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9 pages, 7 figures, PRB accepted, The conductance of electrostatic wire junctions in bilayer graphene, classified as trivial-trivial or trivial-topological regarding the confinement character on each junction side, is calculated. The topological side always corresponds to a kink-antikink system, as required for a proper connection with a trivial side. We report a conductance quench of the trivial-topological junction, with a conductance {\it near} quantization to $4e^2/h$, which is only half of the maximum value allowed by the Chern number of a kink-antikink system. The analysis allowed us to uncover the existence of a chiral edge mode in the trivial wire under quite general conditions. A double junction, trivial-topological-trivial, displays periodic Fano-like conductance resonances (dips or peaks) induced by the created topological loop., We acknowledge support from Grants No. MDM2017-0711 and No. PID2020-117347GB-I00 funded by MCIN/AEI/10.13039/501100011033, and Grant No. PDR2020-12 funded by GOIB.

This article also appears in: 60 years of pss Hot Topic: Magnetic Materials., Herein, two different types of confinement in bilayer graphene by top and bottom gating with symmetrical microelectrodes are discussed and compared. Trivial confinement corresponds to the same polarity of all top gates, which is opposed to that of all bottom ones. Topological confinement requires the polarity of part of the top–bottom pairs of gates to be reversed. It is shown that the main qualitative difference between trivial and topological bound states manifests itself in the magnetic field dependence. The finding is illustrated with an explicit calculation of the energy spectrum for quantum dots and rings. Trivial confinement shows bunching of levels into degenerate Landau bands, with a non-centered gap, while topological confinement shows no field-induced gap and a sequence of state branches always crossing zero energy., The authors acknowledge support from AEI (Spain) Grant no. PID2020-117347GB-I00, MINECO/AEI/FEDER María de Maeztu Program for Units of Excellence MDM2017-0711, and GOIB Grant no. PDR2020-12.

We investigate the electronic confinement in bilayer graphene by topological loops of different shapes. These loops are created by lateral gates acting via gap inversion on the two graphene sheets. For large-area loops the spectrum is well described by a quantization rule depending only on the loop perimeter. For small sizes, the spectrum depends on the loop shape. We find that zero-energy states exhibit a characteristic pattern that strongly depends on the spatial symmetry. We show this by considering loops of higher to lower symmetry (circle, square, rectangle and irregular polygon). Interestingly, magnetic field causes valley splittings of the states, an asymmetry between energy reversal states, flux periodicities and the emergence of persistent currents., We acknowledge support from Grant No. PID2020-117347GB-I00 funded by MCIN/AEI/10.13039/501100011033, MINECO/AEI/FEDER María de Maeztu Program for Units of Excellence MDM2017-0711, and GOIB Grant No. PDR2020-12.

We calculate the linear conductance of a two-dimensional electron-gas-based junction between a normal semiconductor section and a hybrid semiconductor-superconductor section, under perpendicular magnetic field. We consider two important terms often neglected in the literature, the magneto-orbital and transverse Rashba spin-orbit. The strong orbital effect due to the magnetic field yields topological phase transitions to nontrivial phases hosting Majorana modes in the hybrid section. The presence of a potential barrier at the junction interface reveals the Majorana phases as quantized plateaus of high conductance, for low values of the chemical potential. In wide junctions (or large chemical potentials) the phase transitions occur at low magnetic fields but the magneto-conductance becomes anomalous and lacks clearly quantized plateaus., We acknowledge support from MINECO (Spain) Grant No. MAT2017-82639, MINECO/AEI/FEDER María de Maeztu Program for Units of Excellence MDM2017-0711, and from EPSRC (UK) for MQIC Grant No. EP/S019324/1.

We review applications of complex band structure theory to describe Majorana states in nanowires and nanowire junctions. The dimensionality of the considered wires is gradually increased, from strictly 1D to quasi-1D with one and two transverse dimensions. The complex wave number analysis is applied to two main types of Majorana modes: end states in hybrid semiconductor wires and chiral edge states in hybrid wires of quantum-anomalous Hall insulators. In topological NS and NSN junctions with Majorana modes conductance oscillations and spatial distributions of density and current are described. Finally, the optical absorption in finite systems with both types of Majorana modes is considered. Graphical abstract: [Figure not available: see fulltext.]., We acknowledge support from MINECO (Spain), grant MAT2017-82639.

The magnetic-induced orbital motion of quasiparticles affects the conductance properties of a hybrid strip of a quantum-anomalous-Hall topological material with induced superconductivity. We elucidate the scenario of topological normal-superconducting-normal ideal junctions in the presence of orbital magnetic motion, showing how it leads to a halved quantized conductance 0.5e /h even in the absence of Majorana modes. For vanishing energy, the magnetic orbital effect favors Fermionic charged modes with finite wave numbers, in contrast to chiral Majorana modes that are chargeless modes with the vanishing wave number. The bias sensitivity of the 0.5 conductance plateau allows distinguishing the two cases. Conductance oscillations due to backscattering interference are absent in the charged Fermion case., This work was funded by MINECO (Spain), Grant No. MAT2017-82639.

We calculate density and current spatial distributions of a 2D model junction between a normal QAH contact and a superconducting QAH region hosting propagating (chiral) Majorana modes. We use a simplified Hamiltonian describing the spatial coupling of the modes on each side of the junction, as well as the related junction conductance. We study how this coupling is affected by orbital effects caused by an external magnetic field., 11 pages, 8 figures, FQMT'17 proceedings

We predict conductance oscillations in a quantum anomalous Hall two-dimensional strip having a superconducting region of length Lx with a chiral Majorana mode. These oscillations require a finite transverse extension of the strip Ly of a few microns or less. Measuring the conductance periodicity with Lx and a fixed bias, or with bias and a fixed Lx, yields the speed of the chiral Majorana mode. The physical mechanism behind the oscillations is the interference between backscattered chiral modes from the second to first interface of the normal-superconductor-normal double junction. The interferometer effect is enhanced by the presence of side barriers., This work was funded by MINEICO (Spain), Grant No. MAT2017-82639.

Background: Majorana states in condensed matter devices may be of a localized nature, such as in hybrid semiconductor/superconductor nanowires, or chirally propagating along the edges such as in hybrid 2D quantum-anomalous Hall/superconductor structures.Results: We calculate the circular dichroism due to chiral Majorana states in a hybrid structure made of a quantum-anomalous Hall insulator and a superconductor. The optical absorption of chiral Majorana states is characterized by equally spaced absorption peaks of both positive and negative dichroism. In the limit of a very long structure (a 2D ribbon) peaks of a single sign are favored.Conclusion: Circular-dichroism spectroscopy of chiral Majorana states is suggested as a relevant probe for these peculiar states of topological matter.

We consider core-shell nanowires with conductive shell and insulating core and with polygonal cross section. We investigate the implications of this geometry on Majorana states expected in the presence of proximity-induced superconductivity and an external magnetic field. A typical prismatic nanowire has a hexagonal profile, but square and triangular shapes can also be obtained. The low-energy states are localized at the corners of the cross section, i.e., along the prism edges, and are separated by a gap from higher energy states localized on the sides. The corner localization depends on the details of the shell geometry, i.e., thickness, diameter, and sharpness of the corners. We study systematically the low-energy spectrum of prismatic shells using numerical methods and derive the topological phase diagram as a function of magnetic field and chemical potential for triangular, square, and hexagonal geometries. A strong corner localization enhances the stability of Majorana modes to various perturbations, including the orbital effect of the magnetic field, whereas a weaker localization favorizes orbital effects and reduces the critical magnetic field. The prismatic geometry allows the Majorana zero-energy modes to be accompanied by low-energy states, which we call pseudo Majorana, and which converge to real Majoranas in the limit of small shell thickness. We include the Rashba spin-orbit coupling in a phenomenological manner, assuming a radial electric field across the shell., This work was partially financed by Reykjavik University and the Icelandic Research Fund. L.S. was supported by Grant No. FIS2014-52564 (Mineco, Spain). T.D.S. was supported in part by NSF DMR-1414683.

We calculate the electromagnetic absorption cross section of long and narrow nanowires, in the so-called quasi-1D limit. We consider only two transverse bands and compute the dipole absorption cross section taking into account quasiparticle transitions from negative to positive energy eigenstates of the Bogoliubov-de Gennes Hamiltonian. The presence of the zero energy (Majorana) state manifests in the different absorption spectra for x (parallel) and y (transverse) polarizations of the electromagnetic field. In the y -polarized case, the Majorana state causes a low energy absorption plateau extending from mid-gap up to full-gap energy. Increasing further the energy, the plateau is followed by a region of enhanced absorption due to transitions across the full gap. For x polarization the low energy absorption plateau is not observed. (© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)., This work was funded by MINECO-Spain (grant FIS2011-23526), CAIB-Spain (Conselleria d’Educació, Cultura i Universitats) and FEDER. We hereby acknowledge the PhD grant provided by the University of the Balearic Islands.

We calculate current and density distributions in stripe (2D planar) junctions between normal and Majorana nanowires having a finite (y) transverse length. In presence of a magnetic field with vertical and in-plane components, the y-symmetry of the charge current distribution in the normal lead changes strongly across the Majorana phase transition: from center-symmetric if a Majorana mode is present to laterally-shifted (as expected by the Hall effect) if the field is tilted such as to destroy the Majorana mode due to the projection rule. We compare quasi-particle and charge distributions of current and density, as well as spin magnetizations. The Majorana mode causes opposite spin accumulations on the transverse sides of the junction and the emergence of a spin current., This work was funded by MINECO-Spain, grant FIS2014-52564. Discussions with C. Beenakker, R. Sánchez and G. Finkelstein are gratefully acknowledged. J.O. acknowledges a PhD grant from the University of the Balearic Islands.

We study Coulomb interacting electrons confined in polygonal quantum rings. We focus on the interplay of localization at the polygon corners and Coulomb repulsion. Remarkably, the Coulomb repulsion allows the formation of in-gap states, i.e., corner-localized states of electron pairs or clusters shifted to energies that were forbidden for non-interacting electrons, but below the energies of corner-side-localized states. We specify conditions allowing optical excitation to those states., This work was financed by the Research Fund of the University of Iceland and the Icelandic Research Fund.

We discuss a model of random segmented wire, with linear segments of two-dimensional wires joined by circular bends. The joining vertices act as scatterers on the propagating electron waves. The model leads to resonant Anderson localization when all segments are of similar length. The resonant behavior is present with one and also with several propagating modes. The probability distributions evolve from diffusive to localized regimes when increasing the number of segments in a similar way for long and short localization lengths. As a function of the energy, a finite segmented wire typically evolves from localized to diffusive to ballistic behavior in each conductance plateau., This work was funded by MINECO (Spain) (Grant No. FIS2014-52564), CAIB (Spain) (Conselleria d'Educació, Cultura i Universitats), and FEDER.

We consider a quantum wire with a finite region of localized spin-orbit interaction of the Rashba type. For energies above the onset of the second conductance plateau, we find a spin polarization of the transmitted current when a beam of unpolarized electrons is injected into the Rashba region. Our numerical simulations show that the amount of polarization can be tuned with the Rashba coupling strength, thus offering an all-electrical method to generate spin polarized currents. With the aid of a simplified model, we discuss that the polarization effect originates from the interference between subband states with different energy and opposite spin directions (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

We calculate the local quasi-particle current of a Majorana state in a planar hybrid (superconductor-semiconductor) nanowire. In absence of perpendicular components of the magnetic field the current flows in circular trajectories without a preferred orientation. On the other hand, when a perpendicular component of the magnetic field is present the quasi-particle current circulates surrounding the Majorana density peak with an orientation established by the magnetic field., This work was funded by MINECO-Spain (grant FIS2011-23526), CAIB-Spain (Conselleria d'Educació, Cultura i Universitats) and FEDER. We hereby acknowledge the PhD grant provided by the University of the Balearic Islands.

© 2015 American Physical Society. We investigate theoretically polygonal quantum rings and focus mostly on the triangular geometry where the corner effects are maximal. Such rings can be seen as short core-shell nanowires, a generation of semiconductor heterostructures with multiple applications. We show how the geometry of the sample determines the electronic energy spectrum, and also the localization of electrons, with effects on the optical absorption. In particular, we show that irrespective of the ring shape low-energy electrons are always attracted by corners and are localized in their vicinity. The absorption spectrum in the presence of a magnetic field shows only two peaks within the corner-localized state domain, each associated with different circular polarization. This picture may be changed by an external electric field which allows previously forbidden transitions, and thus enables the number of corners to be determined. We show that polygonal quantum rings allow absorption of waves from distant ranges of the electromagnetic spectrum within one sample., This work was financially supported by the Research Fund of the University of Iceland, the Nordic network NANOCONTROL, project No.: P-13053, and by MINECO-Spain (Grant No. FIS2011-23526).

© 2015 IOP Publishing Ltd. We calculate the cross section for the electromagnetic absorption of planar 2D Majorana nanowires. The electromagnetic field is described in the dipole approximation. We discuss the signatures on the cross section of a near-zero-energy mode. A low energy peak for transverse polarization, absent in the longitudinal one, reveals the presence of the Majorana-like state. This peak is relatively robust against the thermal smearing of the level occupations. We consider the influence of optical masks hiding parts of the nanowire from the radiation., This work was funded by MINECO-Spain (grant FIS2011-23526), CAIB-Spain (Conselleria d'Educació, Cultura i Universitats) and FEDER.

The influence of the spin–orbit (SO) coupling on the far infrared response of quantum dots is investigated as a function of the intensity of the coupling, the applied magnetic field and the dot deformation. Analytical results are obtained in the limit of weak magnetic field and SO coupling intensity. Interaction effects are numerically studied within the time-dependent local-spin-density theory using a two-component spinorial formalism.

© 2015 American Physical Society. We consider a spin-orbit-coupled two-dimensional electron system under the influence of a thermal gradient externally applied to two attached reservoirs. We discuss the generated voltage bias (charge Seebeck effect), spin bias (spin Seebeck effect), and magnetization-dependent thermopower (magneto-Seebeck effect) in the ballistic regime of transport at linear response. We find that the charge thermopower is an oscillating function of both the spin-orbit strength and the quantum well width. We also observe that it is always negative for normal leads. We carefully compare the exact results for the linear response coefficients and a Sommerfeld approximation. When the contacts are ferromagnetic, we calculate the spin-resolved Seebeck coefficient for parallel and antiparallel magnetization configuration. Remarkably, the thermopower can change its sign by tuning the Fermi energy. This effect disappears when the Rashba coupling is absent. Additionally, we determine the magneto-Seebeck ratio, which shows dramatic changes in the presence of a the Rashba potential., This work has been supported by MINECO under Grant No. FIS2011-23526.

© 2015 American Physical Society. The Majorana phase boundaries in planar 2D hybrid (semiconductor-superconductor) nanowires are modified by orbital effects due to off plane magnetic components. We show that Majorana zero modes survive sizable vertical field tiltings, uncovering a remarkable phase diagram. Analytical expressions of the phase boundaries are given for the strong orbital limit. These phase boundaries can be fulfilled with attainable setups, such as an InAs nanowire of 150nm in transverse width., This work was funded by MINECO-Spain (Grant No. FIS2011-23526), CAIB-Spain (Conselleria d'Educació, Cultura i Universitats), and FEDER.

We calculate the quantum states of regular polygons made of 1D quantum wires treating each polygon vertex as a scatterer. The vertex scattering matrix is analytically obtained from the model of a circular bend of a given angle of a 2D nanowire. In the single mode limit the spectrum is classified in doublets of vanishing circulation, twofold split by the small vertex reflection, and singlets with circulation degeneracy. Simple analytic expressions of the energy eigenvalues are given. It is shown how each polygon is characterized by a specific spectrum., C.E. gratefully acknowledges a SURF@IFISC fellowship. This work was funded by MINECO-Spain (Grant FIS2011-23526), CAIB-Spain (Conselleria d’Educació, Cultura i Universitats) and FEDER.

The characteristics of the breathing modes of 2-D dots are theoretically investigated as a function of the dot elliptical deformation and intensity of an applied perpendicular magnetic field. Analytic results obtained by neglecting the interelectron Coulomb interaction are compared with numerical results including interactions within the time-dependent local spin density approximation. The existence of four characteristic E0 modes and the evolution of their oscillator strength with both deformation and magnetic field are discussed. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002

The moment of inertia of deformed quantum dots and its experimental relevance in relation to the dot spectroscopic features is theoretically investigated. A strong link to the low-energy orbital current mode that manifests in the magnetic dipole (M1) spectrum is stressed. The moment of inertia is obtained by solving the cranked Kohn–Sham equations within the local-spin-density approximation and the results discussed in comparison with the predictions of an analytical non-interacting model. The results as a function of deformation and size indicate that the existence of spin transitions in the dot ground state has an important effect on the moment of inertia.

The transverse dipole spin response of elliptic quantum dots is analysed as a function of an applied static magnetic field and dot deformation. Interaction effects are numerically studied within the time-dependent local-spin-density theory using a two-component spinorial formalism.

We show that the magnetoconductance oscillations of laterally-confined two-dimensional (2D) normal–superconductor (NS) junctions are completely suppressed when the superconductor side enters a topological phase. This suppression can be attributed to the modification of the vortex structure of local currents at the junction caused by the topological transition of the superconductor. The two regimes (with and without oscillations) could be seen in a semiconductor 2D junction with a cleaved-edge geometry, one of the junction arms having proximitized superconductivity. We predict similar oscillations and suppression as a function of the Rashba coupling. The oscillation suppression is robust against differences in chemical potential and phases of lateral superconductors.

We investigate the effects that a tilting of the magnetic field from the parallel direction has on the states of a one-dimensional Majorana nanowire. Particularly, we focus on the conditions for the existence of Majorana zero modes, uncovering an analytical relation (the projection rule) between the field orientation relative to the wire, its magnitude, and the superconducting parameter of the material. The study is then extended to junctions of nanowires, treated as magnetically inhomogeneous straight nanowires composed of two homogeneous arms. It is shown that their spectrum can be explained in terms of the spectra of two independent arms. Finally, we investigate how the localization of the Majorana mode is transferred from the magnetic interface at the corner of the junction to the end of the nanowire when increasing the arm length. © 2014 American Physical Society., This work was funded by MINECO-Spain (Grant No. FIS2011-23526), CAIB-Spain (Conselleria d'Educació, Cultura i Universitats), and FEDER.

We present a theoretical analysis of the electronic structure and the linear-response dynamics for two-dimensional rings in a perpendicular magnetic field containing two electrons. The exact lower eigenstates are found by numerically solving the Schrodinger equation and are used to build the pertubative dipole response. We show the equivalence of this technique with the integration in real time used in a previous work. Comparison with the predictions of local spin density approximation theory is also done. In narrow rings the solution is shown to correspond to a rigid rotor and thus to a localized structure in the intrinsic frame, i.e., a rotating Wigner molecule. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001

A generalization of the time-dependent density-functional-theory for metal clusters which treats both valence and core polarization on the same microscopic basis is presented. The selfconsistency between valence and core responses is taken into account by means of a modified kernel and external field in the linearized response equations. The general case of an arbitrary external field and cluster structure, with given specific atomic positions, is presented.

arXiv:1403.1755v1, We discuss the robustness of Majorana edge modes in a finite quantum nanowire of cylindrical shape. The nanowire is modeled as a bidimensional cylindrical shell of semiconductor material with proximity-induced superconductivity and an intrinsic Rashba spin-orbit interaction. The latter is characterized by effective electric and magnetic fields in transverse direction of the nanowire. An applied external magnetic field pointing in an arbitrary orientation is also assumed. The numerical diagonalization of the Hamiltonian allows us to study the spectrum of the nanowire for different experimental configurations. The Majorana modes prove robust against tilting of the magnetic field away from the cylinder longitudinal axis, if the tilt direction is perpendicular to the effective spin-orbit magnetic field, but fragile otherwise. On the other hand, we find an increasing number of Majorana modes in the same cylinder edge for increasing values of the nanowire radius. We refer to this phenomenon as >stacking effect> and it occurs due to the orthogonality between Majorana mode wave functions. In this manner, different Majoranas take complementary positions on the nanowire surface. © 2014 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg., Work supported by MINECO Grant No. FIS2011-23526, the Conselleria d’Educació, Cultura i Universitats (CAIB) and FEDER.

© 2015 IOP Publishing Ltd. We consider a two-dimensional magnetic tunnel junction of the FM/I/QW(FM+SO)/I/N structure, where FM, I and QW(FM+SO) stand for a ferromagnet, an insulator and a quantum wire with both magnetic ordering and Rashba spin-orbit (SOC), respectively. The tunneling magneto-resistance (TMR) exhibits strong anisotropy and switches sign as the polarization direction varies relative to the quantum-wire axis, due to interplay among the one-dimensionality, the magnetic ordering, and the strong SOC of the quantum wire., This work was supported by the BK21 Plus Project from the Korean Government and by MINECO (Spain) Grant FIS2011-23526.

The spin response function for electrons confined in a quantum dot is studied within the time-dependent local spin density approximation (TDLSDA) of density functional theory. In the long-wavelength regime we predict the existence of a low-energy collective dipole (l = 1) spin mode. The evolution with electron number of the spin response is studied and compared with that of the density response. Predictions for the static dipole polarizability are given.

We present a generalized time-dependent density-functional theory (TDDFT) for the optical response of metal clusters where both core polarization and valence responses are treated microscopically. It is shown that the valence electrons response is described by an effective external field and residual interaction that are those of the standard TDDFT modified by the self-consistent contributions of the array of polarizable ionic cores. As an application the equations are solved within the adiabatic local-density approximation for silver clusters, where core $4d$ electrons greatly influence the optical response. The experimental data are well reproduced by the present theory.

We present calculations of Majorana edge modes in cylindrical nanowires of a semiconductor material with proximity-induced superconductivity. We consider a Rashba field along the transverse direction and an applied magnetic field in arbitrary orientation. Our analysis is based on exact numerical diagonalizations for the finite cylinder and on the complex band structure for the semi-infinite one. Orbital effects are responsible for a strong anisotropy of the critical field for which the effective gap vanishes. Robust Majorana modes are induced by the parallel-field component and we find regimes with more than one Majorana mode on the same edge. Experimentally, they would manifest as a specific sequence of zero-bias conductances as a function of the magnetic field. In the finite cylinder, a degradation of the Majorana modes due to interference of the two edges leads to oscillating non-zero energies for large enough fields. © Copyright EPLA, 2013., Work supported by MINECO Grants No. FIS2011-23526, CSD2007-00042 (CPAN), the Conselleria d’Educació, Cultura i Universitats (CAIB) and FEDER.

We describe Majorana edge states of a semi-infinite wire using the complex band structure approach. In this method the edge state at a given energy is built as a superposition of evanescent waves. It is shown that the superposition can not always satisfy the required boundary condition, thus restricting the existence of edge modes. We discuss purely 1D and 2D systems, focusing in the latter case on the effect of the Rashba mixing term. © 2013 American Physical Society., This work was funded by MINECO-Spain (Grant No. FIS2011-23526), CAIB-Spain (Conselleria d'Educació, Cultura i Universitats) and FEDER. Discussions with J. S. Lim, R. López, and D. Sánchez are gratefully acknowledged.

A numerical method to obtain the spectrum of smooth normal-superconductor junctions in nanowires, able to host Majorana zero modes, is presented. Softness in the potential and superconductor interfaces yields opposite effects on the protection of Majorana modes. While a soft potential is a hindrance for protection, a soft superconductor gap transition greatly favors it. Our method also points out the possibility of extended Majorana states when propagating modes are active far from the junction, although this requires equal incident fluxes in all open channels. © 2013 American Physical Society., This work was funded by MINECO-Spain (Grant FIS2011-23526), CAIB-Spain (Conselleria d’Educació, Cultura i Universitats), and FEDER.

We investigate the occurrence of Majorana modes in semiconductor quantum wires in close proximity with a superconductor and when both Rashba interaction and magnetic field are present. We consider long, but finite, multiband wires (namely, planar wires with dimensions L xL y). Our results demonstrate that interband mixing coming from the Rashba spin-orbit term hybridizes Majorana pairs originating from different transverse modes while simultaneously closing the effective gap. Consequently, multiple Majorana modes do not coexist in general. On the contrary, Majorana physics is robust provided that only one single transverse mode contributes to a Majorana pair. Finally, we analyze the robustness of Majorana physics with respect to magnetic orbital effects. © 2012 American Physical Society., This work was supported by Grants No. FIS2008-00781, No. FIS2009-08744, No. FIS2011-23526, and No. CSD2007- 00042 (CPAN) of the Spanish Government.

This paper presents a coupled channel model for transport in twodimensional semiconductor Majorana nanowires coupled to normal leads. When the nanowire hosts a zero-mode pair, conspicuous signatures of the linear conductance are predicted. An effective model in second quantization allowing a fully analytical solution is used to clarify the physics. We also discuss the nonlinear current response (dI /dV). © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft., This work was supported by grant numbers FIS2008-00781, FIS2011-23526 and CSD2007-00042 (CPAN) from the Spanish Government

We present calculations of the g factors of hole quantum wires for a magnetic field in the vertical (growth) direction. The energy bands are symmetric with respect to wavenumber inversion and the obtained g factors are larger than those for in-plane fields. For high-enough wire deformations, the g-factors are quenched when the Rashba interaction is increased. A Rashba-induced anisotropy similar to the horizontal one is thus predicted. A simple perturbative model explains qualitatively the numerical results. © 2012 The Royal Swedish Academy of Sciences.

We study the spin-splitting energies in low-potential-barrier quantum dots, finding splitting energies that are orbital state dependent. The theoretical analysis is done with a generalization of the Fock-Darwin states in the presence of spin-orbit interactions. We discuss experimental evidence indicating that the Rashba interaction strength in vertical In${}_{x}$Ga${}_{1\ensuremath{-}x}$As/GaAs quantum dots is in the range 80 meV \AA{} $\ensuremath{\leqslant}{\ensuremath{\lambda}}_{R}\ensuremath{\leqslant}$ 120 meV \AA{}. This enhanced spin-orbit interaction can be understood from the high penetration of the electron wave function into the quantum well with low-potential barrier.

PACS: 73.23.-b, 73.50.Lw, 73.63.Kv, 05.70.Ln, We investigate the basic properties of the thermopower (Seebeck coefficient) of phase-coherent conductors under the influence of dephasing and inelastic processes. Transport across the system is caused by a voltage bias or a thermal gradient applied between two terminals. Inelastic scattering is modeled with the aid of an additional probe acting as an ideal potentiometer and thermometer. We find that inelastic scattering reduces the conductor's thermopower and, more unexpectedly, generates a magnetic field asymmetry in the Seebeck coefficient. The latter effect is shown to be a higher-order effect in the Sommerfeld expansion. We discuss our result by using two illustrative examples. First, we consider a generic mesoscopic system described within random matrix theory and demonstrate that thermopower fluctuations disappear quickly as the number of probe modes increases. Second, the asymmetry is explicitly calculated in the quantum limit of a ballistic microjunction. We find that asymmetric scattering strongly enhances the effect and discuss its dependence on temperature and Fermi energy., We thank M. Buttiker and R. L ¨ opez ´ for fruitful discussions. This work has been supported by the MICINN Grant No. FIS2008-00781.