Fingerprint of different spin–orbit terms for spin transport in HgTe quantum wells

Rothe, D. G.; Reinthaler, R. W.; Liu, C.-X.; Molenkamp, L. W.; Zhang, S.-C.; Hankiewicz, Ewelina M.

doi:10.1088/1367-2630/12/6/065012

Cited by 179 publications

(242 citation statements)

References 29 publications

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“…For HgTe/CdTe quantum wells with thickness of 58Å [5], we have |V(k)/E| ≈ 1mm , which leads to a gap in the quasi-energy spectrum on the order of 10K already for modest electric fields on the order of 1 V m which are experimentally accessible with powers < 1mW. We note that decreasing the well thickness increases [26] the value of |A/M |, which can help achieve even larger gaps in the quasi energy spectrum.…”

Section: Experimental Realization Of the Ftimentioning

confidence: 74%

Floquet topological insulator in semiconductor quantum wells

2011

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Topological phase transitions between a conventional insulator and a state of matter with topological properties have been proposed and observed in mercury telluride -cadmium telluride quantum wells. We show that a topological state can be induced in such a device, initially in the trivial phase, by irradiation with microwave frequencies, without closing the gap and crossing the phase transition. We show that the quasi-energy spectrum exhibits a single pair of helical edge states. The velocity of the edge states can be tuned by adjusting the intensity of the microwave radiation. We discuss the necessary experimental parameters for our proposal. This proposal provides an example and a proof of principle of a new non-equilibrium topological state, Floquet topological insulator, introduced in this paper.Topological phases of matter have captured our imagination over the past few years, with tantalizing properties such as robust edge modes and exotic non-Abelian excitations [1,2], and potential applications ranging from semiconductor spintronics [3] to topological quantum computation [4]. The discovery of topological insulators in solid-state devices such as HgTe/CdTe quantum wells [5,6], and in materials such as Bi 2 Te 3 , Bi 2 Sn 3 [7-9] brings us closer to employing the unique properties of topological phases in technological applications.Despite this success, however, the choice of materials that exhibit these unique topological properties remains rather scarce. In most cases we have to rely on serendipity in looking for topological materials in solidstate structures and our means to engineer Hamiltonians there are very limited. Therefore, to develop new methods to achieve and control topological structures at will would be of great importance.Our work demonstrates that such new methods are indeed possible in non-equilibrium, where external timedependent perturbations represent a rich and versatile resource that can be utilized to achieve topological spectra in systems that are topologically trivial in equilibrium. In particular, we show that periodic-in-time perturbations may give rise to new differential operators with topological insulator spectra, dubbed Floquet topological insulators (FTI), that exhibit chiral edge currents in nonequilibrium and possess other hallmark phenomena associated with topological phases. These ideas, put together with the highly developed technology for controlling lowfrequency electromagnetic modes, can enable devices in which fast switching of edge state transport is possible. Moreover, the spectral properties of the edge states, i.e., their velocity, and the bandgap of the bulk insulator, can be easily controlled. On a less applied perspective, the fast formation of the Floquet topological insulators in response to the external field opens a path to study quench dynamics of topological states in solid-state devices.The Floquet topological insulators discussed here share many features discussed in some previous works: The idea of achieving topological states in a periodic Hamilt...

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Section: Experimental Realization Of the Ftimentioning

confidence: 74%

Floquet topological insulator in semiconductor quantum wells

2011

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“…16 Note that the zero off-diagonal elements in H HgT e (6) imply conservation of the spin projections of |E 1 and |H 1 subbands, which is a good approximation for symmetric HgTe wells. 5,16,59,60 In this case, each of the Dirac cones contributes independently to transport processes, which is accounted for by the factor of 2 in the expressions for the conductivity corrections discussed in subsection III D.…”

Section: A Effective Hamiltonianmentioning

confidence: 99%

Weak antilocalization in HgTe quantum wells and topological surface states: Massive versus massless Dirac fermions

Tkachov

Hankiewicz

2011

Phys. Rev. B

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HgTe quantum wells and surfaces of three-dimensional topological insulators support Dirac fermions with a single-valley band dispersion. In the presence of disorder they experience weak antilocalization, which has been observed in recent transport experiments. In this work we conduct a comparative theoretical study of the weak antilocalization in HgTe quantum wells and topological surface states. The difference between these two single-valley systems comes from a finite band gap (effective Dirac mass) in HgTe quantum wells in contrast to gapless (massless) surface states in topological insulators. The finite effective Dirac mass implies a broken internal symmetry, leading to suppression of the weak antilocalization in HgTe quantum wells at times larger than certain τM, inversely proportional to the Dirac mass. This corresponds to the opening of a relaxation gap τ −1 M in the Cooperon diffusion mode which we obtain from the Bethe-Salpeter equation including relevant spin degrees of freedom. We demonstrate that the relaxation gap exhibits an interesting nonmonotonic dependence on both carrier density and band gap, vanishing at a certain combination of these parameters. The weak-antilocalization conductivity reflects this nonmonotonic behavior which is unique to HgTe QWs and absent for topological surface states. On the other hand, the topological surface states exhibit specific weak-antilocalization magnetoconductivity in a parallel magnetic field due to their exponential decay in the bulk.

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“…Additionally, we take into account the leading order SOI terms ∆ and R, due to bulk-inversion asymmetry (BIA) and structure-inversion asymmetry (SIA) [14], respectively a) (for material parameters in Eq. (1) see supplementary material [15]).…”

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confidence: 99%

Switching Spin and Charge between Edge States in Topological Insulator Constrictions

2011

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We show how the coupling between opposite edge states, which overlap in a constriction made of the topological insulator mercury telluride (HgTe), can be employed both for steering the charge flow into different edge modes and for controlled spin switching. Unlike in a conventional spin transistor, the switching does not rely on a tunable Rashba spin-orbit interaction, but on the energy dependence of the edge state wavefunctions. Based on this mechanism, and supported by extensive numerical transport calculations, we present two different ways to control spin-and charge-currents, depending on the local gating of the constriction, resulting in a high fidelity spin transistor.PACS numbers: 85.75.Hh, 85.35.Ds Since the prediction of a new topological state of matter in graphene [1], materials exhibiting peculiar surface states and acting as topological insulators have attracted wide attention [2]. Shortly after the theoretical proposal for a mercury telluride (HgTe)-based two-dimensional topological insulator [3], the observation of the quantum spin Hall effect [4] and non-local edge transport [5] brought compelling experimental evidence for quantized conductance due to edges states. The transport along the HgTe boundaries can be conveniently explained by an edge channel picture [6]: Two states with opposite spin orientation propagate along opposite device edges in the same direction and thus lead to a quantized conductance of 2e 2 /h. Due to the spatial separation of the spin-states the spin-orbit coupling is suspended, and the system geometry can be employed for spin selection [5].Spin-selectivity is also a crucial element of the DattaDas spin transistor proposal [7], where charge flow is controlled electrically through the gate-dependent Rashba spin orbit interaction [8] (SOI) in a conventional twodimensional semiconductor heterostructure placed in between ferromagnetic contacts. Its realization, however, turns out to be difficult owing to spin relaxation in the semiconductor heterostructure and interfacial effects such as the conductivity mismatch [9] between the different materials. HgTe-based topological insulators appear to be promising candidates for spin processing devices since they also can be gated and exhibit considerable SOI but, on the contrary, are composed of a single material class only. Moreover, the one-dimensional (1d) nature of their edge states suppresses orbital effects present in bulk conductors, leading to high spin polarizations and to a much better (spin) switching quality.To our knowledge there have been only a few proposals for spin-transistors based on two-dimensional topological insulators. Two of them rely on spin switching with a magnetic field at a pn-junction [10] or in an AharonovBohm interferometer [11]. Recently it has further been suggested, also within a phenomenological model, that separate gating of the two branches of an AharonovBohm interferometer allows for manipulating charge-and spin-transport [12]. By contrast, our present proposal relies on an electrical operati...

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Fingerprint of different spin–orbit terms for spin transport in HgTe quantum wells

Cited by 179 publications

References 29 publications

Floquet topological insulator in semiconductor quantum wells

Floquet topological insulator in semiconductor quantum wells

Weak antilocalization in HgTe quantum wells and topological surface states: Massive versus massless Dirac fermions

Switching Spin and Charge between Edge States in Topological Insulator Constrictions

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