Interplay between snake and quantum edge states in a graphene Hall bar with a pn-junction

Milovanović, S. P.; Masir, M. Ramezani; Peeters, F. M.

doi:10.1063/1.4896769

Cited by 22 publications

(26 citation statements)

References 21 publications

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“…This regime of coherent electron focusing has been studied for the first time by van Houten et al in a nonrelativistic two-dimensional electron gas (2DEG) a e-mail: stegmann@fis.unam.mx [13] but it has become a topic of current interest again, since the first focusing experiments in graphene have become possible [14,15]. 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].…”

Section: Introductionmentioning

confidence: 99%

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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: Introductionmentioning

confidence: 99%

“…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%

Edge magnetotransport in graphene: A combined analytical and numerical study

Stegmann

Lorke

2015

Annalen der Physik

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“…The reflectionless one-dimensional channels that appear with the flip of the electric field [25][26][27][28]33] are similar to the edge channels in the quantum Hall spin insulators [34][35][36] only with the valley degree of freedom replacing the spin in protection mechanism against backscattering. Similar confinement of unidirectional currents in the bulk of the monolayer graphene is observed at n-p junctions but only at strong magnetic fields [37][38][39][40][41][42][43].…”

Section: Introductionmentioning

confidence: 75%

Persistent currents in topological and trivial confinement in silicene

Jurkowski

Szafran

2020

Phys. Rev. B

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We consider states bound at the flip of the electric field in buckled silicene. Along the electric flip lines a topological confinement is formed with the orientation of the charge current and the resulting magnetic dipole moment determined by the valley index. We compare the topological confinement to the trivial one that is due to a local reduction of the vertical electric field but without energy gap inversion. For the latter the valley does not protect the orientation of the magnetic dipole moment from inversion by external magnetic field. We demonstrate that the topologically confined states can couple and form extended bonding or antibonding orbitals with the energy splitting influenced by the geometry and the external magnetic field.

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“…Snake states have been observed along graphene p-n junctions in several experiments [23][24][25]. Additionally, the transport of electrons in snake states has been modeled using quantum mechanical [24,[26][27][28] and semiclassical [29][30][31][32][33][34] methods.…”

Section: Introductionmentioning

confidence: 99%

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

LaGasse

Lee

2017

Phys. Rev. B

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We present a quantum model which provides enhanced understanding of recent transverse magnetic focusing experiments on graphene p-n junctions. Spatially resolved flow maps of local particle current density show quantum interference and p-n junction filtering effects, which are crucial to explaining the device operation. The Landauer-Büttiker formula is used alongside dephasing edge contacts to give exceptional agreement between simulated nonlocal resistance and the recent experiment by Chen et al. [Science 353, 1522[Science 353, (2016]. The origin of positive and negative focusing resonances and off-resonance characteristics are explained in terms of quantum transmission functions. Our model also captures subtle features from experiment, such as the p-p − to p-p + transition and the second p-n focusing resonance.

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Interplay between snake and quantum edge states in a graphene Hall bar with a pn-junction

Cited by 22 publications

References 21 publications

Edge magnetotransport in graphene: A combined analytical and numerical study

Edge magnetotransport in graphene: A combined analytical and numerical study

Persistent currents in topological and trivial confinement in silicene

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

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