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

Reinthaler, R. W.; Hankiewicz, Ewelina M.

doi:10.1103/physrevb.85.165450

Cited by 14 publications

(15 citation statements)

References 35 publications

(55 reference statements)

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“…4. At the definite values of the Fermi energy E F and aspect ratio W/L the transmission of the lowest modes through the insulating (or slightly doped) region is resonantly enhanced as a consequence of an effectively propagating solution [41]. This leads to the well pronounced maximum of the differential conductance of the NIS structure for the corresponding values of E F and W/L, in accordance with Eq.…”

Section: Differential Conductance From a Scattering Matrix Approachsupporting

confidence: 81%

Bulk transport through superconducting hybrid structures in HgTe quantum wells

2014

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We investigate the subgap bulk transport through short and wide superconducting hybrid structures based on HgTe quantum wells (QWs). We show that the differential conductance of a normal metal−insulator−superconductor (NIS) proximity structure behaves in a qualitatively different way with respect to the topological phase of the HgTe QW. We compare the differential conductance for the NIS structure within the wave-matching method based on the Bogoliubov-de Gennes equation and the matrix method based on the normal-state scattering matrix and find that the two models agree for highly-doped N and S contacts. We also show that the effect of a possible Rashba spin-orbit interaction on the differential conductance can be significant for weakly doped N and S contacts. Our findings should be important in samples with a large aspect ratio where bulk contributions in transport are dominant.

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Section: Differential Conductance From a Scattering Matrix Approachsupporting

confidence: 81%

Bulk transport through superconducting hybrid structures in HgTe quantum wells

2014

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“…Following the experimental demonstration of the QSH effect in HgTe-based QWs, much effort has been invested in the theoretical investigation of the properties of 2D topological insulators, their helical edge states, and possible applications. [26][27][28][29][30][31][32][33][34] At the heart of the QSH state are relativistic corrections, which can-if strong enoughresult in band inversion, 35,36 that is, a situation where the normal order of the conduction and valence bands is inverted and which can lead to peculiar effects such as the formation of interface states. [37][38][39] In HgTe/CdTe QWs, the band structure of the 2D system formed in the well is inverted if the thickness d of the HgTe QW exceeds the critical thickness d c ≈ 6.3 nm, whereas the band structure is normal for d < d c .…”

Section: Introductionmentioning

confidence: 99%

Probing topological transitions in HgTe/CdTe quantum wells by magneto-optical measurements

et al. 2015

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In two-dimensional topological insulators, such as inverted HgTe/CdTe quantum wells, helical quantum spin Hall (QSH) states persist even at finite magnetic fields below a critical magnetic field Bc, above which only quantum Hall (QH) states can be found. Using linear-response theory, we theoretically investigate the magneto-optical properties of inverted HgTe/CdTe quantum wells, both for infinite two-dimensional and finite-strip geometries, and for possible signatures of the transition between the QSH and QH regimes. In the absorption spectrum, several peaks arise due to nonequidistant Landau levels in both regimes. However, in the QSH regime, we find an additional absorption peak at low energies in the finite-strip geometry. This peak arises due to the presence of edge states in this geometry and persists for any Fermi level in the QSH regime, while in the QH regime the peak vanishes if the Fermi level is situated in the bulk gap. Thus, by sweeping the gate voltage, it is possible to experimentally distinguish between the QSH and QH regimes due to this signature. Moreover, we investigate the effect of spin-orbit coupling and finite temperature on this measurement scheme.

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“…5 to account for additional spin-orbit terms due to out-of-plane inversion breaking in HgTe quantum wells 25 as well as studies on how helical edge states and bulk states interact in two-dimensional topological insulators. 26 The effect of magnetic fields on transport in inverted HgTe quantum wells has been treated in Refs. [27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Magnetic properties of HgTe quantum wells

2012

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Using analytical formulas as well as a finite-difference scheme, we investigate the magnetic field dependence of the energy spectra and magnetic edge states of HgTe/CdTe-based quantum wells in the presence of perpendicular magnetic fields and hard walls for the band-structure parameters corresponding to the normal and inverted regimes. Whereas one can not find counterpropagating, spin-polarized states in the normal regime, below the crossover point between the uppermost (electronlike) valence and lowest (holelike) conduction Landau levels, one can still observe such states at finite magnetic fields in the inverted regime, although these states are no longer protected by time-reversal symmetry. Furthermore, the bulk magnetization and susceptibility in HgTe quantum wells are studied, in particular their dependence on the magnetic field, chemical potential, and carrier densities. We find that for fixed chemical potentials as well as for fixed carrier densities, the magnetization and magnetic susceptibility in both the normal and the inverted regimes exhibit de Haas-van Alphen oscillations, the amplitude of which decreases with increasing temperature. Moreover, if the band structure is inverted, the ground-state magnetization (and consequently also the ground-state susceptibility) is discontinuous at the crossover point between the uppermost valence and lowest conduction Landau levels. At finite temperatures and/or doping, this discontinuity is canceled by the contribution from the electrons and holes and the total magnetization and susceptibility are continuous. In the normal regime, this discontinuity of the ground-state magnetization does not arise and the magnetization is continuous for zero as well as finite temperatures.

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

Cited by 14 publications

References 35 publications

Bulk transport through superconducting hybrid structures in HgTe quantum wells

Bulk transport through superconducting hybrid structures in HgTe quantum wells

Probing topological transitions in HgTe/CdTe quantum wells by magneto-optical measurements

Magnetic properties of HgTe quantum wells

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