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Using a generalized wave matching method we solve the full scattering problem for quantum spin Hall insulator-superconductor (SC)-quantum spin Hall insulator junctions. We find that for systems narrow enough so that the bulk states in the SC part couple both edges, the crossed Andreev reflection (CAR) is significant and the electron cotunneling (T) and CAR become spatially separated. We study the effectiveness of this separation as a function of the system geometry and the level of doping in the SC. Moreover, we show that the spatial separation of both effects allows for an all-electrical measurement of CAR and T separately in a five-terminal setup or by using the spin selection of the quantum spin Hall effect in an H-bar structure.

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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.

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 ...

Topological aspects of superconductivity in quantum spin-Hall systems (QSHSs) such as thin layers of three-dimensional topological insulators (3D Tis) or two-dimensional Tis are in the focus of current research. We examine hybrid QSHS/superconductor structures in an external magnetic field and predict a gapless superconducting state with protected edge modes. It originates entirely from the orbital magnetic-field effect caused by the locking of the electron spin to the momentum of the superconducting condensate flow. We show that such spin-momentum locking can generate a giant orbital g-factor of order of several hundreds, allowing one to achieve significant spin polarization in the QSHS in the fields well below the critical field of the superconducting material. We propose a three-terminal setup in which the spin-polarized edge superconductivity can be probed by Andreev reflection, leading to unusual transport characteristics: a non-monotonic excess current and a zerobias conductance splitting in the absence of the Zeeman interaction.PACS numbers: 72.25. Dc, 73.23.Ad, 74.45.+c Introduction. Spin-Hall effects are one of the most active fields in modern solid state physics [1][2][3][4][5][6][7][8]. In particular, the quantum spin-Hall effect [5, 6, 9, 10] allows one to generate and convert charge and spin currents in protected edge channels [11]. Combining quantum spin-Hall systems (QSHSs) with superconductors (SCs) leads to a broader spectrum of interesting observable phenomena [12][13][14]. These include quantum interference effects reported in [13,14], indicating superconducting transport through the edge states in the QSH regime. Understanding edge superconductivity in QSHS/SC hybrids is also instrumental to the proposals to realize Majorana zero modes in topological insulators (see, e.g., [15] and reviews [16,17]).In this paper we predict a unique magnetic-field response of QSHS/SC hybrids which is characterized by very large effective g-factors reaching the order of several hundreds. It originates from the locking of the electron spin to the momentum of the superconducting condensate flow generated by an external magnetic field. We show that this orbital effect has the form similar to the Zeeman spin splitting in thin superconducting films [18], but involves an effective g-factor determined by the parameters of the QSHS/SC structure, viz.: the edge-state velocity, v, the thickness of the SC material, d SC , and the London penetration depth, λ L :