Effective Magnetic Fields in Graphene Superlattices

Abstract

We demonstrate that the electronic spectrum of graphene in a one-dimensional periodic potential will develop a Landau level spectrum when the potential magnitude varies slowly in space. The effect is related to extra Dirac points generated by the potential whose positions are sensitive to its magnitude. We develop an effective theory that exploits a chiral symmetry in the Dirac Hamiltonian description with a superlattice potential, to show that the low energy theory contains an effective magnetic field. Numerical diagonalization of the Dirac equation confirms the presence of Landau levels. Possible consequences for transport are discussed.

4 pages (+ 2 pages of supplementary material), 3 figures

References in corpus (17)

• The electronic properties of graphene
• Energy gaps, topological insulator state and zero-field quantum Hall effect in graphene by strain engineering
• Ripple Texturing of Suspended Graphene Atomic Membranes
• Andreev reflection and Klein tunneling in graphene
• Quantum interference and Klein tunneling in graphene heterojunctions
• Veselago Lens for Electrons: Focusing and Caustics in Graphene p-n Junctions
• Quantum-limited shot noise in graphene
• Evidence of Klein tunneling in graphene p-n junctions
• Aharonov-Bohm effect and broken valley-degeneracy in graphene rings
• Edge States and the Quantized Hall Effect in Graphene
• Emerging Zero Modes for Graphene in a Periodic Potential
• Landau Levels and Quantum Hall Effect in Graphene Superlattices
• Nonlinear screening and ballistic transport in a graphene p-n junction
• Gauge fields, ripples and wrinkles in graphene layers
• MagnetoResistance of graphene-based spin valves
• Energy Anomaly and Polarizability of Carbon Nanotubes
• Effective Time Reversal Symmetry Breaking and Energy Spectra of Graphene Armchair Rings

Cited by in corpus (16)

• Emergence of Superlattice Dirac Points in Graphene on Hexagonal Boron Nitride
• New generation of moiré superlattices in doubly aligned hBN/graphene/hBN heterostructures
• Electrically tunable gauge fields in tiny-angle twisted bilayer graphene
• Graphene on Hexagonal Boron Nitride
• Graphene on incommensurate substrates: trigonal warping and emerging Dirac cone replicas with halved group velocity
• Single-layer and bilayer graphene superlattices: collimation, additional Dirac points and Dirac lines
• Moire superlattice effects in graphene/boron-nitride van der Waals heterostructures
• Transport in superlattices on single layer graphene
• Evidence for Superlattice Dirac Points and Space-dependent Fermi Velocity in Corrugated Graphene Monolayer
• Adsorption by design: tuning atom-graphene van der Waals interactions via mechanical strain
• Landau level splitting due to graphene superlattices
• Magnetic Phases in Periodically Rippled Graphene
• Confining and repulsive potentials from effective non-Abelian gauge fields in graphene bilayers
• Transport in Graphene superimposed by a moving Electrical Superlattice Potential
• Semiclassical Approach to the Physics of Smooth Superlattice Potentials in Graphene
• Band Structure and Topological Properties of Graphene in a Superlattice Spin Exchange Field