Electronic properties of graphene in a strong magnetic field

Abstract

The basic aspects of electrons in graphene (two-dimensional graphite) exposed to a strong perpendicular magnetic field are reviewed. One of its most salient features is the relativistic quantum Hall effect, the observation of which has been the experimental breakthrough in identifying pseudorelativistic massless charge carriers as the low-energy excitations in graphene. The effect may be understood in terms of Landau quantization for massless Dirac fermions, which is also the theoretical basis for the understanding of more involved phenomena due to electronic interactions. The role of electron-electron interactions both in the weakcoupling limit, where the electron-hole excitations are determined by collective modes, and in the strong-coupling regime of partially filled relativistic Landau levels are presented. In the latter limit, exotic ferromagnetic phases and incompressible quantum liquids are expected to be at the origin of recently observed (fractional) quantum Hall states. Furthermore, the electronphonon coupling in a strong magnetic field is discussed. Although the present review has a dominant theoretical character, a close connection with available experimental observation is intended.

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

“…Due to the hexagonal symmetry with a rotational angle of 60 • , a non-doped graphene is a zero-gap semiconductor with a vanishing density of state at the Fermi level. The essential electronic properties can be drastically changed by the layer number [35][36][37], stacking configuration [37][38][39][40][41][42], magnetic field [43,44], electric field [45][46][47], dopping [48,49], mechanical strain [50][51][52], and temperature variation [53,54]. Few-and multi-layer graphenes have been successfully produced by experimental methods such as exfoliation of highly orientated pyrolytic graphite [55][56][57][58], metalorganic chemical vapour deposition (MOCVD) [61][62][63][64][65][66], chemical and electrochemical reduction of graphene oxide [67][68][69], and arc discharge [70,71].…”

TDDFT study of time-dependent and static screening in graphene

“…Graphene is a very simple, strong, and easily synthesized material, [1][2][3][4][5][6] which makes it interesting for many practical applications, [7][8][9][10] culminating in the award of a Nobel prize in 2011. 11,12 For example, bilayer and monolayer graphene on substrates 13 have become promising materials for both nanoelectronics 14 and optoelectronics.…”

Analytic approach to magneto-strain tuning of electronic transport through a graphene nanobubble: perspectives for a strain sensor

“…This particular feature allows for the description of graphene electronic properties in terms of an effective Dirac Hamiltonian, whose eigenstates are given by two-component spinors, where a pseudo-spin property emerges as a consequence of the two sub-lattices [3][4][5][6][7]. Those states exhibit pseudo-relativistic properties, such as relativistic Landau levels in the presence of an external magnetic field [3,8,9], where the two Dirac points are connected by time-reversal symmetry, and hence the two valleys are degenerate [8]. Perhaps an even more interesting feature arises under the presence of mechanical strain.…”