Edge magnetotransport in graphene: A combined analytical and numerical study

Abstract

The current flow along the boundary of graphene stripes in a perpendicular magnetic field is studied theoretically by the nonequilibrium Green's function method. In the case of specular reflections at the boundary, the Hall resistance shows equidistant peaks, which are due to classical cyclotron motion. When the strength of the magnetic field is increased, anomalous resistance oscillations are observed, similar to those found in a nonrelativistic 2D electron gas [New. J. Phys. 15:113047 (2013)]. Using a simplified model, which allows to solve the Dirac equation analytically, the oscillations are explained by the interference between the occupied edge states causing beatings in the Hall resistance. A rule of thumb is given for the experimental observability. Furthermore, the local current flow in graphene is affected significantly by the boundary geometry. A finite edge current flows on armchair edges, while the current on zigzag edges vanishes completely. The quantum Hall staircase can be observed in the case of diffusive boundary scattering. The number of spatially separated edge channels in the local current equals the number of occupied Landau levels. The edge channels in the local density of states are smeared out but can be made visible if only a subset of the carbon atoms is taken into account.

Understanding magnetic focusing in graphene p−n junctions through quantum modeling

“…2(a) and 2(b), respectively. For the relatively small magnetic fields considered in this paper, the orientation of the edges has been shown to have a minimal effect on the TMF characteristics [39]; switching the edge types in our simulation yields nearly identical results to what we present here.…”

“…This process is governed by the LandauerBüttiker equation [21], explained in the next paragraph. This type of virtual dephasing contact has been used in quantum transport calculations in the past [38][39][40] and is critical for tying our results to experiment. Additionally, dephasing has been included in a mathematically identical way to handle graphene p-n junctions in the quantum Hall regime [41].…”

Giant magneto-photoelectric effect in suspended graphene

“…Note that the eigenenergies E n k , y can be positive (particle states) as well as negative (hole states) and even zero (zero mode), see below. Insertion into equation (4) ) , see, e.g., [30][31][32]. The solutions can be expressed in terms of parabolic cylinder functions D ν via In complete analogy to Fermi's golden rule, we estimate the probability (per unit time) for secondary particle-hole pair creation via time-dependent perturbation theory.…”

Coherent control of current injection in zigzag graphene nanoribbons

“…We can indicate any of the edge or confined states simply by |nκ x , where if |n| ≥ 2 the state is confined, while if |n| = 1 then the state is confined for κ x ≤W −1 , but it is an edge state if κ x > W −1 . Equations (16) and (22) describe the bandstructure of ZGNR, shown in Figs. 2 and 3.…”

“…Given that a 2D graphene sheet lacks of these localized states, a ZGNR offers the advantage of having optical responses that are easily tuneable. Over the last years, a number of studies have reported the special properties of these localized states [2][3][4][7][8][9][10] and recent investigations have described more novel properties and applications [11][12][13][14][15][16]. At zero energy they have an important role in the electronic transport properties of both clean and disordered ZGNR, as Luck et al [12] (and references therein) have recently shown using a tight-binding formalism with a transfer-matrix approach.…”