Exploring the graphene edges with coherent electron focusing

Rakyta, Péter; Kormányos, Andor; Cserti, József; Koskinen, Pekka

doi:10.1103/physrevb.81.115411

Cited by 57 publications

(80 citation statements)

References 25 publications

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“…These resistance oscillations can be understood by means of the solution of the Dirac equation. In the zigzag stripe the edge states are given by (18) and (19). We superimpose the plane wave part of the occupied edge states…”

Section: Anomalous Resistance Oscillationsmentioning

confidence: 99%

“…The magnetic focusing in graphene pn junctions has been studied theoretically [16] and snake states at such a pn interface have been predicted [17,18]. It has also been suggested to study by coherent electron focusing the structure of graphene edges [19]. Recently, also the effects of disorder [20] and spin-orbit interaction [21][22][23][24][25] have been investigated in a nonrelativistic 2DEG.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Edge magnetotransport in graphene: A combined analytical and numerical study

Stegmann

Lorke

2015

Annalen der Physik

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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.

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Section: Anomalous Resistance Oscillationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Edge magnetotransport in graphene: A combined analytical and numerical study

Stegmann

Lorke

2015

Annalen der Physik

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“…[47][48][49][50] We note that semiclassical methods have also been used to study graphene in magnetic fields. [51][52][53] Following the concepts outlined above we address edge effects on the electronic spectra of closed graphene cavities and quantum transport through open graphene systems in two consecutive papers. In the present paper we first derive the single-particle Green's function and its semiclassical approximation for graphene cavities and calculate the density of states.…”

Section: B Scope Of This Workmentioning

confidence: 99%

Edge effects in graphene nanostructures: From multiple reflection expansion to density of states

2011

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We study the influence of different edge types on the electronic density of states of graphene nanostructures. To this end we develop an exact expansion for the single-particle Green's function of ballistic graphene structures in terms of multiple reflections from the system boundary, which allows for a natural treatment of edge effects. We first apply this formalism to calculate the average density of states of graphene billiards. While the leading term in the corresponding Weyl expansion is proportional to the billiard area, we find that the contribution that usually scales with the total length of the system boundary differs significantly from what one finds in semiconductor-based, Schrödinger-type billiards: The latter term vanishes for armchair and infinite-mass edges and is proportional to the zigzag edge length, highlighting the prominent role of zigzag edges in graphene. We then compute analytical expressions for the density of states oscillations and energy levels within a trajectory-based semiclassical approach. We derive a Dirac version of Gutzwiller's trace formula for classically chaotic graphene billiards and further obtain semiclassical trace formulas for the density of states oscillations in regular graphene cavities. We find that edge-dependent interference of pseudospins in graphene crucially affects the quantum spectrum.

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“…Before discussing the single particle properties of graphene nanorings with zigzag edges, we would like to point out that the stability of zigzag edges in graphene nanostructures is an active research subject. [55][56][57][58][59][60][61] Theoretical calculations 55,56,59,60 show that if the dangling bonds on the zigzag edges are passivated by a single hydrogen each, then a stable zigzag edge can be obtained. Otherwise an edge reconstruction may occur.…”

Section: Single Particle Properties Of Graphene Nanoribbon Rings mentioning

confidence: 99%

Electron-electron interactions and topology in the electronic properties of gated graphene nanoribbon rings in Möbius and cylindrical configurations

2013

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We present a theory of the electronic properties of gated graphene nanoribbon rings with zigzag edges in Möbius and cylindrical configurations. The finite width opens a gap and nontrivial topology of the Möbius ring leads to a single edge with edge states with an induced, effective gauge field, in analogy to topological insulators. The single zigzag edge leads to a shell of degenerate states at the Fermi level and a ferromagnetic (FM) ground state at half-filling, i.e., at charge neutrality, due to electron-electron interactions. For fractional fillings, both the magnetic moment and the energy gap are found to oscillate as a function of the shell filling. In cylindrical rings, the two edges lead to AF ground state at half-filling but FM ground state at fractional fillings.

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Exploring the graphene edges with coherent electron focusing

Cited by 57 publications

References 25 publications

Edge magnetotransport in graphene: A combined analytical and numerical study

Edge magnetotransport in graphene: A combined analytical and numerical study

Edge effects in graphene nanostructures: From multiple reflection expansion to density of states

Electron-electron interactions and topology in the electronic properties of gated graphene nanoribbon rings in Möbius and cylindrical configurations

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