Reentrant topological phases in Mn-doped HgTe quantum wells

Beugeling, Wouter; Liu, C. X.; Novik, E. G.; Molenkamp, L. W.; Smith, C. Morais

doi:10.1103/physrevb.85.195304

Cited by 30 publications

(50 citation statements)

References 40 publications

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“…In insulating phases, the Hall conductances are proportional to the Chern number. Thus, the total Chern number is n tot = n + + n − , while the spin Chern number is given by n s = n + − n − [10,21]. In this study, we calculate the energy levels, the Hall conductance and the associated Chern number in the presence of a titled magnetic field.…”

Section: Model Hamiltonianmentioning

confidence: 99%

“…In a Kane-Mele model with magnetization, the QSH effect and edge states survive till the bulk gap closes and reopens [13]. For a QSH insulator in the presence of an out-of-plane magnetic field, the spin Chern number is shown to remain unchanged up to the magnetic field when the Landau levels cross [15,17,21]. While for an inverted InAs/GaSb quantum well in the presence of an in-plane magnetic field, the edge states and the quantized conductance are shown to be robust till a strong magnetic field of 20 T [20].…”

Section: Introductionmentioning

confidence: 99%

“…The two pseudo spin components of the Hamiltonian are independent. Consequently, the energy bands and the Hall conductance σ ± H of each block Hamiltonian h ± can be evaluated independently by the Kubo formula [7,17,24] [21]. In insulating phases, the Hall conductances are proportional to the Chern number.…”

Section: Model Hamiltonianmentioning

confidence: 99%

See 2 more Smart Citations

Topological phase transitions in an inverted InAs/GaSb quantum well driven by tilted magnetic fields

Hsu¹,

Jhang²,

Chen³

et al. 2017

Phys. Rev. B

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The helical edge states in a quantum spin Hall insulator are presumably protected by timereversal symmetry. However, even in the presence of magnetic field which breaks time-reversal symmetry, the helical edge conduction can still exist, dubbed as pseudo quantum spin Hall effect. In this work, the effects of the magnetic fields on the pseudo quantum spin Hall effect and the phase transitions are studied. We show that an in-plane magnetic field drives a pseudo quantum spin Hall state to metallic state at a high field. Moreover, at a fixed in-plane magnetic field, an increasing out-of-plane magnetic field leads to a reentrance of pseudo quantum spin Hall state in an inverted InAs/GaSb quantum well. The edge state probability distribution and Chern numbers are calculated to verify that the reentrant states are topologically nontrivial. The origin of the reentrant behavior is attributed to the nonmonotonic bending of Landau levels and the Landau level mixing caused by the orbital effect induced by the in-plane magnetic field. The robustness to disorder is demonstrated by the numerically calculated quantized conductance for disordered nanowires within Landauer-Büttiker formalism.

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Section: Model Hamiltonianmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Topological phase transitions in an inverted InAs/GaSb quantum well driven by tilted magnetic fields

Hsu¹,

Jhang²,

Chen³

et al. 2017

Phys. Rev. B

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show abstract

“…III B. For illustration, 2,10 Whereas the energy spectrum of a semi-infinite system is calculated using the transcendental equation (29), both procedures described above, solving the transcendental equation (30) or diagonalizing the finite-difference Hamiltonian (31), can be used to calculate the eigenspectrum of the Hamiltonian (2) in a finite-strip geometry. The finite-difference calculations for Fig for which we get a relative error of 10 −6 -10 −5 .…”

Section: Comparison Between the Analytical And Numerical Solutionsmentioning

confidence: 99%

“…It has also been predicted that the magnetic moments in Mn-doped HgTe quantum wells induce an effective nonlinear Zeeman effect, which in turn results in a reentrant behavior of the quantized (spin) Hall conductivity with increasing magnetic field. 30 Moreover, the effect of finite sizes on the QSH edge states in HgTe quantum wells has been investigated, and it has been shown that for small widths the edge states of the opposite sides in a finite system can overlap and produce a gap in the spectrum. 31 Based on this coupling of the wave functions from opposite edges, a spin transistor based on a constriction made of HgTe has been proposed.…”

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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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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Reentrant topological phases in Mn-doped HgTe quantum wells

Cited by 30 publications

References 40 publications

Topological phase transitions in an inverted InAs/GaSb quantum well driven by tilted magnetic fields

Topological phase transitions in an inverted InAs/GaSb quantum well driven by tilted magnetic fields

Magnetic properties of HgTe quantum wells

Spin‐helical transport in normal and superconducting topological insulators

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