Optimal traps in graphene

Downing, C. A.; Pearce, A. R.; Churchill, R. J.; Portnoi, M. E.

doi:10.1103/physrevb.92.165401

Cited by 32 publications

(34 citation statements)

References 86 publications

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“…In doing so, we make use of both exact solutions and a quasi-exactly solvable [37,38] (QES) model, which most clearly display the underlying physics. Furthermore, studies of inhomogeneous * downing@ipcms.unistra.fr † m.e.portnoi@exeter.ac.uk electric fields [39,40] have already been shown to be important in Dirac materials as compared to electrostatic square-well models. We find here that a characteristic of magnetic quantum dots with decreasing field strength is the removal one-by-one of quantum states with diminishing angular momentum, until a plateau is reached where only bound states with negative angular momentum exist.…”

Section: Introductionmentioning

confidence: 99%

Massless Dirac fermions in two dimensions: Confinement in nonuniform magnetic fields

Downing

Portnoi

2016

Phys. Rev. B

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We show how it is possible to trap two-dimensional massless Dirac fermions in spatially inhomogeneous magnetic fields, as long as the formed magnetic quantum dot (or ring) is of a slowly decaying nature. It is found that a modulation of the depth of the magnetic quantum dot leads to successive confinement-deconfinement transitions of vortexlike states with a certain angular momentum, until a regime is reached where only states with one sign of angular momentum are supported. We illustrate these characteristics with both exact solutions and a hitherto unknown quasi-exactly solvable model utilizing confluent Heun functions.

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Section: Introductionmentioning

confidence: 99%

Massless Dirac fermions in two dimensions: Confinement in nonuniform magnetic fields

Downing

Portnoi

2016

Phys. Rev. B

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“…We mention in passing that circular geometries have also been studied for electrostatic potentials in Refs. [47][48][49].…”

Section: Introductionmentioning

confidence: 99%

Chiral interface states in graphene p−n junctions

et al. 2016

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We present a theoretical analysis of unidirectional interface states which form near p-n junctions in a graphene monolayer subject to a homogeneous magnetic field. The semiclassical limit of these states corresponds to trajectories propagating along the p-n interface by a combined skippingsnaking motion. Studying the two-dimensional Dirac equation with a magnetic field and an electrostatic potential step, we provide and discuss the exact and essentially analytical solution of the quantum-mechanical eigenproblem for both a straight and a circularly shaped junction. The spectrum consists of localized Landau-like and unidirectional snaking-skipping interface states, where we always find at least one chiral interface state. For a straight junction and at energies near the Dirac point, when increasing the potential step height, the group velocity of this state interpolates in an oscillatory manner between the classical drift velocity in a crossed electromagnetic field and the semiclassical value expected for a purely snaking motion. Away from the Dirac point, chiral interface states instead resemble the conventional skipping (edge-type) motion found also in the corresponding Schrödinger case. We also investigate the circular geometry, where chiral interface states are predicted to induce sizeable equilibrium ring currents.

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“…It is found that the periodic potential induces new Dirac points, and resonance occurs for specific conditions [41][42][43] . It is shown that confinement of the charge carriers in graphene by electrostatic potentials is possible for zeroenergy states 44,45 . Most recently, Ferreira and Mucciolo studied vacancy-induced zero-energy modes in graphene, and they proved that the early field-theoretical picture for the BDI class 46 is valid well beyond its controlled weak-coupling regime 47 .…”

Section: Since Graphene Was Isolated In 2004mentioning

confidence: 99%

Tunable electronic band structures and zero-energy modes of heterosubstrate-induced graphene superlattices

Fan

Huang

et al. 2016

Phys. Rev. B

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We propose a tunable electronic band gap and zero-energy modes in periodic heterosubstrateinduced graphene superlattices. Interestingly, there is an approximate linear relation between the band gap and the proportion of an inhomogeneous substrate (i.e., percentages of different components) in the proposed superlattice, and the effect of structural disorder on the relation is discussed. In an inhomogeneous substrate with equal widths, zero-energy states emerge in the form of Dirac points by using asymmetric potentials, and the positions of Dirac points are addressed analytically. Further, the Dirac point exists at k = 0 only for specific potentials; every time it appears, the group velocity vanishes in the ky direction, and the resonance occurs. For general cases of an inhomogeneous substrate with unequal widths, part of the zero-energy states are described analytically, and differently, they are not always Dirac points. Our prediction may be realized on a heterosubstrate such as SiO2/BN.

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Optimal traps in graphene

Cited by 32 publications

References 86 publications

Massless Dirac fermions in two dimensions: Confinement in nonuniform magnetic fields

Massless Dirac fermions in two dimensions: Confinement in nonuniform magnetic fields

Chiral interface states in graphene p−n junctions

Tunable electronic band structures and zero-energy modes of heterosubstrate-induced graphene superlattices

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