Magnetic scattering of Dirac fermions in topological insulators and graphene

Zazunov, Alex; Kundu, Arijit; Hütten, Artur; Egger, Reinhold

doi:10.1103/physrevb.82.155431

Cited by 23 publications

(22 citation statements)

References 67 publications

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“…The Pauli matrices in Eq. (1) are directly connected to the electronic spin density in a topological insulator surface via the relation 3,38 s(r) = (s x , s y ) T = 2 ê z × σ .…”

Section: Hartree-fock Results For N > 2 Particlesmentioning

confidence: 99%

Signatures of Wigner molecule formation in interacting Dirac fermion quantum dots

2011

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We study N interacting massless Dirac fermions confined in a two-dimensional quantum dot. Physical realizations of this problem include a graphene monolayer and the surface state of a strong topological insulator. We consider both a magnetic confinement and an infinite mass confinement. The ground state energy is computed as a function of the effective interaction parameter α from the Hartree-Fock approximation and, alternatively, by employing the Müller exchange functional. For N = 2, we compare those approximations to exact diagonalization results. The Hartree-Fock energies are highly accurate for the most relevant interaction range α 2, but the Müller functional leads to an unphysical instability when α 0.756. Up to 20 particles were studied using HartreeFock calculations. Wigner molecule formation was observed for strong but realistic interactions, accompanied by a rich peak structure in the addition energy spectrum.

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“…The Pauli matrices in Eq. (1) are directly connected to the electronic spin density in a topological insulator surface via the relation 3,38 s(r) = (s x , s y ) T = 2 ê z × σ .…”

Section: Hartree-fock Results For N > 2 Particlesmentioning

confidence: 99%

Signatures of Wigner molecule formation in interacting Dirac fermion quantum dots

2011

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“…Beside the ARPES and band structure calculations, there has been a growing number of experiments 97–124 and theoretical studies 125–187 devoted to helical transport in 3DTI materials. Like in the QSHIs, the surface charge carriers in 3DTIs are characterized by a well‐defined spin helicity, i.e., the locking of the spin and momentum directions.…”

Section: Introductionmentioning

confidence: 99%

Spin‐helical transport in normal and superconducting topological insulators

Tkachov

Hankiewicz

2013

Physica Status Solidi (b)

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31 85141In a topological insulator (TI) the character of electron transport varies from insulating in the interior of the material to metallic near its surface. Unlike, however, ordinary metals, conducting surface states in TIs are topologically protected and characterized by spin helicity whereby the direction of the electron spin is locked to the momentum direction. In this paper we review selected topics regarding recent theoretical and experimental work on electron transport and related phenomena in two-dimensional (2D) and three-dimensional (3D) TIs.The review provides a focused introductory discussion of the quantum spin Hall effect in HgTe quantum wells as well as transport properties of 3DTIs such as surface weak antilocalization, the half-integer quantum Hall effect, s þ p-wave induced superconductivity, superconducting Klein tunneling, topological Andreev bound states and related Majorana midgap states. These properties of TIs are of practical interest, guiding the search for the routes towards topological spin electronics. 1 Introduction The situation when a material behaves as a metal in terms of its electric conductivity and, at the same time, as an insulator in terms of its band structure is extremely unconventional from the viewpoint of the standard classification of solids. That is why the recent discovery of a class of such materials -topological insulators (TIs) -has generated much interest (see e.g., reviews [1,2]). The dual properties of the TIs are especially well pronounced in two-dimensional (2D) systems which are also known as quantum spin-Hall insulators (QSHIs) [3][4][5][6][7]. In QSHIs, the metallic electric conduction is associated with propagating states that occur only near the sample edges, while the conduction in the interior is suppressed by a band gap like in ordinary band insulators. These edge states originate from intrinsic spin-orbit (SO) coupling and are profoundly different from those appearing in quantum Hall systems in a strong perpendicular magnetic field [8,9]. The key distinction lies in the role of the time reversal symmetry. In the QSHIs the SO coupling preserves the time-reversal symmetry, resulting in a pair of counter-propagating channels on the same edge as opposed to one-way directed (chiral) edge states in quantum Hall systems. Remarkably, the spin and momentum directions of the two QSHI edge channels are locked in the opposite ways so that these states are characterized by opposite spin helicities and orthogonal

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“…(4). For simplicity, we consider jEj ≫ Δ, where the Born approximation [7,37] is applicable. For an incoming plane wave with momentum k and σ ¼ sgnðEÞ ¼ AE, the asymptotic scattering state is [7] Ψ k;σ ðr; θÞ ≃ e ik·r U k;σ þ fðθ;…”

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Electric-Dipole-Induced Universality for Dirac Fermions in Graphene

et al. 2014

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This is the published version of the paper.This version of the publication may differ from the final published version. We study electric dipole effects for massive Dirac fermions in graphene and related materials. The dipole potential accommodates towers of infinitely many bound states exhibiting a universal Efimov-like scaling hierarchy. The dipole moment determines the number of towers, but there is always at least one tower. The corresponding eigenstates show a characteristic angular asymmetry, observable in tunnel spectroscopy. However, charge transport properties inferred from scattering states are highly isotropic. Permanent

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Magnetic scattering of Dirac fermions in topological insulators and graphene

Cited by 23 publications

References 67 publications

Signatures of Wigner molecule formation in interacting Dirac fermion quantum dots

Signatures of Wigner molecule formation in interacting Dirac fermion quantum dots

Spin‐helical transport in normal and superconducting topological insulators

Electric-Dipole-Induced Universality for Dirac Fermions in Graphene

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