Renormalization of the Majorana bound state decay length in a perpendicular magnetic field

Orbital effects of a magnetic field in a proximitized semiconductor nanowire are studied in the context of the spatial extent of Majorana bound states. We develop analytical model that explains the impact of concurring effects of paramagnetic coupling of the nanowire bands via the kinetic energy operator and spin-orbit interaction on the Majorana modes. We find, that the perpendicular field, so far considered as to be detrimental to the Majorana fermion formation, is in fact helpful in establishing the topological zero-energy-modes in a finite system due to significant decrease in the Majorana decay length

Fulde-Ferrell state in superconducting core/shell nanowires: role of the orbital effect

The orbital effect on the Fulde-Ferrell (FF) phase is investigated in superconducting core/shell nanowires subjected to the axial magnetic field. The confinement in the radial direction results in the quantization of the electron motion with energies determined by the radial $j$ and orbital $m$ quantum numbers. In the external magnetic field the twofold degeneracy with respect to the orbital magnetic quantum number $m$ is lifted which leads to the Fermi wave vector mismatch between the paired electrons $(k, j,m,\uparrow) \leftrightarrow (-k, j,-m,\downarrow)$. This mismatch is transfered to the nonzero total momentum of the Cooper pairs which results in the formation of FF phase occurring sequentially with increasing magnetic field. By changing the nanowire radius $R$ and the superconducting shell thickness $d$, we discuss the role of the orbital effect in the FF phase formation in both the nanowire-like ($R/d \ll 1$) and nanofilm-like ($R/d \gg 1$) regime. We have found that the irregular pattern of the FF phase, which appears for the case of the nanowire-like regime, evolves towards the regular distribution, in which the FF phase stability regions appear periodically between the BCS state, for the nanofilm-like geometry. The crossover between these two different phase diagrams is explained as resulting from the orbital effect and the multigap character of superconductivity in core/shell nanowires.Comment: 10 pages, 7 figure

Quantum size effect on the paramagnetic critical field in Pb nanofilms

The quantum size effect on the in-plane paramagnetic critical field in Pb nanofilms is investigated with the use of the spin-generalized Bogolubov-de Gennes equations. It is shown that the critical field oscillates as a function of the nanofilm thickness with the period of $\sim2$ ML (even-odd oscillations) modulated by the beating effect. This phenomena is studied in terms of the quantization of the electron energy spectra caused by the confinement of the electron motion in the direction perpendicular to the sample. The calculated values of critical fields for different nanofilm thicknesses are analyzed in the context of Clogston-Chandrasekhar limit. The influence of the thermal effect on the magnetic field induced superconductor to normal metal transition is also discussed. Furthermore, the thickness-dependence of the electron-phonon coupling and its influence on the value of the critical magnetic field are studied.Comment: 9 pages, 9 figure

Electrically controlled spin-transistor operation in helical magnetic field

A proposal of electrically controlled spin transistor in helical magnetic field is presented. In the proposed device, the transistor action is driven by the Landau-Zener transitions that lead to a backscattering of spin polarized electrons and switching the transistor into the high-resistance state (off state). The on/off state of the transistor can be controlled by the all-electric means using Rashba spin-orbit coupling that can be tuned by the voltages applied to the side electrodes.Comment: 5 pages, 6 figure

Spin filtering effect generated by the inter-subband spin-orbit coupling in the bilayer nanowire with the quantum point contact

The spin filtering effect in the bilayer nanowire with quantum point contact is investigated theoretically. We demonstrate the new mechanism of the spin filtering based on the lateral inter-subband spin-orbit coupling, which for the bilayer nanowires has been reported to be strong. The proposed spin filtering effect is explained as the joint effect of the Landau-Zener inter-subband transitions caused by the hybridization of states with opposite spin (due to the lateral Rashba SO interaction) and the confinement of carriers in the quantum point contact region.Comment: 14 pages, 11 figure

Influence of the electron density on the thickness-dependent energy gap oscillations in superconducting metallic nanofilms

The thickness-dependent energy gap oscillations in the metallic nanofilms are investigated by the use of the self-consistent numerical solutions of the Bogoliubov-de Gennes equations. It is shown, that the oscillations are induced by the quasi-particle energy quantization triggered by the confinement of electrons in the direction perpendicular to the sample. We have analyzed, how the changes in the electron density of states ($n_e$) and the electron-phonon coupling constant ($g$) influence the amplitude of the considered oscillations. It has been found, that the increase in $n_e$ and the decrease in $g$, can lead to a significant reduction of the oscillations amplitude. As a result, for the values of the mentioned parameters corresponding to some of the realistic situations the thickness-dependent superconducting gap oscillations can be almost completely suppressed

Probing Andreev reflection reach in semiconductor-superconductor hybrids by Aharonov-Bohm effect

Recent development in fabrication of hybrid nanostructures allows for creation of quantum interferometers that combine semiconductor and superconductor materials. We show that in those nanostructures the joint phenomena of Aharonov-Bohm effect and Andreev reflections can be used to determine the length on which the electron is retro-reflected as a hole. We propose to exploit this feature for probing of the quasiparticle coherence length in semiconductor-superconductor hybrids by a magnetoconductance measurement

Orbital effect on the in-plane critical field in free-standing superconducting nanofilms

The superconductor to normal metal phase transition induced by the in-plane magnetic field is studied in free-standing Pb(111) nanofilms. In the considered structures the energy quantization induced by the confinement leads to the thickness-dependent oscillations of the critical field (the so-called 'shape resonances'). In this paper we examine the influence of the orbital effect on the in-plane critical magnetic field in nanofilms. We demonstrate that the orbital term suppresses the critical field and reduces the amplitude of the thickness-dependent critical field oscillations. Moreover, due to the orbital effect, the slope $H_{c,||}-T_c$ at $T_c(0)$ becomes finite and decreases with increasing film thickness in agreement with recent experiments. The temperature $t^*$ at which the superconductor to normal metal phase transition becomes of the first order is also analyzed.Comment: 8 pages, 7 figure

Nonlocal Andreev Reflections as a Source of Spin Exchange and Kondo Screening

We report on a novel exchange mechanism, mediating the Kondo screening, in a correlated double quantum dot structure in the proximity of superconductor, stemming from nonlocal Andreev reflection processes. We estimate its strength perturbatively and corroborate analytical predictions with accurate numerical renormalization group calculations using an effective model for the superconductor-proximized nanostructure. We demonstrate that superconductor-induced exchange leads to a two-stage Kondo screening. We determine the dependence of the Kondo temperature on the coupling to superconductor and predict a characteristic modification of conventional low-temperature transport behavior, which can be used to experimentally distinguish this phenomenon from other Kondo effects.Comment: 10 pages, 6 figures. Version accepted in Phys. Rev. B, before proof-stage editin

Strong spin Seebeck effect in Kondo T-shaped double quantum dots

We theoretically investigate the thermoelectric and spin thermoelectric properties of a T-shaped double quantum dot strongly coupled to two ferromagnetic leads, focusing on transport regime where the system exhibits the two-stage Kondo effect. We study the dependence of the (spin) Seebeck coefficient, the corresponding power factor and the figure of merit on temperature, leads' spin polarization and dot level position. We show that the thermal conductance fulfills a modified Wiedemann-Franz law. We also demonstrate that the spin thermopower is enhanced at temperatures corresponding to the second stage of Kondo screening. Very interestingly, the spin-thermoelectric response of the system is found to be highly sensitive to the spin polarization of the leads. In some cases spin polarization of the order of 1% is sufficient for a strong spin Seebeck effect to occur. This is explained as a consequence of the interplay between the two-stage Kondo effect and the exchange field induced in the double quantum dot. All calculations are performed with the aid of numerical renormalization group technique.Comment: 10 pages, 7 figure