Graphene under spatially varying external potentials: Landau levels, magnetotransport, and topological modes

Abstract

Superlattices (SLs) in monolayer and bilayer graphene, formed by spatially periodic potential variations, lead to a modified bandstructure with extra finite-energy and zero-energy Dirac fermions with tunable anisotropic velocities. We theoretically show that transport in a weak perpendicular (orbital) magnetic field allows one to not only probe the number of emergent Dirac points but also yields further information about their dispersion. For monolayer graphene, we find that a moderate magnetic field can lead to a strong reversal of the transport anisotropy imposed by the SL potential, an effect that arises due to the SL-induced dispersion of the zero-energy Landau levels. This effect may find useful applications in switching or other devices. For bilayer graphene, we discuss the structure of Landau level wave functions and local density of states in the presence of a uniform bias, as well as in the presence of a kink in the bias that leads to topologically bound "edge states." We consider implications of these results for scanning tunneling spectroscopy measurements, valley filtering, and impurity-induced breakdown of the quantum Hall effect in bilayer graphene.

Beating oscillation and Fano resonance in the laser assisted electron transmission through graphene δ-function magnetic barriers

“…in the study of the 2DEG conventional semiconductor hetero-structures. All these effects were also reported in the periodically modulated graphene in presence of the inhomogeneous magnetic field [20][21][22][23] . The periodic modulation in graphene can be considered either in the spatial domain (real space) or in the temporal domain (momentum space).…”

“…The periodic modulation in graphene can be considered either in the spatial domain (real space) or in the temporal domain (momentum space). The former can be realized through the application of time independent electrostatic or magnetic periodic potentials (also called graphene super-lattices) by the deposition of an array of parallel metallic or ferromagnetic strips on the surface 20,21,[24][25][26][27][28][29] . On the other hand, the latter can be achieved by the use of a periodic time dependent potential or by an electromagnetic radiation (particularly the laser).…”

Collective edge modes of a quantum Hall ferromagnet in graphene

“…18,19 The unusual bulk spectrum of Landau levels in undoped graphene dictates an interesting structure of the edge states near the physical edge of a ribbon, [20][21][22] or at the interface between two opposite polarities of the gate voltage in a bilayer system. 23 Most prominently it gives rise to level crossings between an electronlike edge mode with a given spin or isospin state and a holelike mode with the opposite spin/isospin state, localized on the same edge. This implies a spatial reversal in the direction of the effective Zeeman field, which in the presence of interactions induces a coherent domain wall (DW) between regions with distinct configurations of the QHFM ground state.…”

Configuration-enriched magneto-electronic spectra of AAB-stacked trilayer graphene

“…These energy bands are further quantized by the application a uniform perpendicular magnetic field B = B 0ẑ [72]. The magneto-electronic spectrum of the isotropic Dirac cones satisfies a simple E c,v ∝ ± √ nB 0 relationship, where n is the quantum number, and c and v denote the conduction and valence Landau levels (LLs), respectively.…”