Graphene: Kinks, Superlattices, Landau levels, and Magnetotransport

Abstract

We review recent work on superlattices in monolayer and bilayer graphene. We highlight the role of the quasiparticle chirality in generating new Dirac fermion modes with tunable anisotropic velocities in one dimensional (1D) superlattices in both monolayer and bilayer graphene. We discuss the structure of the Landau levels and magnetotransport in such superlattices over a wide range of perpendicular (orbital) magnetic fields. In monolayer graphene, we show that an orbital magnetic field can reverse the anisotropy of the transport imposed by the superlattice potential, suggesting possible switching-type device applications. We also consider topological modes localized at a kink in an electric field applied perpendicular to bilayer graphene, and show how interactions convert these modes into a two-band Luttinger liquid with tunable Luttinger parameters. The band structures of electric field superlattices in bilayer graphene (with or without a magnetic field) are shown to arise naturally from a coupled array of such topological modes. We briefly review some bandstructure results for 2D superlattices. We conclude with a discussion of recent tunneling and transport experiments and point out open issues.

Invited Review Article for Special Issue on Graphene, References added, Typos corrected

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Cited by in corpus (8)

• Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals
• Tunable Superlattice in Graphene To Control the Number of Dirac Points
• Kink-Antikink Collisions and Multi-Bounce Resonance Windows in Higher-Order Field Theories
• Zero-line modes at stacking faulted domain walls in multilayer graphene
• Double-periodic quasi-periodic graphene superlattice: non-Bragg band gap and electronic transport
• A primer on twistronics: A massless Dirac fermion's journey to moiré patterns and flat bands in twisted bilayer graphene
• Interplay between topological protected valley and quantum Hall edge transport
• Tuning equilibration of quantum Hall edge states in graphene - role of crossed electric and magnetic fields