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We theoretically investigate the localization properties of Majorana states (MSs) in proximitized, planar Josephson Junctions (JJs) oriented along different crystallographic orientations and in the presence of an in-plane magnetic field and Rashba and Dresselhaus spin-orbit couplings. We show that two types of MSs may emerge when the junction transits into the topological superconducting state. In one case, referred to as end-like MSs, the Majorana quasiparticles are mainly localized inside the normal region at the opposite ends of the junction. In contrast, edge-like MSs extend along the opposite edges of the system, perpendicular to the junction channel. We show how the MSs can transit from end-like to edge-like and vice versa by tuning the magnetic field strength and/or the superconducting phase difference across the junction. In the case of phase-unbiased JJs the transition may occur as the ground state phase difference self-adjusts its value when the Zeeman field is varied., Comment: 12 pages, 6 figures

The superconducting diode effect (SDE) is a magneto-electric phenomenon where an external magnetic field imparts a non-zero center-of-mass momentum to Cooper pairs, either facilitating or hindering the flow of supercurrent depending on its direction. We propose that quantum spin Hall insulator (QSHI)-based Josephson junctions can serve as versatile platforms for non-dissipative electronics exhibiting the SDE when triggered by a phase bias and an out-of-plane magnetic field. By computing the contributions from Andreev bound states and the continuum of quasi-particle states, we provide both numerical and analytical results scrutinizing various aspects of the SDE, including its quality Q-factor. The maximum value of the $Q$-factor is found to be universal at low (zero) temperatures, which ties its origin to underlying topological properties that are independent of the junction's specific details. As the magnetic field increases, the SDE diminishes due to the closing of the induced superconducting gap caused by orbital effects. To observe the SDE, the QSHI-based Josephson junction must be designed so that its edges are transport-wise non-equivalent. Additionally, we explore the SDE in a more exotic yet realistic scenario, where the fermionic ground-state parity of the Josephson junction remains conserved while driving a current. In this 4$\pi$-periodic situation, we predict an enhancement of the SDE compared to its 2$\pi$-periodic, parity-unconstrained counterpart., Comment: 11 pages, 9 figures

A planar Josephson junction is a versatile platform to realize topological superconductivity over a large parameter space and host Majorana bound states. With a change in Zeeman field, this system undergoes a transition from trivial to topological superconductivity accompanied by a jump in the superconducting phase difference between the two superconductors. A standard model of these Josephson junctions, which can be fabricated to have a nearly perfect interfacial transparency, predicts a simple universal behavior. In that model, at the same value of Zeeman field for the topological transition, there is a $\pi$ phase jump and a minimum in the critical superconducting current, while applying a controllable phase difference yields a diamond-shaped topological region as a function of that phase difference and a Zeeman field. In contrast, even for a perfect interfacial transparency, we find a much richer and nonuniversal behavior as the width of the superconductor is varied or the Dresselhaus spin-orbit coupling is considered. The Zeeman field for the phase jump, not necessarily $\pi$, is different from the value for the minimum critical current, while there is a strong deviation from the diamond-like topological region. These Josephson junctions show a striking example of a nonreciprocal transport and superconducting diode effect, revealing the importance of our findings not only for topological superconductivity and fault-tolerant quantum computing, but also for superconducting spintronics., Comment: Invited to APL Special Topic Issue: "Josephson Junctions and Related Proximity Effects: From Basic Science to Emerging Applications in Advanced Technologies", accepted version

There has recently been a surge of interest in studying the superconducting diode effect (SDE) partly due to the possibility of uncovering the intrinsic properties of a material system. A change of sign of the SDE at finite magnetic field has previously been attributed to different mechanisms. Here, we observe the SDE in epitaxial Al-InAs Josephson junctions with strong Rashba spin-orbit coupling (SOC). We show that this effect strongly depends on the orientation of the in-plane magnetic field. In the presence of a strong magnetic field, we observe a change of sign in the SDE. Simulation and measurement of supercurrent suggest that depending on the superconducting widths, $W_\text{S}$, this sign change may not necessarily be related to 0--$\pi$ or topological transitions. We find that the strongest sign change in junctions with narrow $W_\text{S}$ is consistent with SOC-induced asymmetry of the critical current under magnetic-field inversion, while in wider $W_\text{S}$, the sign reversal could be related to 0--$\pi$ transitions and topological superconductivity.

We explain how Rashba spin-orbit coupling (SOC) in a two-dimensional electron gas (2DEG), or in a conventional $s$-wave superconductor, can lead to a large magnetoresistance even with one ferromagnet. However, such enhanced magnetoresistance is not generic and can be nonmonotonic and change its sign with Rashba SOC. For an in-plane rotation of magnetization, it is typically negligibly small for a 2DEG and depends on the perfect transmission which emerges from a spin-parity-time symmetry of the scattering states, while this symmetry is generally absent from the Hamiltonian of the system. The key difference from considering the normal-state magnetoresistance is the presence of the spin-dependent Andreev reflection at superconducting interfaces. In the fabricated junctions of quasi-2D van der Waals ferromagnets with conventional $s$-wave superconductors (Fe$_{0.29}$TaS$_2$/NbN) we find another example of enhanced magnetoresistance where the presence of Rashba SOC reduces the effective interfacial strength and is responsible for an equal-spin Andreev reflection. The observed nonmonotonic trend in the out-of-plane magnetoresistance with the interfacial barrier is an evidence for the proximity-induced equal-spin-triplet superconductivity., Comment: This work is submitted to the special issue of Phys. Rev. B dedicated to Professor Emmanuel Rashba

We investigate the effects of an in-plane magnetic field on the weak antilocalization signature of near-surface quantum wells lacking bulk and inversion symmetry. The measured magnetoconductivity exhibits a strong anisotropy with respect to the direction of the in-plane magnetic field. The two-fold symmetry of the observed magneto-anisotropy originates from the competition between Rashba and Dresselhaus spin-orbit couplings. The high sensitivity of the weak antilocalization to the spin texture produced by the combined Zeeman and spin-orbit fields results in very large anisotropy ratios, reaching 100%. Using a semiclassical universal model in quantitative agreement with the experimental data, we uniquely determine the values of the Dresselhaus and Rashba parameters as well as the effective in-plane g-factor of the electrons. Understanding these parameters provides new prospects for novel applications ranging from spintronics to topological quantum computing.

We theoretically investigate the effects of tunable magnetic fringe fields generated by arrays of switchable magnetic junctions (MJs) on the quantum states of an underlying two-dimensional (2D) system formed in a semiconductor quantum well. The magnetic landscape generated by the MJ-array can be reconfigured on the nanometer scale by electrically switching the magnetic state of individual MJs. The interaction between the spin of the carriers and the fringe fields generates effective spin-dependent potentials acting like quantum dots (barriers) for carriers with spin parallel (antiparallel) to the magnetic texture. The position and depth (height) of the magnetically generated quantum dots (barriers), as well as the coupling between them, can be tuned by modulating the magnetic texture through switchings of individual MJs. This enables the magnetic control, manipulation, and design of quantum states, their spin, and transport properties., Comment: 9 pages, 8 figures

The use of advanced quantum neuron models for pattern recognition applications requires fault tolerance. Therefore, it is not yet possible to test such models on a large scale in currently available quantum processors. As an alternative, we propose a quantum perceptron (QP) model that uses a reduced number of multi-qubit gates and is therefore less susceptible to quantum errors in current actual quantum computers with limited tolerance. The proposed quantum algorithm is superior to its classical counterpart, although since it does not take full advantage of quantum entanglement, it provides a lower encoding power than other quantum algorithms using multiple qubit entanglement. However, the use of separable-sate encoding allows for testing the algorithm and different training schemes at a large scale in currently available non-fault tolerant quantum computers. We demonstrate the performance of the proposed model by implementing a few qubits version of the QP in a simulated quantum computer. The proposed QP uses an N-ary encoding of the binary input data characterizing the patterns. We develop a hybrid (quantum-classical) training procedure for simulating the learning process of the QP and test their efficiency.

We investigate the effects of magnetic and crystalline anisotropies on the topological superconducting state of planar Josephson junctions (JJs). In junctions where only Rashba spin-orbit coupling (SOC) is present, the topological phase diagram is insensitive to the supercurrent direction, but exhibits a strong dependence on the magnetic field orientation. However, when both Rashba and Dresselhaus SOCs coexist, the topological phase diagram strongly depends on both the magnetic field and junction crystallographic orientations. We examine the impact of the magnetic and crystalline anisotropy on the current-phase relation (CPR), energy spectrum, and topological gap of phase-biased JJs, where the junction is connected in a loop and the superconducting phase difference is fixed by a loop-threading magnetic flux. The anisotropic CPR can be used to extract the ground-sate phase (i.e. the superconducting phase difference that minimizes the system free energy) behavior in phase-unbiased JJs with no magnetic flux. Under appropriate conditions, phase-unbiased JJs can self-tune into or out of the topological superconducting state by rotating the in-plane magnetic field. The magnetic field orientations at which topological transitions occur strongly depend on both the junction crystallographic orientation and the relative strength between Rashba and Dresselhaus SOCs. We find that for an optimal practical application, in which the junction exhibits topological superconductivity with a sizable topological gap, a careful balancing of the magnetic field direction, the junction crystallographic orientation, and the relative strengths of the Rashba and Dresselhaus SOCs is required. We discuss the considerations that must be undertaken to achieve this balancing for various junction types and parameters., Comment: 12 pages, 9 figures

We theoretically investigate how the spin susceptibility of a planar Josephson junction is affected when the system transits into the topological superconducting state. We show that the magnetic flux and magnetic field dependence of the spin susceptibility closely maps the phase diagram of the system. In the absence of an external magnetic flux the system can self-tune into the topological superconducting state by minimizing its free energy. Self-tuned topological transitions are accompanied by sharp peaks in the spin susceptibility, which can therefore be use as measurable fingerprints for detecting the topological superconducting state. Away from the peaks, the amplitude of the spin susceptibility can provide qualitative information about the relative size of the topological gap. The signatures in the spin susceptibility are robust, even in junctions with narrow superconducting leads, where critical current minima may no longer serve as an indication of topological phase transitions. Numerical simulations are complemented with simplified analytical models capable of capturing the main features predicted for the spin susceptibility behavior. The predicted results could be particularly relevant for future experiments on realization and detection of the topological superconducting state in planar Josephson junctions.

A hallmark of topological superconductivity is the non-Abelian statistics of Majorana bound states (MBS), its chargeless zero-energy emergent quasiparticles. The resulting fractionalization of a single electron, stored nonlocally as a two spatially-separated MBS, provides a powerful platform for implementing fault-tolerant topological quantum computing. However, despite intensive efforts, experimental support for MBS remains indirect and does not probe their non-Abelian statistics. Here we propose how to overcome this obstacle in mini-gate controlled planar Josephson junctions (JJs) and demonstrate non-Abelian statistics through MBS fusion, detected by charge sensing using a quantum point contact, based on dynamical simulations. The feasibility of preparing, manipulating, and fusing MBS in two-dimensional (2D) systems is supported in our experiments which demonstrate the gate control of topological transition and superconducting properties with five mini gates in InAs/Al-based JJs. While we focus on this well-established platform, where the topological superconductivity was already experimentally detected, our proposal to identify elusive non-Abelian statistics motivates also further MBS studies in other gate-controlled 2D systems., Comment: 10 pages, 7 figures; Accepted in Nature Communications

We theoretically investigate the crystalline anisotropy of topological phase transitions in phase-controlled planar Josephson junctions (JJs) subject to spin-orbit coupling and in-plane magnetic fields. It is shown how topological superconductivity (TS) is affected by the interplay between the magnetic field and the orientation of the junction with respect to its crystallographic axes. This interplay can be used to electrically tune between different symmetry classes in a controlled fashion and thereby optimize the stability and localization of Majorana bound states in planar Josephson junctions. Our findings can be used as a guide for achieving the most favorable conditions when engineering TS in planar JJs and can be particularly relevant for setups containing non-collinear junctions which have been proposed for performing braiding operations on multiple Majorana pairs.

We reveal that the interplay between Rashba spin-orbit coupling and proximity-induced magnetization in a two-dimensional electron gas leads to peculiar transport properties and large anisotropy of magnetoresistance. While the related tunneling anisotropic magnetoresistance (TAMR) has been extensively studied before, we predict an effect with a different origin arising from the evolution of a resonant condition with the in-plane rotation of magnetization and having a much larger magnitude. The resonances in the tunneling emerge from a spin-parity-time symmetry of the scattering states. However, such a symmetry is generally absent from the system itself and only appears for certain parameter values. Without resonant behavior in the topological surface states of a proximitized three-dimensional topological insulator (TI), TAMR measurements can readily distinguish them from often misinterpreted trivial Rashba-like states inherent to many TIs.

Topological superconductivity supports exotic Majorana bound states (MBS) which are chargeless zero-energy emergent quasiparticles. With their non-Abelian exchange statistics and fractionalization of a single electron stored nonlocally as a spatially separated MBS, they are particularly suitable for implementing fault-tolerant topological quantum computing. While the main efforts to realize MBS have focused on one-dimensional systems, the onset of topological superconductivity requires delicate parameter tuning and geometric constraints pose significant challenges for their control and demonstration of non-Abelian statistics. To overcome these challenges, building on recent experimental advances in planar Josephson junctions (JJs), we propose a MBS platform of X-shaped JJs. This versatile implementation reveals how external flux control of the superconducting phase difference can generate and manipulate multiple MBS pairs to probe non-Abelian statistics. The underlying topological superconductivity exists over a large parameter space, consistent with materials used in our fabrication of such X junctions, as an important step towards scalable topological quantum computing., Comment: 6 pages, 4 figures, accepted in PRL

Topological superconductivity holds promise for fault-tolerant quantum computing. While planar Josephson junctions are attractive candidates to realize this exotic state, direct phase-measurements as the fingerprint of the topological transition are missing. By embedding two gate-tunable Al/InAs Josephson junctions in a loop geometry, we measure a $\pi$-jump in the junction phase with increasing in-plane magnetic field, ${\bf B}_\|$. This jump is accompanied by a minimum of the critical current, indicating a closing and reopening of the superconducting gap, strongly anisotropic in ${\bf B}_\|$. Our theory confirms that these signatures of a topological transition are compatible with the emergence of Majorana states.

Andreev reflection (AR) in ferromagnet/superconductor junctions is an indispensable spectroscopic tool for measuring spin polarization. We study theoretically how the presence of a thin semiconducting interface in such junctions, inducing Rashba and Dresselhaus spin-orbit coupling, modifies AR processes. The interface gives rise to an effective momentum- and spin-dependent scattering potential, making the probability of AR strongly asymmetric with respect to the sign of the incident electrons' transverse momenta. This skew AR creates spatial charge carrier imbalances and transverse Hall currents flow in the ferromagnet. We show that the effect is giant, as compared to the normal regime. We provide a quantitative analysis and a qualitative picture of this phenomenon, and finally show that skew AR also leads to a widely tunable transverse supercurrent response in the superconductor., Comment: 21 pages, 11 figures

A hybrid semiconductor-superconductor nanowire on the top of a magnetic film in the stripe phase experiences a magnetic texture from the underlying fringing fields. The Zeeman interaction with the highly inhomogeneous magnetic textures generates a large synthetic spin-orbit coupling. We show that this platform can support the formation of Majorana bound states (MBS) localized at the ends of the nanowire. The transition to the topological superconducting phase not only depends on the nanowire parameters and stripe size but also on the relative orientation of the stripes with respect to the nanowire axis. Topological phase transitions with the corresponding emergence or destruction of MBS can be induced by reorienting the stripes or shifting their position, which can be achieved by passing a charge current through the magnetic film or by applying electrically-controlled strain to it. The proposed platform removes the need for external magnetic fields and offers a non-invasive electrical tuning of MBS with the perturbation (current or strain) acting only on thee magnetic film., Comment: 9 pages, 6 figures

Spin-valve structures in which a change of magnetic configuration is responsible for magnetoresistance have enabled impressive advances in spintronics, focusing on magnetically storing and sensing information. However, this mature technology also offers versatile control of the underlying fringing fields and entirely different applications by realizing topologically-nontrivial states. Together with proximity-induced superconductivity in a two-dimensional electron gas, these fringing fields realized in commercially-available spin valves could control Majorana bound states (MBS). Detailed support for the existence and control of MBS is obtained by combining accurate micromagnetic simulation of fringing fields used as an input in Bogoliubov de Gennes equation to calculate low-energy spectrum, wavefunction localization, and local charge neutrality. A generalized condition for quantum phase transition in these structures provides valuable guidance for the MBS evolution and implementing reconfigurable effective topological wires., Comment: 8 pages, 7 figures

Spin-orbit coupling (SOC) is a key interaction in spintronics, allowing an electrical control of spin or magnetization and, vice versa, a magnetic control of electrical current. However, recent advances have revealed much broader implications of SOC that is also central to the design of topological states, including topological insulators, skyrmions, and Majorana fermions, or to overcome the exclusion of two-dimensional ferro-magnetism expected from the Mermin-Wagner theorem. SOC and the resulting emergent interfacial spin-orbit fields are simply realized in junctions through structural inversion asymmetry, while the anisotropy in magnetoresistance (MR) allows for their experimental detection. Surprisingly, we demonstrate that an all-epitaxial ferromagnet/MgO/metal junction with only a negligible MR anisotropy undergoes a remarkable transformation below the superconducting transition temperature of the metal. The superconducting junction has a three orders of magnitude higher MR anisotropy and supports the formation of spin-triplet superconductivity, crucial for superconducting spintronics, and topologically-protected quantum computing. Our findings call for revisiting the role of SOC in other systems which, even when it seems negligible in the normal state, could have a profound influence on the superconducting response., Comment: Accepted for publication in Physical Review Applied

Advances in scaling down heterostructures and having an improved interface quality together with atomically-thin two-dimensional materials suggest a novel approach to systematically design materials. A given material can be transformed through proximity effects whereby it acquires properties of its neighbors, for example, becoming superconducting, magnetic, topologically nontrivial, or with an enhanced spin-orbit coupling. Such proximity effects not only complement the conventional methods of designing materials by doping or functionalization, but can also overcome their various limitations. In proximitized materials it is possible to realize properties that are not present in any constituent region of the considered heterostructure. While the focus is on magnetic and spin-orbit proximity effects with their applications in spintronics, the outlined principles provide also a broader framework for employing other proximity effects to tailor materials and realize novel phenomena., Comment: Invited Review to appear in Materials Today, 28 pages, 22 figures

The two-dimensional character and reduced screening in monolayer transition-metal dichalcogenides (TMDs) lead to the ubiquitous formation of robust excitons with binding energies orders of magnitude larger than in bulk semiconductors. Focusing on neutral excitons, bound electron-hole pairs, that dominate the optical response in TMDs, it is shown that they can provide fingerprints for magnetic proximity effects in magnetic heterostructures. These proximity effects cannot be described by the widely used single-particle description, but instead reveal the possibility of a conversion between optically inactive and active excitons by rotating the magnetization of the magnetic substrate. With recent breakthroughs in fabricating Mo- and W-based magnetic TMD-heterostructures, this emergent optical response can be directly tested experimentally., Comment: 10 pages, pages 7-10 contain supplemental material

A versatile control of magnetic systems, widely used to store information, can also enable manipulating Majorana bounds states (MBS) and implementing fault-tolerant quantum information processing. The proposed platform relies on the proximity-induced superconductivity in a two-dimensional electron gas placed next to an array of magnetic tunnel junctions (MTJs). A change in the magnetization configuration in the MTJ array creates tunable magnetic textures thereby removing several typical requirements for MBS: strong spin-orbit coupling, applied magnetic field, and confinement by one-dimensional structures which complicates demonstrating non-Abelian statistics through braiding. Recent advances in fabricating two-dimensional epitaxial superconductor/semiconductor heterostructures and designing tunable magnetic textures support the feasibility of this novel platform for MBS., Comment: 7 pages, 5 figures

We investigate tunneling across a single ferromagnetic barrier on the surface of a three-dimensional topological insulator. In the presence of a magnetization component along the bias direction, a tunneling planar Hall conductance (TPHC), transverse to the applied bias, develops. Electrostatic control of the barrier enables a giant Hall angle, with the TPHC exceeding the longitudinal tunneling conductance. By changing the in-plane magnetization direction it is possible to change the sign of both the longitudinal and transverse differential conductance without opening a gap in the topological surface state. The transport in a topological insulator/ferromagnet junction can thus be drastically altered from a simple spin-valve to an amplifier., Comment: 13 pages, pages 6-13 contain supplemental material

We propose a versatile platform to investigate the existence of Majorana bound states (MBSs) and their non-Abelian statistics through braiding. This implementation combines a two-dimensional electron gas formed in a semiconductor quantum well grown on the surface of an s-wave superconductor with a nearby array of magnetic tunnel junctions (MTJs). The underlying magnetic textures produced by MTJs provide highly controllable topological phase transitions to confine and transport MBSs in two dimensions, overcoming the requirement for a network of wires. Obtained scaling relations confirm that various semiconductor quantum well materials are suitable for this proposal., Comment: Expanded published version, 6 pages, 4 figures

Andreev reflection spectroscopy of ferromagnet/superconductor (FS) junctions is an important probe of spin polarization. We theoretically investigate spin-polarized transport in FS junctions in the presence of Rashba and Dresselhaus interfacial spin-orbit fields and show that Andreev reflection can be controlled by changing the magnetization orientation. We predict a giant in- and out-of-plane magnetoanisotropy of the junction conductance. If the ferromagnet is highly spin polarized---in the half-metal limit---the magnetoanisotropic Andreev reflection depends universally on the spin-orbit fields only. Our results show that Andreev reflection spectroscopy can be used for sensitive probing of interfacial spin-orbit fields in FS junction., Comment: Pages 6-10 contain supplemental material

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 $B_\mathrm{c}$, 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 possible signatures of the transition between the QSH and QH regimes. In the absorption spectrum, several peaks arise due to non-equidistant 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., Comment: 14 pages, 13 figures

Thermally induced spin-dependent transport across magnetic tunnel junctions is theoretically investigated. We analyze the thermal analog of Slonczewski's model (as well as its limiting case---Julliere's model) of tunneling magnetoresistance and obtain analytical expressions for the junction thermopower and the tunneling magneto-thermopower (TMT). The analytical model is tested numerically for the special case of an Al$_2$O$_3$-based MTJ, for which we analyze the dependence of the thermopower and TMT on the relative magnetization orientations, as well as on the barrier height and thickness. We show that at a certain barrier height TMT vanishes, separating the region of positive and negative TMT. As its electrical prototype, this thermal spin transport model should serve as a phenomenological benchmark for analyzing experimental and first-principles calculations of thermopower in magnetic tunnel junctions. The analytical expressions can be used as a first estimate of the magneto-thermopower of the junctions using {\it ab initio} band structure data of the junction ferromagnets., Comment: 7 pages, 4 figures. Submitted for publication to Physical Review B

The Tunneling Anisotropic Magneto-Thermopower (TAMT) and the Tunneling Anisotropic Spin-Seebeck (TASS) effects are studied for a magnetic tunnel junction (MTJ) composed of a ferromagnetic electrode, a zinc-blende semiconductor and a normal metal. We develop a theoretical model for describing the dependence of a thermally induced tunneling current across the MTJ on the in-plane orientation of the magnetization in the ferromagnetic layer. The model accounts for the specific Bychkov-Rashba and Dresselhaus spin-orbit interactions present in these systems, which are responsible for the $C_{2v}$ symmetry we find in the TAMT and the TASS., Comment: 11 pages, 4 figures. Submitted for publication to Physical Review B

The charge density relaxation propagator of a two dimensional electron system, which is the slope of the imaginary part of the polarization function, exhibits singularities for bosonic momenta having the order of the spin-orbit momentum and depending on the momentum orientation. We have provided an intuitive understanding for this non-analytic behavior in terms of the inter chirality subband electronic transitions, induced by the combined action of Bychkov-Rashba (BR) and Dresselhaus (D) spin-orbit coupling. It is shown that the regular behavior of the relaxation propagator is recovered in the presence of only one BR or D spin-orbit field or for spin-orbit interaction with equal BR and D coupling strengths. This creates a new possibility to influence carrier relaxation properties by means of an applied electric field., Comment: 4 figures

The presence of edges locally breaks the inversion symmetry of heterostructures and gives rise to lateral (edge) spin-orbit coupling (SOC), which, under some conditions, can lead to the formation of helical edge states. If the edge SOC is strong enough, the helical edge states can penetrate the band-gap and be energetically isolated from the bulk-like states. As a result backward scattering is suppressed, dissipationless helical edge channels protected against time-inversion symmetric perturbations emerge, and the system behaves as a 2D topological insulator (TI). However, unlike in previous works on TIs, the mechanism proposed here for the creation of protected helical edge states relies on the strong edge SOC rather than on band inversion., Comment: This paper has been withdrawn by the author due to some wrong conclusions extracted from an oversimplified model

The microscopic structure of spin-orbit fields for the technologically important Fe/GaAs interface is uncovered from first principles. A symmetry based method allows to obtain the spin-orbit fields---both their magnitude and orientation---for a generic Bloch state, from the electronic band structure for any in-plane magnetization orientation. It is demonstrated that the spin-orbit fields depend not only on the electric field across the interface, but also surprisingly strongly on the Fe magnetization orientation, opening prospects for their magnetic control. These results give important clues in searching for spin-orbit transport and optical phenomena in ferromagnetic/nonmagnetic systems., Comment: 5 pages, 4 figures, supplemental material

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 cannot find counterpropagating, spin-polarized states in the normal regime, below the crossover point between the uppermost (electron-like) valence and lowest (hole-like) 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, whose amplitude 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., Comment: 19 pages, 26 figures

We theoretically investigate the frictional drag induced by the Coulomb interaction between spa- tially separated massless and massive fermions at low temperatures. As a model system, we use a double-layer structure composed of a two-dimensional electron gas (2DEG) and a n-doped graphene layer. We analyze this system numerically and also present analytical formulae for the drag re- sistivity in the limit of large and small interlayer separation. Both, the temperature and density dependence are investigated and compared to 2DEG-2DEG and graphene-graphene double-layer structures. Whereas the density dependence of the transresistivity for small interlayer separation differs already in the leading order for each of those three structures, we find the leading order con- tribution of density dependence in the large interlayer separation limit to exhibit the same density dependence in each case. In order to distinguish between the different systems in the large interlayer separation limit, we also investigate the subleading contribution to the transresistivity. Furthermore, we study the Coulomb drag in a double-layer structure consisting of n-doped bilayer and monolayer graphene, which we find to possess the same qualitative behavior as the 2DEG-graphene system., Comment: 11 pages, 4 figures

The interplay between spin transport and thermoelectricity offers several novel ways of generating, manipulating, and detecting nonequilibrium spin in a wide range of materials. Here we formulate a phenomenological model in the spirit of the standard model of electrical spin injection to describe the electronic mechanism coupling charge, spin, and heat transport and employ the model to analyze several different geometries containing ferromagnetic (F) and nonmagnetic (N) regions: F, F/N, and F/N/F junctions which are subject to thermal gradients. We present analytical formulas for the spin accumulation and spin current profiles in those junctions that are valid for both tunnel and transparent (as well as intermediate) contacts. For F/N junctions we calculate the thermal spin injection efficiency and the spin accumulation induced nonequilibrium thermopower. We find conditions for countering thermal spin effects in the N region with electrical spin injection. This compensating effect should be particularly useful for distinguishing electronic from other mechanisms of spin injection by thermal gradients. For F/N/F junctions we analyze the differences in the nonequilibrium thermopower (and chemical potentials) for parallel and antiparallel orientations of the F magnetizations, as evidence and a quantitative measure of the spin accumulation in N. Furthermore, we study the Peltier and spin Peltier effects in F/N and F/N/F junctions and present analytical formulas for the heat evolution at the interfaces of isothermal junctions., Comment: to be published in PRB (in press), 19 pages, 19 figures

The existence of a spin-orbit coupling (SOC) induced by the gradient of the effective mass in low-dimensional heterostructures is revealed. In structurally asymmetric quasi-two-dimensional semiconductor heterostructures the presence of a mass gradient across the interfaces results in a SOC which competes with the SOC created by the electric field in the valence band. However, in graded quantum wells subjected to an external electric field, the mass-gradient induced SOC can be finite even when the electric field in the valence band vanishes., Comment: 4 pages, 2 figures, 1 table

By exploiting our recently derived exact formula for the Lindhard polarization function in the presence of Bychkov-Rashba (BR) and Dresselhaus (D) spin-orbit interaction (SOI), we show that the interplay of different SOI mechanisms induces highly anisotropic modifications of the static dielectric function. We find that under certain circumstances the polarization function exhibits doubly-singular behavior, which leads to an intriguing novel phenomenon, beating of Friedel oscillations. This effect is a general feature of systems with BR+D SOI and should be observed in structures with a sufficiently strong SOI., Comment: 3 figures

In a 2DEG confined to two coaxial tubes the `tube degree of freedom' can be described in terms of pseudospin-1/2 dynamics. The presence of tunneling between the two tubes leads to a collective oscillation known as pseudospin resonance. We employ perturbation theory to examine the dependence of the frequency of this mode with respect to a coaxial magnetic field for the case of small intertube distances. Coulomb interaction leads to a shift of the resonance frequency and to a finite lifetime of the pseudospin excitations. The presence of the coaxial magnetic field gives rise to pronounced peaks in the shift of the resonance frequency. For large magnetic fields this shift vanishes due to the effects of Zeeman splitting. Finally, an expression for the linewidth of the resonance is derived. Numerical analysis of this expression suggests that the linewidth strongly depends on the coaxial magnetic field, which leads to several peaks of the linewidth as well as regions where damping is almost completely suppressed., Comment: 11 pages, 7 figures

The methodology used to obtain the values of the spin-orbit couplings from the spin expectation values from perturbation theory was incorrect. As a result Figs. 2 and 3 are incorrect., Comment: This paper has been withdrawn

We report experiments on epitaxially grown Fe/GaAs/Au tunnel junctions demonstrating that the tunneling anisotropic magnetoresistance (TAMR) effect can be controlled by a magnetic field. Theoretical modelling shows that the interplay of the orbital effects of a magnetic field and the Dresselhaus spin-orbit coupling in the GaAs barrier leads to an independent contribution to the TAMR effect with uniaxial symmetry, whereas the Bychkov-Rashba spin-orbit coupling does not play a role. The effect is intrinsic to barriers with bulk inversion asymmetry., Comment: 5 pages, 3 figures

Based on general symmetry considerations we investigate how the dependence of the tunneling anisotropic magnetoresistance (TAMR) on the magnetization direction is determined by the specific form of the spin-orbit coupling field. By extending a phenomenological model, previously proposed for explaining the main trends of the TAMR in (001) ferromagnet/semiconductor/normal-metal magnetic tunnel junctions (MTJs) [J. Moser {\it et al.}, Phys. Rev. Lett. 99, 056601 (2007)], we provide a unified qualitative description of the TAMR in MTJs with different growth directions. In particular, we predict the forms of the angular dependence of the TAMR in (001),(110), and (111) MTJs with structure inversion asymmetry and/or bulk inversion asymmetry. The effects of in-plane uniaxial strain on the TAMR are also investigated., Comment: 6 pages, 1 figure

Spintronics has attracted wide attention by promising novel functionalities derived from both the electron charge and spin. While branching into new areas and creating new themes over the past years, the principal goals remain the spin and magnetic control of the electrical properties, essentially the I-V characteristics, and vice versa. There are great challenges ahead to meet these goals. One challenge is to find niche applications for ferromagnetic semiconductors, such as GaMnAs. Another is to develop further the science of hybrid ferromagnetic metal/semiconductor heterostructures, as alternatives to all-semiconductor room temperature spintronics. Here we present our representative recent efiorts to address such challenges. We show how to make a digital magnetoresistor by combining two magnetic resonant diodes, or how introducing ferromagnetic semiconductors as active regions in resonant tunneling diodes leads to novel efiects of digital magnetoresistance and of magnetoelectric current oscillations. We also discuss the phenomenon of tunneling anisotropic magnetoresistance in Fe/GaAs junctions by introducing the concept of the spin-orbit coupling field, as an analog of such fields in all-semiconductor junctions. Finally, we look at fundamental electronic and optical properties of GaMnAs by employing reasonable tight-binding models to study disorder efiects., Comment: 13 pages, 7 figures; in the Proceedings of the International Conference on Theoretical Physics'DUBNA-NANO2008'

The effects of the spin-orbit interaction on the tunneling magnetoresistance of ferromagnet/semiconductor/normal metal tunnel junctions are investigated. Analytical expressions for the tunneling anisotropic magnetoresistance (TAMR) are derived within an approximation in which the dependence of the magnetoresistance on the magnetization orientation in the ferromagnet originates from the interference between Bychkov-Rashba and Dresselhaus spin-orbit couplings that appear at junction interfaces and in the tunneling region. We also investigate the transport properties of ferromagnet/semiconductor/ferromagnet tunnel junctions and show that in such structures the spin-orbit interaction leads not only to the TAMR effect but also to the anisotropy of the conventional tunneling magnetoresistance (TMR). The resulting anisotropic tunneling magnetoresistance (ATMR) depends on the absolute magnetization directions in the ferromagnets. Within the proposed model, depending on the magnetization directions in the ferromagnets, the interplay of Bychkov-Rashba and Dresselhaus spin-orbit couplings produces differences between the rates of transmitted and reflected spins at the ferromagnet/seminconductor interfaces, which results in an anisotropic local density of states at the Fermi surface and in the TAMR and ATMR effects. Model calculations for Fe/GaAs/Fe tunnel junctions are presented. Furthermore, based on rather general symmetry considerations, we deduce the form of the magnetoresistance dependence on the absolute orientations of the magnetizations in the ferromagnets., Comment: 17 pages, 10 figures

Spin-orbit coupling induced anisotropies of plasmon dynamics are investigated in two-dimensional semiconductor structures. The interplay of the linear Bychkov-Rashba and Dresselhaus spin-orbit interactions drastically affects the plasmon spectrum: the dynamical structure factor exhibits variations over several decades, prohibiting plasmon propagation in specific directions. While this plasmon filtering makes the presence of spin-orbit coupling in plasmon dynamics observable, it also offers a control tool for plasmonic devices. Remarkably, if the strengths of the two interactions are equal, not only the anisotropy, but all the traces of the linear spin-orbit coupling in the collective response disappear., Comment: 4 figures