How branching can change the conductance of ballistic semiconductor devices

Maryenko, D.; Ospald, F.; Klitzing, K. von; Smet, J. H.; Metzger, Jakob; Fleischmann, Ragnar; Geisel, Theo; Umansky, V.

doi:10.1103/physrevb.85.195329

Cited by 25 publications

(22 citation statements)

References 30 publications

(33 reference statements)

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“…This regime of coherent electron focusing has been studied for the first time by van Houten et al [2]. Recently, the effects of disorder [3] and spin-orbit interaction [4][5][6][7][8] were investigated and focusing experiments in graphene were performed [9]. It was also discussed to study by coherent electron focusing the structure of graphene edges [10] as well as Andreev reflections in normal-superconductor systems [11][12][13].…”

Section: Introductionmentioning

confidence: 98%

Magnetotransport along a boundary: from coherent electron focusing to edge channel transport

2013

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We study theoretically how electrons, coherently injected at one point on the boundary of a two-dimensional electron system, are focused by a perpendicular magnetic field B onto another point on the boundary. Using the non-equilibrium Green's function approach, we calculate the generalized four-point Hall resistance R x y as a function of B. In weak fields, R x y shows the characteristic equidistant peaks observed in the experiment and explained by classical cyclotron motion along the boundary. In strong fields, R x y shows a single extended plateau reflecting the quantum Hall effect. In intermediate fields, we find superimposed upon the lower Hall plateaus anomalous oscillations, which are neither periodic in 1/B (quantum Hall effect) nor in B (classical cyclotron motion). The oscillations are explained by the interference between the occupied edge channels, which causes beatings in R x y . In the case of two occupied edge channels, these beatings constitute a new commensurability between the magnetic flux enclosed within the edge channels and the flux quantum. Introducing decoherence and a partially specular boundary shows that this new effect is quite robust.

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Section: Introductionmentioning

confidence: 98%

Magnetotransport along a boundary: from coherent electron focusing to edge channel transport

2013

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“…Finally, when only a single edge channel is occupied, the beating and thus, the oscillations in the Hall resistance vanish. In the armchair stripe, the solution of the Dirac equation is more complicated, see (20), (21), and (22), because the valleys are intermixed. We found best agreement to our Green's function calculations, see figure 7 (bottom), if we use also for the armchair stripe (24), where the k i and q i denote the two sets of solutions.…”

Section: Anomalous Resistance Oscillationsmentioning

confidence: 99%

“…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. On the other hand, graphene stripes in a strong magnetic field show the quantum Hall effect [26,27], which is explained by the transport through edge channels along the boundary of the system, see the red lines in figure 1.…”

Section: Introductionmentioning

confidence: 99%

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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“…Breathers have been extensively studied both theoretically and experimentally in optics and water waves [12][13][14][15][16][17]. Likewise have branched flows been studied in a variety of systems ranging from transport of electrons in the two-dimensional electron gas scattered by the disorder potential of impurities [18][19][20], via the scattering of wind driven ocean waves by ocean currents [21,22] to the focusing of tsunamis by small variations of the ocean floor topography [5]. Not only do branched flows in general lead to heavy-tailed intensity distributions [10,23], but experiments on microwave transmissions through disordered arrays of scatterers have shown that in combination with fluctuating sources they can lead to breather-like isolated rogue events [2].…”

Section: Introductionmentioning

confidence: 99%

Branched flow and caustics in nonlinear waves

Green

Fleischmann

2019

New J. Phys.

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Rogue waves, i.e.high amplitude fluctuations in random wave fields, have been studied in several contexts, ranging from optics via acoustics to the propagation of ocean waves. Scattering by disorder, like current fields and wind fluctuations in the ocean, as well as nonlinearities in the wave equations provide widely studied mechanisms for their creation. However, the interaction of these mechanisms is largely unexplored. Hence, we study wave propagation under the concurrent influence of geometrical (disorder) and nonlinear focusing in the (current-modified) nonlinear Schrödinger equation. We show how nonlinearity shifts the onset distance of geometrical (disorder) focusing and alters the peak intensities of the fluctuations. We find an intricate interplay of both mechanisms that is reflected in the observation of optimal ratios of nonlinearity and disorder strength for the generation of rogue waves.

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How branching can change the conductance of ballistic semiconductor devices

Cited by 25 publications

References 30 publications

Magnetotransport along a boundary: from coherent electron focusing to edge channel transport

Magnetotransport along a boundary: from coherent electron focusing to edge channel transport

Edge magnetotransport in graphene: A combined analytical and numerical study

Branched flow and caustics in nonlinear waves

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