hall Effect in Graphene Superlattices

Abstract

We show that, when graphene is subjected to an appropriate one-dimensional external periodic potential, additional branches of massless fermions are generated with nearly the same electron-hole crossing energy as that at the original Dirac point of graphene. Because of these new zero-energy branches, the Landau levels at charge neutral filling becomes 4(2N+1)-fold degenerate (with N=0,1,2,..., tunable by the potential strength and periodicity) with the corresponding Hall conductivity ${\sigma }_{xy}$ showing a step of size 4(2N+1)$e^2/h$. These theoretical findings are robust against variations in the details of the external potential and provide measurable signatures of the unusual electronic structure of graphene superlattices.

7 pages, 7 figures

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Cited by in corpus (24)

• Physics of the Riemann Hypothesis
• Transport in superlattices on single layer graphene
• Evidence for Superlattice Dirac Points and Space-dependent Fermi Velocity in Corrugated Graphene Monolayer
• Band structure and gaps of triangular graphene superlattices
• Engineering high quality graphene superlattices via ion milled ultra-thin etching masks
• Dirac-Kronig-Penney model for strain-engineered graphene
• Effective Magnetic Fields in Graphene Superlattices
• Electron optics with dirac fermions: electron transport in monolayer and bilayer graphene through magnetic barrier and their superlattices
• Theory of the electronic and transport properties of graphene under a periodic electric or magnetic field
• Electronic structure of a graphene superlattice with massive Dirac fermions
• Dot-bound and dispersive states in graphene quantum dot superlattices
• Double-periodic quasi-periodic graphene superlattice: non-Bragg band gap and electronic transport
• Zero and Finite Energy Dirac Points in the Energy Band Structure of Magnetic Bilayer Graphene Superlattices
• Tunnelling through finite graphene superlattices: resonance splitting effect
• Transport Anisotropy in One-dimensional Graphene Superlattice in the High Kronig-Penney Potential Limit
• Landau level splitting due to graphene superlattices
• Transport in graphene nanostructures with spatially modulated gap and potential
• Edge magnetoplasmons in a wide armchair graphene ribbon with a weak superlattice potential: finite frequency gaps and zero group velocity
• Superlattice induced electron percolation within a single Landau level
• Relativistic particles in super-periodic potentials: exploring graphene and fractal systems
• Designer gapped and tilted Dirac cones in lateral graphene superlattices
• Touching points in the energy band structure of bilayer graphene superlattices
• Theory of engineering flat bands in graphene using doubly-periodic electrostatic gating
• Magnetic Bloch bands and Weiss oscillations in Dirac mass superlattices