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We analyze thermally induced spin and charge transport in HgTe/CdTe quantum wells on the basis of the numerical non-equilibrium Green's function technique in the linear response regime. In the topologically non-trivial regime, we find a clear signature of the gap of the edge states due to their finite overlap from opposite sample boundaries -both in the charge Seebeck and spin Nernst signal. We are able to fully understand the physical origin of the thermoelectric transport signatures of edge and bulk states based on simple analytical models. Interestingly, we derive that the spin Nernst signal is related to the spin Hall conductance by a Mott-like relation which is exact to all orders in the temperature difference between the warm and the cold reservoir.

We demonstrate how non-Abelian geometric phases can be used to universally process a spin qubit in heavy hole quantum dots in the absence of magnetic fields. A time dependent electric quadrupole field is used to perform any desired single qubit operation by virtue of non-Abelian holonomy. During the proposed operations, the degeneracy of the time dependent two level system representing the qubit is not split. Since time reversal symmetry is preserved and hyperfine coupling is known to be weak in spin qubits based on heavy holes, we expect very long coherence times in the proposed setup.PACS numbers: 03.67. Lx,03.65.Vf,81.07.Ta Coherent spin control by all-electric means (without breaking time reversal symmetry (TRS)) is among the major goals of spintronics. One of the reasons why is that the presence of TRS is known to forbid several dephasing mechanisms, for example, in spin qubits [1], due to the interplay of electron phonon coupling and Rashba spin orbit coupling [2]. In the original work by Loss and DiVincenzo [1], the proposed scheme for universal quantum computing based on spin qubits in quantum dots (QDs) relied, on the one hand, on all-electric two qubit operations but, on the other hand, on single qubit operations based on magnetic fields or ferromagnetic auxiliary devices that both break TRS. A few years later, electric-dipole-induced spin resonance (EDSR) has been proposed [3] and experimentally realized [4] as a way to process spins electrically in presence of a static magnetic field which is still breaking TRS. Rather recently, it has been theoretically shown that in spin qubits based on carbon nanotube QDs it is indeed possible to accomplish allelectric single qubit operations using EDSR [5,6]. This is true because the specific spin orbit interaction in carbon nanotubes provides a way to split spin up and spin down states in the absence of magnetic fields. However, spin qubits based on carbon nanotubes face other problems and it is fair to say that all host materials for spin qubits have advantages and disadvantages.In this work, we are interested in spin qubits based on heavy hole (HH) QDs. We show how universal single qubit operations can be performed by all-electric means in the framework of holonomic quantum computing [7] in these systems. The adiabatic evolution in presence of a time dependent electric quadrupole field is employed to control the HH qubit (see Fig. 1 for a schematic). For our purposes, HH spin qubits (composed of J = 3 2 states) are the simplest two level system that can be manipulated in the desired way. However, HH spin qubits are, of course, a very active research area by itself beyond holonomic quantum computing. Two reasons why HH QDs are promising and interesting candidates for spin qubits FIG. 1. (Color online) Schematic of single particle (red ball) with a HH (pseudo)spin (yellow arrow) in a J = 3 2 valence band QD. The three-dimensional QD is surrounded by 18 gates that allow to generate an electrostatic potential with quadrupole symmetry in any direction in space. T...

We calculate bulk transport properties of two-dimensional topological insulators based on HgTe quantum wells in the ballistic regime. Interestingly, we find that the conductance and the shot noise are distinctively different for the so-called normal regime (the topologically trivial case) and the so-called inverted regime (the topologically non-trivial case). Thus, it is possible to verify the topological order of a two-dimensional topological insulator not only via observable edge properties but also via observable bulk properties. This is important because we show that under certain conditions the bulk contribution can dominate the edge contribution which makes it essential to fully understand the former for the interpretation of future experiments in clean samples. The physics of topological insulators, that are bulk insulators with certain topological properties, is one of the most active areas in modern condensed matter research. These insulators can be either characterized by bulk Chern numbers [1] or by a so-called Z 2 topological order, in which a system, that is invariant under timereversal symmetry (TRS), is classified into two classes according to whether there are an even or odd number of Kramers partners of edge states at a given boundary of the system [2]. The latter classification makes it illustrative how to distinguish a topologically trivial from a topologically non-trivial insulator with respect to TRS. If there is an odd number of Kramers partners at a given edge then the system is considered to be topologically non-trivial because no scattering potential that preserves TRS can scatter a left-mover into a right-mover. This scattering process is strictly forbidden by TRS [3]. If instead there is an even number of Kramers partners at a given edge, the system is called topologically trivial because the edge states are not protected anymore against potential scattering by TRS and, hence, a left-mover can rather easily scatter into a right-mover and vice versa.Only one year after the prediction has been made that HgTe quantum wells (QWs) are prime candidates for two-dimensional topological insulators [4], experimental evidence based on edge state transport has been found [5]. In HgTe QWs, the thickness of the well controls the topology, meaning that thinner wells (below a critical thickness) are topologically trivial insulators and thicker wells (above a critical thickness) are topologically nontrivial insulators. The former is called normal regime, the latter inverted regime, and the critical thickness has been coined mass-inversion point with respect to the effective model discussed in more detail below. To the best of our knowledge, all experimental evidence both in twodimensional [5] as well as three-dimensional topological insulators [6] is based on the physics of the edges. In this Letter, we propose a way to experimentally distinguish a trivial from a non-trivial two-dimensional topological insulator using bulk properties only. We calculate the linear conductance as well as the Fano factor ...

The typical bulk model describing 2D topological insulators (TI) consists of two types of spinorbit terms, the so-called Dirac term which induces out-of plane spin polarization and the Rashba term which induces in-plane spin polarization. We show that for some parameters of the Fermi energy, the beam splitter device built on 2D TIs can achieve higher in-plane spin polarization than one built on materials described by the Rashba model itself. Further, due to high tunability of the electron density and the asymmetry of the quantum well, spin polarization in different directions can be obtained. While in the normal (topologically trivial) regime the in-plane spin polarization would dominate, in the inverted regime the out-of-plane polarization is more significant not only in the band gap but also for small Fermi energies above the gap. Further, we suggest a double beam splitter scheme, to measure in-plane spin current all electrically. Although we consider here as an example HgTe/CdTe quantum wells, this scheme could be also promising for InAs/GaSb QWs where the in-and out-of-plane polarization could be achieved in a single device. arXiv:1310.7213v2 [cond-mat.mes-hall]