Relativistic quantum Hall effect

Schakel, Adriaan M. J.

doi:10.1103/physrevd.43.1428

Cited by 144 publications

(119 citation statements)

References 18 publications

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“…We now continue by decreasing the magnetic field to q = 4 and then q = 6, see Fig [6]. For q = 4 we have σ xy = 1 for a Fermi level in the first gap, σ xy = 2 for Fermi level in second gap, and σ xy = 1 for Fermi level in third gap.…”

Section: Hall Conductance In Graphenementioning

confidence: 99%

“…Although unrelated to the parity anomaly, this behavior of the Hall conductance was in fact obvious in the seminal work of Jackiw and Rebbi 13 . On the basis of the argument for the RQHE 6,7,8 the experimental groups conclude that this is an interesting new phenomena completely explained by the relativistic Dirac spectrum of graphene. We want to improve on this argument for several reasons.…”

mentioning

confidence: 99%

“…The bands can be effectively characterized by massless (2+1)d Dirac fermions 4 . This continuum model of graphene has been subsequently used to study the (2 + 1)d parity anomaly 5 and as a model system for the relativistic quantum Hall effect (RQHE) 6,7,8 . A quantum spin Hall effect has also been predicted in graphene 9,10 , but the intrinsic spin orbit gap is probably too small to support a measurable phase 11,12 .…”

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confidence: 99%

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Band Collapse and the Quantum Hall Effect in Graphene

Bernevig

Hughes

Zhang

et al. 2006

Int. J. Mod. Phys. B

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The recent Quantum Hall experiments in graphene have confirmed the theoretically well-understood picture of the quantum Hall (QH) conductance in fermion systems with continuum Dirac spectrum. In this paper we take into account the lattice, and perform an exact diagonalization of the Landau problem on the hexagonal lattice. At very large magnetic fields the Dirac argument fails completely and the Hall conductance, given by the number of edge states present in the gaps of the spectrum, is dominated by lattice effects. As the field is lowered, the experimentally observed situation is recovered through a phenomenon which we call band collapse. As a corollary, for low magnetic field, graphene will exhibit two qualitatively different QHE's: at low filling, the QHE will be dominated by the "relativistic" Dirac spectrum and the Hall conductance will be odd-integer; above a certain filling, the QHE will be dominated by a non-relativistic spectrum, and the Hall conductance will span all integers, even and odd.The quantum Hall effect (QHE) is one of the richest phenomena studied in condensed matter physics. This effect is characterized by certain conductance properties in two-dimensional samples i.e. the vanishing of the longitudinal conductance σ xx ∼ 0 along with the onset of a quantized transverse conductance σ xy = ν e 2 h . Recently several experimental groups have produced twodimensional plane films of graphite, commonly known as graphene sheets 1,2 , which exhibit interesting QHE behavior.Graphene has a theoretical history beginning with the study of the band structure of this planar system in 3 . From these humble beginnings it has gone on to be studied intensely because of its Dirac structure. The bands can be effectively characterized by massless (2+1)d Dirac fermions4 . This continuum model of graphene has been subsequently used to study the (2 + 1)d parity anomaly 5 and as a model system for the relativistic quantum Hall effect (RQHE) 6,7,8 . A quantum spin Hall effect has also been predicted in graphene 9,10 , but the intrinsic spin orbit gap is probably too small to support a measurable phase 11,12 . The latter studies were based on the recent experimental work done on the QHE in graphene by two independent groups 1,2 . These two groups confirm an interesting behavior in graphene in which the transverse conductance is quantized as an integer plus a half-integer σ xy = (n + 1 2 )4e 2 /h, where band and spin degeneracies have been taken into account. Although unrelated to the parity anomaly, this behavior of the Hall conductance was in fact obvious in the seminal work of Jackiw and Rebbi 13 . On the basis of the argument for the RQHE 6,7,8 the experimental groups conclude that this is an interesting new phenomena completely explained by the relativistic Dirac spectrum of graphene. We want to improve on this argument for several reasons. For very large B the lattice is expected to dominate the behavior of the Hall conductance. In this regime the Dirac argument cannot be valid, since, by virtue of being a continu...

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Section: Hall Conductance In Graphenementioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Band Collapse and the Quantum Hall Effect in Graphene

Bernevig

Hughes

Zhang

et al. 2006

Int. J. Mod. Phys. B

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“…In particular, several condensed matter phenomena point out to the existence of a (2 +1)-dimensional energy spectrum determined by the relativistic Dirac equation [1]. For very recent works, one may consult references [2][3][4][5][6][7] and for early works relevant to our subject we cite [8,9].…”

Section: Introductionmentioning

confidence: 99%

Path integral for confined Dirac fermions in a constant magnetic field

Merdaci

Jellal

Chétouani

2015

Int. J. Mod. Phys. A

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We consider Dirac fermion confined in harmonic potential and submitted to a constant magnetic field. The corresponding solutions of the energy spectrum are obtained by using the path integral techniques. For this, we begin by establishing a symmetric global projection, which provides a symmetric form for the Green function. Based on this, we show that it is possible to end up with the propagator of the harmonic oscillator for one charged particle. After some transformations, we derive the normalized wave functions and the eigenvalues in terms of different physical parameters and quantum numbers. By interchanging quantum numbers, we show that our solutions have interesting properties. The density of current and the non-relativistic limit are analyzed where different conclusions are obtained. Finally, the completeness of the Dirac oscillator eigenfunctions is proved by using the standard properties of the generalized Laguerre polynomials.

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“…It is worth mentioning the generalization of the quantum Hall effect made with Dirac particles in [19,20].…”

Section: Introductionmentioning

confidence: 99%

A geometric approach to confining a Dirac neutral particle in analogous way to a quantum dot

Bakke

2012

Eur. Phys. J. B

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We discuss a geometric approach to confining a Dirac neutral particle with a permanent magnetic dipole moment interacting with external fields to a hard-wall confining potential in the Minkowski spacetime through noninertial effects. We discuss the behaviour of external fields induced by noninertial effects, and a case where relativistic bound states can be achieved in analogous way to having a Dirac particle confined to a quantum dot. We show that this confinement of a Dirac neutral particle analogous to a quantum dot arises from noninertial effects that give rise to the geometry of the manifold playing the role of a hard-wall confining potential. We also discuss the possible use of this mathematical model in studies of noninertial effects on condensed matter systems described by the Dirac equation.

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Relativistic quantum Hall effect

Cited by 144 publications

References 18 publications

Band Collapse and the Quantum Hall Effect in Graphene

Band Collapse and the Quantum Hall Effect in Graphene

Path integral for confined Dirac fermions in a constant magnetic field

A geometric approach to confining a Dirac neutral particle in analogous way to a quantum dot

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