Effect of transverse electric field on helical edge states in a quantum spin-Hall system

Liu, Genhua; Zhou, Guanghui; Chen, Yonghai

doi:10.1063/1.3664776

Cited by 26 publications

(23 citation statements)

References 23 publications

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“…The change of the sign can be easily explained by the fact that the classical motion along the loop is now subject to the conservation of the spin-helicity [see Eq. (38)]. Indeed, upon returning to its original location the particle with momentum Àk must have the same helicity as it had initially with momentum k. This requires the change of the direction of the electron spin from s to Às (see also Fig.…”

Section: Surface Weak Antilocalization In 3d Tismentioning

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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Section: Surface Weak Antilocalization In 3d Tismentioning

confidence: 99%

Spin‐helical transport in normal and superconducting topological insulators

Tkachov

Hankiewicz

2013

Physica Status Solidi (b)

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“…So doubling the dimension of the system of equations by introducing χ m allows to reduce the problem of finding k m x to a linear eigenvalue equation 19,20 . The sub-matrices in Eq.…”

Section: Brief Description Of Modelmentioning

confidence: 99%

Interplay of bulk and edge states in transport of two-dimensional topological insulators

Reinthaler

Hankiewicz

2012

Phys. Rev. B

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We study transport in two-terminal metal/quantum spin-Hall insulator (QSHI)/metal junctions. We show that the conductance signals originating from the bulk and the edge contributions are not additive. While for a long junction the transport is determined by the edge states contribution, for a short junction, the conductance signal is built from both bulk and edge states in the ratio which depends on the width of the sample. Further, in the topological insulator regime the conductance for short junctions shows a non-monotonic behavior as a function of the sample length. Surprisingly this non-monotonic behavior of conductance can be traced to the formation of an "effectively propagating" solution which is robust against scalar disorder. Our predictions should be experimentally verifiable in HgTe QWs and Bi2Se3 thin films.

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“…30 Moreover, because of the transverse confinement across the finite width, the edge states on the two sides of Hall bar are coupled together to generate a gap in the energy spectrum. 19,35,36 However, this gap can be decreased in amplitude with the increase of the bar width. Interestingly, in the presence of magnetic impurities, the two spin degenerate bands are split with spin-up band gap decreasing and spindown one increasing.…”

Section: Resultsmentioning

confidence: 99%

Controllable fully spin-polarized transport in a ferromagnetically doped topological insulator junction

Zhou

Tang

Zhou

2014

Journal of Applied Physics

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We investigate the energy band structure and the spin-dependent transport for a normal/ ferromagnetic/normal two-dimension topological insulator (TI) junction. By diagonalizing Hamiltonian for the system, the band structure shows that the edge states on two sides are coupled resulting in a gap opening due to the transverse spatial confinement. Further, the exchange field induced by magnetic impurities can also modulate the band structure with two spin degenerate bands splitting. By using the nonequilibrium Green's function method, the dependence of spin-dependent conductance and spinpolarization on the Fermi energy, the exchange field strength and the ferromagnetic TI (FTI) length are also analyzed, respectively. Interestingly, the degenerate conductance plateaus for spin-up and -down channels are broken, and both the conductances are suppressed by magnetic impurities due to the time-reversal symmetry broken and inelastic scattering. The spin-dependent conductance shows different behaviors when the Fermi energy is tuned into different ranges. Moreover, the conductance can be fully spin polarized by tuning the Fermi energy and the exchange field strength, or by tuning the Fermi energy and the FTI length. Consequently, the junction can transform from a quantum spin Hall state to a quantum anomalous Hall state, which is very important to enable dissipationless charge current for designing perfect spin filter. V C 2014 AIP Publishing LLC. [http://dx.

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Effect of transverse electric field on helical edge states in a quantum spin-Hall system

Cited by 26 publications

References 23 publications

Spin‐helical transport in normal and superconducting topological insulators

Spin‐helical transport in normal and superconducting topological insulators

Interplay of bulk and edge states in transport of two-dimensional topological insulators

Controllable fully spin-polarized transport in a ferromagnetically doped topological insulator junction

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