Sub-gap states in semiconducting-superconducting nanowire hybrid devices are controversially discussed as potential topologically non-trivial quantum states. One source of ambiguity is the lack of an energetically and spatially well defined tunnel spectrometer. Here, we use quantum dots directly integrated into the nanowire during the growth process to perform tunnel spectroscopy of discrete sub-gap states in a long nanowire segment. In addition to sub-gap states with a standard magnetic field dependence, we find topologically trivial sub-gap states that are independent of the external magnetic field, i.e. that are pinned to a constant energy as a function of field. We explain this effect qualitatively and quantitatively by taking into account the strong spin-orbit interaction in the nanowire, which can lead to a decoupling of Andreev bound states from the field due to a spatial spin texture of the confined eigenstates.
We investigate the properties of a weak link between two Rashba-based superconducting nanowires with geometric misalignment. By applying an external magnetic field the system can be driven into a topological non-trivial regime. We demonstrate that the Josephson current can be modulated in amplitude and sign through the variation of the applied field and, remarkably, via the angle controlling the spin-orbit locking mismatch at the interface of the nanowires. The proposed setup with misaligned coplanar nanowires provides the building block configuration for the manipulation of coherent transport…
We analyze influence of a dimerization on the topological phases of the Rashba nanowire proximitized to a superconducting substrate. We find that periodic alternations of the hopping integral and spin-orbit coupling can lead to band inversion, inducing transition to topologically nontrivial superconducting phase that hosts the Majorana zero-energy modes. This "dimerization-induced topological superconductivity" completely repels the topological phase of the uniform nanowire, whenever they happen to overlap. We provide an analytical justification for this puzzling behavior based on the symmetry…
We theoretically analyze the Andreev bound states and their coupling to external radiation in superconductor-nanowire-superconductor Josephson junctions. We provide an effective Hamiltonian for the junction projected onto the Andreev level subspace and incorporating the effects of nanowire multichannel structure, Rashba spin-orbit coupling, and Zeeman field. Based on this effective model, we investigate the dependence of the Andreev levels and the matrix elements of the current operator on system parameters such as chemical potential, nanowire dimensions, and normal transmission. We show that …
The critical current of a superconductor can depend on the direction of current flow due to magnetochiral anisotropy when both inversion and time-reversal symmetry are broken, an effect known as the superconducting (SC) diode effect. Here, we consider one-dimensional (1D) systems in which superconductivity is induced via the proximity effect. In both topological insulator and Rashba nanowires, the SC diode effect due to a magnetic field applied along the spin-polarization axis and perpendicular to the nanowire provides a measure of inversion symmetry breaking in the presence of a superconducto…
We consider a Rashba nanowire with proximity gap which can be brought into the topological phase by tuning external magnetic field or chemical potential. We study spin and charge of the bulk quasiparticle states when passing through the topological transition for open and closed systems. We show, analytically and numerically, that the spin of bulk states around the topological gap reverses its sign when crossing the transition due to band inversion, independent of the presence of Majorana fermions in the system. This spin reversal can be considered as a bulk signature of topological supercondu…
Recent experiments in semiconductor nanowires with a spin-orbit coupling and proximity-induced superconductivity exhibit signatures of Majorana bound states predicted to exist in the topological phase. In this work we predict that these nanowire systems exhibit unconventional magnetoelectric effects showing a sharp crossover behavior at the topological phase transition. We find that magnetic fields with a component parallel to the spin-orbit field can give rise to currents in equilibrium. Surprisingly, also fields perpendicular to the spin-orbit field may induce currents and can be employed in…
We investigated Pt-induced nanowires on the Si(110) surface using scanning tunneling microscopy (STM) and angle-resolved photoemission (ARP). High resolution STM images show a well-ordered nanowire array of 1.6 nm width and 2.7 nm separation. ARP reveals fully occupied one dimensional (1D) bands with a Rashba-type split dispersion. Local dI/dV spectra further indicate well confined 1D electron channels on the nanowires, whose density of states characteristics are consistent with the Rashba-type band splitting. The observed energy and momentum splitting of the bands are among the largest ever r…
We show anomalous features of Majorana Bound State leakage in the situation where topological Rashba nanowire is dimerized according to the Su-Schrieffer-Heeger (SSH) scenario and an impurity is present at one of the ends of the system. We find that two topological branches: usual, indigenous to Rashba nanowire and dimerized one, existing as a result of SSH dimerization of nanowire, have different asymmetry of spin polarization that can be explained by opposite order of bands taking part in topological transitions. Additionally, introduction of an impurity to the dimerized nanowire influences …
A key concept in the emerging field of spintronics is the gate voltage or electric field control of spin precession via the effective magnetic field generated by the Rashba spin orbit interaction. Here, we demonstrate the generation and tuning of electric field induced Rashba spin orbit interaction in InAs nanowires where a strong electric field is created either by a double gate or a solid electrolyte surrounding gate. In particular, the electrolyte gating enables six-fold tuning of Rashba coefficient and nearly three orders of magnitude tuning of spin relaxation time within only 1 V of gate …
We study theoretically the detection of the topological phase transition occurring in Rashba nanowires with proximity-induced superconductivity using a quantum dot. The bulk states lowest in energy of such a nanowire have a spin polarization parallel or antiparallel to the applied magnetic field in the topological or trivial phase, respectively. We show that this property can be probed by the quantum dot created at the end of the nanowire by external gates. By tuning one of the two spin-split levels of the quantum dot to be in resonance with nanowire bulk states, one can detect the spin polari…
We study the nuclear spin relaxation in a ballistic nanowire with hyperfine and Rashba spin-orbit interactions (SOI) and in the presence of magnetic field and electron interactions. The relaxation rate shows pronounced peaks as function of magnetic field and chemical potential due to van Hove singularities in the Rashba bands. As a result, the regimes of weak and strong SOIs can be distinguished by the number of peaks in the rate. The relaxation rate increases with increasing magnetic field if both Rashba subbands are occupied, whereas it decreases if only the lowest one is occupied.
By modeling a Rashba nanowire contacted to leads via an inhomogeneous spin-orbit coupling profile, we investigate the equilibrium properties of the spin sector when a uniform magnetic field is applied along the nanowire axis. We find that the interplay between magnetic field and Rashba coupling generates a spin current, polarised perpendicularly to the applied field and flowing through the nanowire even at equilibrium. In the nanowire bulk such effect persists far beyond the regime where the nanowire mimics the helical states of a quantum spin Hall system, while in the leads the spin current i…
We study an analytical model of a Rashba nanowire that is partially covered by and coupled to a thin superconducting layer, where the uncovered region of the nanowire forms a quantum dot. We find that, even if there is no topological superconducting phase possible, there is a trivial Andreev bound state that becomes pinned exponentially close to zero energy as a function of magnetic field strength when the length of the quantum dot is tuned with respect to its spin-orbit length such that a resonance condition of Fabry-Perot type is satisfied. In this case, we find that the Andreev bound state …
We report on $\vec{k}\cdot\vec{p}$ calculations of Rashba spin-orbit coupling controlled by external gates in InAs/InAsP core-shell nanowires. We show that charge spilling in the barrier material allows for a stronger symmetry breaking than in homoegenous nano-materials, inducing a specific interface-related contribution to spin-orbit coupling. Our results qualitatively agree with recent experiments [S. Futhemeier \textit{et al.}, Nat. Commun. \textbf{7}, 12413 (2016)] and suggest additional wavefunction engineering strategies to enhance and control spin-orbit coupling.
We consider periodically-driven arrays of weakly coupled wires with conduction and valence bands of Rashba type and study the resulting Floquet states. This non-equilibrium system can be tuned into non-trivial phases such as of topological insulators, Weyl semimetals, and dispersionless zero-energy edge mode regimes. In the presence of strong electron-electron interactions, we generalize these regimes to the fractional case, where elementary excitations have fractional charges $e/m$ with $m$ being an odd integer.
The local spin polarisation (LSP) of electrons in two typical semiconductor nanowires under the modulation of Rashba spin-orbit interaction (SOI) is investigated theoretically. The influence of both the SOI- and structure-induced bound states on the LSP is taken into account via the spin-resolved lattice Green function method. It is discovered that high spin-density islands with alternative signs of polarisation are formed inside the nanowires due to the interaction between the bound states and the Rashba effective magnetic field. Further study shows that the spin-density islands caused by the…
We study a periodically driven nanowire with Rashba-like conduction and valence bands in the presence of a magnetic field. We identify topological regimes in which the system hosts zero-energy Majorana fermions. We further investigate the effect of strong electron-electron interactions that give rise to parafermion zero energy modes hosted at the nanowire ends. The first setup we consider allows for topological phases by applying only static magnetic fields without the need of superconductivity. The second setup involves both superconductivity and time-dependent magnetic fields and allows one …
We analyze, analytically and numerically, a periodically driven Rashba nanowire proximity coupled to an $s$-wave superconductor using bosonization and renormalization group analysis in the regime of strong electron-electron interactions. Due to the repulsive interactions, the superconducting gap is suppressed, whereas the Floquet Zeeman gap is enhanced, resulting in a higher effective value of $g$-factor compared to the non-interacting case. The flow equations for different coupling constants, velocities, and Luttinger-liquid parameters explicitly establish that even for small initial values o…
We consider a semiconducting nanowire with Rashba spin-orbit interaction subjected to a magnetic field and in the presence of strong electron-electron interactions. When the ratio between Fermi and Rashba momenta is tuned to $1/2$, two competing resonant multi-particle scattering processes are present simultaneously and the interplay between them brings the system into a gapless critical parafermion phase. This critical phase is described by a self-dual sine-Gordon model, which we are able to map explicitly onto the low-energy sector of the $\mathbb{Z}_4$ parafermion clock chain model. Finally…
We demonstrate the appearance of zero-energy bound states satisfying the $\mathbb{Z}_4$ parafermionic algebra in interacting quantum wires with Rashba spin-orbit coupling and proximity-induced superconductivity. The fourfold degeneracy of these states is protected by time-reversal symmetry and fermion-parity conservation, and leads to an $8 π$ periodicity of the Josephson current due to the tunneling of fractionalized excitations with charge $e/2$. Even in the presence of perturbations, we propose that this periodicity will remain visible in driven, current-biased Shapiro step measurements on …
Rashba nanowires in a magnetic field exhibit a helical regime when the spin-orbit momentum is close to the Fermi momentum, k_F \approx k_{SO}. We show that this regime is characterized by a strongly anisotropic electron spin susceptibility, with an exponentially suppressed signal along one direction in spin space, and that there are no low frequency spin fluctuations along this direction. Since the spin response in the gapless regime k_F \not \approx k_{SO} has a power law behavior in all three directions, spin measurements provide a signature of the helical regime that complements spin-insens…
We investigate the influence of Rashba spin-orbit coupling in a parabolic nanowire modulated by longitudinal periodic potential. The modulation potential can be obtained from realistically grown supperlattices (SLs). Our study shows that the Rashba spin-orbit interaction induces the level crossing point in the parabolic nanowire SLs. We estimate large anticrossing width (approximately 117 $μeV$) between singlet-triplet states. We study the phonon and electromagnetic field mediated spin transition rates in the parabolic nanowire SLs. We report that the phonon mediated spin transition rate is se…
We study theoretically transport through a semiconducting nanowire (NW) in the presence of Rashba spin orbit interaction, uniform magnetic field, and spatially modulated magnetic field. The system is fully gapped, and the interplay between the spin orbit interaction and the magnetic fields leads to fractionally charged fermion (FF) bound states of Jackiw-Rebbi type at each end of the nanowire. We investigate the transport and noise behavior of a N/NW/N system, where the wire is contacted by two normal leads (N), and we look for possible signatures that could help in the experimental detection …
A key concept in the field of semiconductor spintronics is an electric field control of spins via the spin-orbit coupling (SOC) and the SOC strength governs efficiency of this control. We propose a new approach that allows the experimental determination of the Rashba SOC strength for ballistic InAs nanowires. The energy spectrum and ballistic transport of carriers through the nanowire with surface two-dimensional electron gas (2DEG) in a homogeneous magnetic field are studied. A general formula for the linear-response one-dimensional ballistic thermopower is derived in the case of complex subb…
We present numerical calculations of the ballistic spin-transport properties of quasi-one-dimensional wires in the presence of the spin-orbit (Rashba) interaction. A tight-binding analog of the Rashba Hamiltonian which models the Rashba effect is used. By varying the robustness of the Rashba coupling and the width of the wire, weak and strong coupling regimes are identified. Perfect electron spin-modulation is found for the former regime, regardless of the incident Fermi energy and mode number. In the latter however, the spin-conductance has a strong energy dependence due to a nontrivial subba…
We use $\vec{k}\cdot\vec{p}$ theory to estimate the Rashba spin-orbit coupling (SOC) in large semiconductor nanowires. We specifically investigate GaAs- and InSb-based devices with different gate configurations to control symmetry and localization of the electron charge density. We explore gate-controlled SOC for wires of different size and doping, and we show that in high carrier density SOC has a non-linear electric field susceptibility, due to large reshaping of the quantum states. We analyze recent experiments with InSb nanowires in light of our calculations. Good agreement is found with S…
We analyze Andreev bound states (ABSs) that form in normal sections of a Rashba nanowire that is only partially covered by a superconducting layer. These ABSs are localized close to the ends of the superconducting section and can be pinned to zero energy over a wide range of magnetic field strengths even if the nanowire is in the non-topological regime. For finite-size nanowires (typically $\lesssim 1$ $μ$m in current experiments), the ABS localization length is comparable to the length of the nanowire. The probability density of an ABS is therefore non-zero throughout the nanowire and differe…
We theoretically investigate a practically realizable Floquet topological superconductor model, based on a one-dimensional Rashba nanowire and proximity induced $s$-wave superconductivity in the presence of a Zeeman field. The driven system hosts regular $0$- and anomalous $π$-Majorana end modes~(MEMs). By tuning the chemical potential and the frequency of the drive, we illustrate the generation of multiple MEMs in our theoretical set up. We utilize the chiral symmetry operator to topologically characterize these MEMs via a dynamical winding number constructed out of the periodized evolution o…
We analyze the effects of electron-electron interactions and disorder on a Rashba double-nanowire setup coupled to an s-wave superconductor, which has been recently proposed as a versatile platform to generate Kramers pairs of Majorana bound states in the absence of magnetic fields. We identify the regime of parameters for which these Kramers pairs are stable against interaction and disorder effects. We use bosonization, perturbative renormalization group, and replica techniques to derive the flow equations for various parameters of the model and evaluate the corresponding phase diagram with t…
We study the effects of spin-orbit interaction (SOI) on the current-induced motion of a magnetic (Bloch) domain wall in ultrathin ferromagnetic nanowires. The conspiracy of spin relaxation and SOI is shown to generate a novel strong nonequilibrium Rashba field, which is dominant even for moderate SOI. This field causes intricate spin precession and a transition from translatory to oscillatory wall dynamics with increasing SOI. We show that current pulses of different lengths can efficiently be used to control the domain wall motion.
The spin precession in a cylindrical semiconductor nanowire due to Rashba spin-orbit coupling has been investigated theoretically using an InAs nanowire containing a surface two-dimensional electron gas as a model. The eigenstates, energy-momentum dispersion, and the energy-magnetic field dispersion relation are determined by solving the Schrödinger equation in a cylindrical symmetry The combination of states with the same total angular momentum but opposite spin orientation results in a periodic modulation of the axial spin component along the axis of the wire. Spin-precession about the wires…
We propose a scheme to generate pairs of time-reversal invariant parafermions. Our setup consists of two quantum wires with opposite Rashba spin orbit interactions coupled to an $s$-wave superconductor, in the presence of electron-electron interactions. The zero-energy bound states localized at the wire ends arise from the interplay between two types of proximity induced superconductivity: the usual intrawire superconductivity and the interwire superconductivity due to crossed Andreev reflections. If the latter dominates, which is the case for strong electron-electron interactions, the system …
We study hybrid superconducting-semiconducting nanowires in the presence of Rashba spin-orbit interaction as well as helical magnetic fields. We show that the interplay between them leads to a competition of phases with two topological gaps closing and reopening, resulting in unexpected reentrance behavior. Besides the topological phase with localized Majorana fermions (MFs) we find new phases characterized by fractionally charged fermion (FF) bound states of Jackiw-Rebbi type. The system can be fully gapped by the magnetic fields alone, giving rise to FFs that transmute into MFs upon turning …
Semiconductor Rashba nanowires are quasi-one dimensional systems that have large spin-orbit (SO) coupling arising from a broken inversion symmetry due to an external electric field. There exist parametrized multiband models that can describe accurately this effect. However, simplified single band models are highly desirable to study geometries of recent experimental interest, since they may allow to incorporate the effects of the low dimensionality and the nanowire electrostatic environment at a reduced computational cost. Commonly used conduction band approximations, valid for bulk materials,…
Tunneling experiment is a key technique for detecting Majorana fermion in solid state systems. We use Keldysh non-equilibrium Green function method to study multi-lead tunneling in superconducting nanowire with Rashba and Dresselhaus spin-orbit couplings. A zero-bias \textit{dc} conductance peak appears in our setup which signifies the existence of Majorana fermion and is in accordance with previous experimental results on InSb nanowire. Interestingly, due to the exotic property of Majorana fermion, there exists a hole transmission channel which makes the currents asymmetric at the left and ri…
The experimental assessment of the strength ($α_R$) of the Rashba spin-orbit coupling is rather indirect and involves the measurement of the spin relaxation length from magnetotransport, together with a model of weak antilocalization. The analysis of the spin relaxation length in nanowires, however, clouds the experimental assessment of the $α_R$ and leads to the prevailing belief that it can be tuned freely with electric field--a central tenant of spintronics. Here, we report direct theory of $α_R$ leading to atomistic calculations of the spin band structure of InAs nanowires upon application…
We study topological phase transitions in one dimensional (1-D) Rashba nanowire under a spatially varying Zeeman field when coupled to an $s$-wave superconductor substrate. We show that this system supports both Majorana bound states (MBS) and fractionally charged bound states (FBS) of Jackiw-Rebbi type. By disassembling Zeeman Hamiltonian into multiple helical components, we find that each helical component is relating to a corresponding topological region, characterized by the emergence of MBS. FBS arises in the overlapping gapped area created by any two helical components with topologically…
Suspended nanowires are shown to provide mechanically-controlled coherent mixing/splitting of the spin states of transmitted electrons, caused by the Rashba spin-orbit interaction. The sensitivity of the latter to mechanical bending makes the wire a tunable nano-electro-mechanical (NEM) weak link between reservoirs. When the reservoirs are populated with misbalanced "spin up/down" electrons, the wire becomes a source of split spin currents, which are not associated with electric charge transfer and which do not depend on temperature or driving voltages. The mechanical vibrations of the bended …
We study the lifetime of topological qubits based on Majorana bound states hosted in a one-dimensional Rashba nanowire (NW) with proximity-induced superconductivity and non-uniform chemical potential needed for manipulation and read-out. If nearby gates tune the chemical potential locally so that part of the NW is in the trivial phase, Andreev bound states (ABSs) can emerge which are localized at the interface between topological and trivial phases with energies significantly less than the gap. The emergence of such subgap states strongly decreases the Majorana qubit lifetime at finite tempera…
A partially gapped spectrum due to the application of a magnetic field is one of the main probes of Rashba spin-orbit coupling in nanowires. Such a "helical gap" manifests itself in the linear conductance, as well as in dynamic response functions such as the spectral function, the structure factor, or the tunnelling density of states. In this paper, we investigate theoretically the signature of the helical gap in these observables with a particular focus on the interplay between Rashba spin-orbit coupling and electron-electron interactions. We show that in a quasi-one-dimensional wire, interac…
We consider a single electron confined within a quantum wire in a system of two electrostatically-induced QDs defined by nearby gates. The time-varying electric field, of single GHz frequency, perpendicular to the quantum wire, is used to induce the Rashba coupling and enable spin-dependent resonant tunneling of the electron between two adjacent potential wells with fidelity over 99.5%. This effect can be used for the high fidelity all-electrical electron-spin initialization or readout in the spin-based quantum computer. In contrast to other spin initialization methods, our technique can be pe…
Indium arsenide (InAs) nanowires (NWs) are a promising platform to fabricate quantum electronic devices, among others they have strong spin-orbit interaction (SOI). The controlled tuning of the SOI is desired in spin based quantum devices. In this study we investigate the possibility of tuning the SOI by electrostatic field, which is generated by a back gate and two side gates placed on the opposite sides of the NW. The strength of the SOI is analyzed by weak anti-localization effect. We demonstrate that the strength of SOI can be strongly tuned by a factor of 2 with the electric field across …
Theoretical studies have shown that Majorana bound states can be induced at the ends of a one dimensional wire, a phenomenon possible due to the interplay between s-wave superconductivity, spin-orbit coupling, and an external magnetic field. These states have been observed in superconductor-semiconductor hybrid nanostructures in the presence of a Zeeman field, and in the limit of a low density of particles. In this paper, we demonstrate and discuss the possibility of the emergence of Majorana bound states in a superconducting Rashba nanowire deposited on an antiferromagnetically ordered surfac…
We prove that curvature effects in low-dimensional nanomaterials can promote the generation of topological states of matter by considering the paradigmatic example of quantum wires with Rashba spin-orbit coupling, which are periodically corrugated at the nanometer scale. The effect of the periodic curvature generally results in the appearance of insulating phases with a corresponding novel butterfly spectrum characterized by the formation of fine measure complex regions of forbidden energies. When the Fermi energy lies in the gaps, the system displays localized end states protected by topology…
We study the phenomenon of adiabatic quantum charge pumping in systems supporting fractionally charged fermionic bound states, in two different setups. The first quantum pump setup consists of a charge-density-modulated quantum wire, and the second one is based on a semiconducting nanowire with Rashba spin-orbit interaction, in the presence of a spatially oscillating magnetic field. In both these quantum pumps transport is investigated in a N-X-N geometry, with the system of interest (X) connected to two normal-metal leads (N), and the two pumping parameters are the strengths of the effective …
Recent experiments show the possibility of realization of the Majorana quasiparticles at the end of the low dimensional structures. In this type of systems, interplay between spin orbit coupling, superconductivity and magnetic field leads to the emergence of the Majorana bound states in the topologically non-trivial phase. Here, we study the nanowire located partially at the normal and superconducting base, using microscopic model of this structure and the Bogoliubov--de~Gennes technique. We discuss the possibility of the leakage of the Majorana bound state, located at the part above supercond…
We study theoretically the low-energy hole states in Si, Ge, and Ge/Si core/shell nanowires (NWs). The NW core in our model has a rectangular cross section, the results for a square cross section are presented in detail. In the case of Ge and Ge/Si core/shell NWs, we obtain very good agreement with previous theoretical results for cylindrically symmetric NWs. In particular, the NWs allow for an unusually strong and electrically controllable spin-orbit interaction (SOI) of Rashba type. We find that the dominant contribution to the SOI is the "direct Rashba spin-orbit interaction" (DRSOI), which…
The theoretical description has been proposed for the operation of the spin transistor in the gate-controlled InAs nanowire. The calculated current-voltage characteristics show that the current flowing from the source (spin injector) to the drain (spin detector) oscillates as a function of the gate voltage, which results from the precession of the electron spin caused by the Rashba spin-orbit interaction in the vicinity of the gate. We have studied two operation modes of the spin transistor: (A) the ideal operation mode with the full spin polarization of electrons in the contacts, the zero tem…
We study analytically and numerically the renormalization of the $g$-factor in semiconducting Rashba nanowires (NWs), consisting of a normal and superconducting section. If the potential barrier between the sections is high, a quantum dot (QD) is formed in the normal section. For harmonic (hard-wall) confinement, the effective $g$-factor of all QD levels is suppressed exponentially (power-law) in the product of the spin-orbit interaction (SOI) wavevector and the QD length. If the barrier between the two sections is removed, the $g$-factor of the emerging Andreev bound states is suppressed less…
We study Josephson junctions made of semiconducting nanowires with Rashba spin-orbit coupling, where superconducting correlations are induced by the proximity effect. In the presence of a suitably directed magnetic field, the system displays the anomalous Josephson effect: a nonzero supercurrent in the absence of a phase bias between two superconductors. We show that this anomalous current can be increased significantly by tuning the nanowire into the helical regime. In particular, in a short junction, a large anomalous current is a signature for topologically nontrivial superconductivity in t…
