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We theoretically study the thermoelectric transport properties through a triple quantum dots (QDs) device with the central QD coupled to a ferromagnetic lead, a superconducting one, and two side QDs with spin-dependent interdot tunneling coupling. The thermoelectric coefficients are calculated in the linear response regime by means of nonequilibrium Green's function method. The thermopower is determined by the single-electron tunneling processes at the edge of superconducting gap. Near the outside of the gap edge the thermopower is enhanced while thermal conductance is suppressed, as a result, the charge figure of merit can be greatly improved as the gap appropriately increases. In the same way, charge figure of merit also can be greatly improved near the outside of the gap edge by adjusting interdot tunneling coupling and asymmetry coupling of the side QDs to central QD. Moreover, the appropriate increase of the interdot tunneling splitting and spin polarization of ferromagnetic lead not only can improve charge thermopower and charge figure of merit, but also can enhance spin thermopower and spin figure of merit. Especially, the interdot tunneling splitting scheme provides a method of controlling charge (spin) figure merit by external magnetic field.

${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$ has recently emerged as a ferromagnetic Weyl semimetal. Theoretical investigation of the spin-split bands predicted half metallicity in the compound. Here, we report the detection of a spin-polarized supercurrent through a $\mathrm{Nb}/{\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$ point contact where Andreev reflection is seen to be large, indicating a large deviation from half metallicity. In fact, analysis of the Andreev reflection spectra reveals very small spin polarization at different points with the degree of spin polarization ranging from 20% to 50% at the Fermi level of ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$. Our theoretical calculations of electronic density of states reveal a spin-depolarizing effect near the Fermi energy when the role of spin-orbit coupling is included. The inclusion of spin-orbit coupling also reveals particle-hole asymmetry that explains a large asymmetry observed in our experimental Andreev reflection spectra.

Magnetic Weyl semimetals (WSMs) with broken time-reversal symmetry (TRS) hosting topological band structures are expected to provide an ideal platform for investigating topological superconductivity and spintronics. However, the experimental verification of magnetic WSMs is very challenging. Very recently, the kagome magnet Co3Sn2S2 was confirmed to be a magnetic WSM by both angle-resolved photoemission spectroscopy and scanning tunneling spectroscopy and consequently has become the focus of great attention. This paper reports a point-contact Andreev-reflection spectroscopy (PCARS) investigation on the (001) surface and the side surface of the Co3Sn2S2 single crystals, respectively. The measurements from the sample’s (001) and side surfaces provide experimental evidence for transport spin polarization in the Co3Sn2S2 magnetic WSM. Furthermore, the superconducting proximity effect in the Co3Sn2S2 single crystal is successfully detected. The point-contact spectra (PCS) along the in-plane direction cannot be well fitted by theoretical models based on s-wave pairing, indicating that possible triplet p-wave superconductivity may be triggered at the interface, which paves the way for the future exploration of the topological superconductivity and Majorana states in broken TRS WSMs.

We investigate spin-polarized transport in graphene-based ferromagnet-superconductor junctions within the Blonder-Tinkham-Klapwijk formalism by using spin-polarized Dirac-Bogoliubov-de-Gennes equations. We consider superconductor in spin-singlet s-wave pairing state and ferromagnet is modeled by an exchange field with energy of E x . We have found that graphene-based junctions can be used to produce highly spin-polarized current in different situations. For example, if we design a junction with high E x and E F compared to order parameter of superconductor, then one can have a large spin-polarized current which is tunable in magnitude and sign by bias voltage and E x . Therefore graphene-based superconducting junction can be used in spintronic devices in alternative to conventional junctions or half-metallic ferromagnets. Also, we have found that the calculated spin polarization can be used as a tool to distinguish specular Andreev reflection (SAR ) from the conventional Andreev reflection (CAR ) such that in the case of CAR, spin polarization in sub-gap region is completely negative which means that spin-down current is greater than spin-up current. When the SAR is dominated, the spin polarization is positive at all bias-voltages, which itself shows that spin-up current is greater than spin-down current.

RhGe synthesized at high pressure crystallizes in the noncentrosymmetric B20 cubic structure. Measurements of electrical resistivity and magnetization demonstrate a superconducting state below T c ∼ 4.3 K and weak ferromagnetism below T m ∼ 140 K. Specific heat data confirm the bulk nature of superconductivity in this ferromagnetic superconductor. Point contact spectra in the superconducting state exhibit the complex Andreev reflection signal which may indicate a mixed singlet-triplet order parameter. The superconducting region forms a dome on the P-T diagram with a maximum of T c near 4 GPa. It was also found that the superconductivity of RhGe 4 is suppressed at high pressure in contrast with RhGe. Ab initio simulations suggest that the observed weak magnetization emerges from the pronounced toroidal-like spin polarization with magnetic quadrupole and toroidal moments located at Rh and Ge sites.

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

We study the transport properties and superconducting proximity effect in NSN junctions formed by a time-reversal symmetry broken Weyl semimetal (WSM) in proximity to an $s$-wave superconductor. We find that the differential conductance and induced pairing amplitudes strongly depend on the angle between the junction direction in real space and the axis separating the Weyl nodes in momentum space. We identify the influence of a chiral chemical potential, i.e., the electron population imbalance between Weyl nodes of opposite chirality, on the transport characteristics of the junction. Remarkably, we observe a net spin polarization of Cooper pairs that are generated via Andreev reflection in the two WSM regions. The spin polarization is opposite in the two WSM regions and highly sensitive to the chirality imbalance and excitation energy., Comment: 11 pages, 8 figures

We propose a new method, using the Andreev reflection at superconductors, to measure parity violation induced by the standard electroweak theory, which in turn constrains the possible parity-violating effects of new physics. The weak neutral currents induce parity-violating, marginal effective operators, though quite tiny, in superconductors. We estimate their effects on superconducting gaps and propose a method to measure the parity-violation from the spin polarization effect, when electrons or holes get Andreev-reflected at the interface between normal metal and a superconductor. Such polarization effects might be comparable to the atomic parity violation and thus naturally give an interesting bound on certain models of new physics, that couples to electrons, such as Majorana mass of active neutrinos or doubly charged Higgs., 11 pages, 6 figures. v2: minor changes, to appear in Physics Letters B

The resonant behaviors of spin-dependent linear AR conductance, the spin-dependent AR current, the electron occupation number and spin accumulation in the QD are theoretically investigated in the FM/QD/SC system with intradot spin-flip scattering. The novel resonant behaviors of spin-dependent AR conductance versus Fermi energy are revealed, which are rather different from the AR conductance versus the dot's energy level case [Cao et al., Phys. Rev. B 70 (2004) 235341]. It is proved that the split of the resonant peak can be induced by the competition between the coupling strengths to the FM and SC leads, the intradot spin-flip scattering, and the gate voltage. The number, the widths, and the distance of the peaks could be controlled by tuning the relevant parameters. The resonance of AR current can take place only when the energy level of QD lines up with the right lead chemical potential and blows the left lead chemical potential. The magnitude of the resonant AR current depends on the number of resonant levels involved in the Andreev tunneling process. It is also proved that the spin-flip scattering can suppress the spin accumulation effectively, and induce the spin polarization of AR conductance and AR current simultaneously. The results make us understand better the fundamental in this system, and are useful for the design of spintronic devices.

We study an effective transport and Andreev reflection through a quantum dot-Majorana bound state (QD-MBS) hybrid nanostructure coupling between ferromagnetic and superconductor leads. Due to MBSs, the Andreev conductance spectrum experience the transition in the configuration of different lineshape geometry such as spin split and Fano effect. The spin-flip scattering process can suppress the electron and hole reflection. Spin polarization decreases electron reflection but increases the conductance.

In this paper, we investigate the electronic transport properties of a quantum dot (QD) connected to two ferromagnetic leads and one superconductor lead in the Kondo regime by means of the finite-$U$ slave boson mean field approach and nonequilibrium Green function technique. In this three-terminal hybrid nano-device, we will focus our attention on the joint effects of the Konod correlation, superconducting proximity pairing, and spin polarization of leads. It is found that: the superconducting proximity effect will suppress the linear local conductance (LLC) stemming from the weakened Kondo peak, and when its coupling $\Gamma_s$ is bigger than the tunnel-coupling $\Gamma$ of two normal leads, the linear cross conductance (LCC) becomes negative in the Kondo region; for antiparallel configuration, increasing spin polarization further suppresses LLC but enhances LCC, i.e. causing larger negative values of LCC, since it is benefit for emergence of cross Andreev reflection; On the contrary, for parallel configuration, with increasing spin polarization, the LLC descends and greatly widens with the appearance of shoulders, and eventually splits into four peaks, and meanwhile the LCC reduces relatively rapidly to the normal conductance., Comment: 9 pages, 6 figures

Majority of the A(2)B(3)-type chalcogenide systems with strong spin-orbit coupling (SOC), such as Bi2Se3, Bi2Te3, and Sb2Te3, etc., are topological insulators. One important exception is Sb2Se3 where a topological nontrivial phase was argued to be possible under ambient conditions, but such a phase could be detected to exist only under pressure. In this paper, we show that Sb2Se3 like Bi2Se3 displays a generation of highly spin-polarized current under mesoscopic superconducting point contacts as measured by point-contact Andreev reflection spectroscopy. In addition, we observe a large negative and anisotropic magnetoresistance of the mesoscopic metallic point contacts formed on Sb2Se3. Our band-structure calculations confirm the trivial nature of Sb2Se3 crystals and reveal two trivial surface states one of which shows large spin splitting due to Rashba-type SOC. The observed high spin polarization and related phenomena in Sb2Se3 can be attributed to this spin splitting.

The surface states of topological insulators (TI) are protected by time reversal symmetry and they display intrinsic spin helicity where the momentum of the charge carriers decides their spin states. As a consequence, a current injected through the surface states becomes spin polarized and this transport spin-polarization leads to a proportionate suppression of Andreev reflection in superconductor/TI junctions. Here we show that upon doping Bi2Se3 with Mn, the transport spin-polarization is seen to be monotonically suppressed. The parent compound Bi2Se3 is found to exhibit a transport spin-polarization of about 63% whereas crystals with 10% Mn doping show transport spin-polarization of about 48%. This suppression is accompanied by an increasing ferromagnetic order of the crystals with Mn doping. Scanning tunneling spectroscopy shows that the topological protection of the surface states reduce due to Mn doping. The net measured transport spin-polarization is due to a competition of this effect with the increased magnetization on Mn doping. The present results provide important insights for the choice of magnetic topological insulators for spintronic applications., Comment: Accepted in Journal of Physics: Condensed Matter, 5 PAGES, 5 FIGURES

As charge carriers traverse a single superconductor ferromagnet interface they experience an additional spin-dependent phase angle which results in spin mixing and the formation of a bound state called the Andreev Bound State. This state is an essential component in the generation of long range spin triplet proximity induced superconductivity and yet the factors controlling the degree of spin mixing and the formation of the bound state remain elusive. Here we demonstrate that point contact Andreev reflection can be used to detect the bound state and extract the resulting spin mixing angle. By examining spectra taken from La1.15Sr1.85Mn2O7 single crystal - Pb junctions, together with a compilation of literature data on highly spin polarised systems, we show that the existence of the Andreev Bound State both resolves a number of long standing controversies in the Andreev literature as well as defining a route to quantify the strength of spin mixing at superconductor-ferromagnet interfaces. Intriguingly we find that for these high transparency junctions, the spin mixing angle appears to take a relatively narrow range of values across all the samples studied. The ferromagnets we have chosen to study share a common property in terms of their spin arrangement, and our observations may point to the importance of this property in determining the spin mixing angle under these circumstances., 17 pages, 1 table, 3 figures. arXiv admin note: substantial text overlap with arXiv:1503.00533

Sau, Lutchyn, Tewari and Das Sarma (SLTD) proposed a heterostructure consisting of a semiconducting thin film sandwiched between an s-wave superconductor and a magnetic insulator and showed possible Majorana zero mode. Here we study spin polarization of the vortex core states and spin selective Andreev reflection at the vortex center of the SLTD model. In the topological phase, the differential conductance at the vortex center contributed from the Andreev reflection, is spin selective and has a quantized value $${(dI/dV)}_{A}^{topo}=2{e}^{2}/h$$ ( d I / d V ) A t o p o = 2 e 2 / h at zero bias. In the topological trivial phase, $${(dI/dV)}_{A}^{trivial}$$ ( d I / d V ) A t r i v i a l at the lowest quasiparticle energy of the vortex core is spin selective due to the spin-orbit coupling (SOC). Unlike in the topological phase, $${(dI/dV)}_{A}^{trivial}$$ ( d I / d V ) A t r i v i a l is suppressed in the Giaever limit and vanishes exactly at zero bias due to the quantum destruction interference.

Non-centrosymmetric superconductors exhibit the magnetoelectric effect which manifests itself in the appearance of the magnetic spin polarization in response to a dissipationless electric current (supercurrent). While much attention has been dedicated to the thermodynamic version of this phenomenon (Edelstein effect), non-equilibrium transport magnetoelectric effects have not been explored yet. We propose the magnetoelectric Andreev effect (MAE) which consists in the generation of spin-polarized triplet Andreev conductance by an electric supercurrent. The MAE stems from the spin polarization of the Cooper-pair condensate due to a supercurrent-induced non-unitary triplet pairing. We propose the realization of such non-unitary pairing and MAE in superconducting proximity structures based on two-dimensional helical metals -- strongly spin-orbit-coupled electronic systems with the Dirac spectrum such as the topological surface states. Our results uncover an unexplored route towards electrically controlled superconducting spintronics and are a smoking gun for induced unconventional superconductivity in spin-orbit-coupled materials., Comment: 4.5 + 9 pages, 3 figures, version accepted by Physical Review Letters. Supplemental material includes discussion of a generic non-centrosymmetric superconductor

A Weyl semimetal is a topologically non-trivial phase of matter that hosts mass-less Weyl fermions, the particles that remained elusive for more than 80 years since their theoretical discovery. The Weyl semimetals exhibit unique transport and magneto-transport properties and remarkably high surface spin polarization. Here we show that a unique mesoscopic superconducting phase with a critical temperature up to 7 K can be realized by forming metallic point contacts with silver (Ag) on single crystals of TaAs, while neither Ag nor TaAs are superconductors. The Andreev reflection spectra obtained from such point contacts are fitted well within a modified Blonder-Tinkham-Klapwijk (BTK) model with a superconducting energy gap up to 1.2 meV. The analysis within this model also reveals high transport spin polarization up to 60\% indicating a spin polarized supercurrent flowing through the point contacts on TaAs. Such point contacts also show a large anisotropic magnetoresistance (AMR) originating from the spin polarized current. Therefore, apart from the discovery of a novel mesoscopic superconducting phase and it's coexistence with a large spin polarization, our results also show that the point contacts on Weyl semimetals are potentially important for applications in spintronics., Comment: Contains supplemental materials at the end

We performed point contact spectroscopy experiment by pushing gold tip on the ferromagnetic side of Nb / Pd 0.84 Ni 0.16 bilayers. Several contacts have been measured at temperature 4.2 K evidencing a wide variety of features (zero bias peak, conductance dips, etc.) appearing in the differential conductance spectra at energies up to Nb energy gap. A theoretical model has been developed within the scattering theory for ferromagnetic/superconductor heterostructures to fit experimental data. All different features can be consistently explained in our model by taking into account the spin polarization as well as the thickness of the ferromagnetic layer. We also show that we can give very precise estimation of such ferromagnetic characteristics.

The Zn0.32Co0.68O1-v/Pb hybrid junctions were prepared, where the concentrated magnetic semiconductor Zn0.32Co0.68O1-v is in the region of variable range hopping transport instead of the ballistic or diffusive transport. The high differential conductance peak at gap voltage and two above-gap peaks were observed below the superconducting critical temperature. Moreover, both the zero bias conductance peak and the finite bias conductance peak were observed below the gap voltage. All these differential conductance peaks systematically evolve and finally disappear as the temperature or the magnetic field increases. These transport phenomena were explained by phase coherent Andreev reflection in the presence of strong disorder, magnetic impurity scattering, and spin polarization. (C) 2013 Elsevier B.V. All rights reserved.

Majorana zero modes (MZMs) have been predicted to exist in a topological insulator (TI)/superconductor (SC) heterostructure. A recent spin-polarized scanning tunneling microscope (STM) experiment [Sun et al., Phys. Rev. Lett. 116, 257003 (2016)] has observed a spin-polarization dependence of the zero bias differential tunneling conductance at the center of a vortex core. Here, we consider a helical electron system described by a Rashba spin-orbit coupling Hamiltonian on a spherical surface with an $s$-wave superconducting pairing due to proximity effect. We examine the in-gap excitations of a pair of vortices with one at the north pole and the other at the south pole. While the MZM is not a spin eigenstate, the spin wave function of the MZM at the center of the vortex core, $r=0$, is parallel to the magnetic field, and the local Andreev reflection of the MZM is spin selective, namely, occurs only when the STM tip has the spin polarization parallel to the magnetic field, similar to the case in a one-dimensional nanowire [He et al., Phys. Rev. Lett. 112, 037001 (2014)]. The total local differential tunneling conductance consists of the normal term proportional to the local density of states and an additional term arising from the Andreev reflection. We also discuss the finite size effect, for which the MZM at the north pole is hybridized with the MZM at the south pole. We apply our theory to examine the recently reported spin-polarized STM experiments and show good agreement with the experiments.

The spin-galvanic (inverse Edelstein) and inverse spin-Hall effects are calculated for a hybrid system that combines thin superconductor and Rashba-metal layers. These effects are produced by a nonequilibrium spin polarization which is injected into the normal metal layer. This polarization gives rise to an electric potential that relaxes within some characteristic length, which is determined by Andreev reflection. Within this length the dissipative electric current of quasiparticles in the normal layer converts into the supercurrent. This process involves only subgap states and at low temperature the inelastic electron-phonon interactions are not important. It is discussed how such a hybrid system can be integrated into a SQUID where it produces an effect similar to a magnetic flux., 12 pages, 2 figures, final version

Point Contact Andreev Reflection (PCAR) is one of the few available methods for the determination of the Fermi level spin polarisation in metals and degenerate semiconductors. It has traditionally been applied at fixed (liquid He) temperatures, using pure niobium as the superconductor, and at essentially zero applied magnetic fields, all of which limit the amount of information that it can provide – i.e. do not allow for the extraction of the sign of the spin polarisation and make the assignment of the transport regime to ballistic or diffusive almost impossible. Here a series of experiments is described, aimed at the expansion of this parameter space to higher magnetic fields and to higher temperatures. These require redesigned experimental setups and the use of higher performance superconductors. Demonstrations are described of the determination of the sign of the spin polarisation, at fields of more than 5 Tesla using a low-Z superconductor, as well as operations beyond 9.2 K. Doubts about the practical reliability of the PCAR technique are dispersed using systematic series of samples – the heavy rare-earths and comparisons with alternatives, such as spin-polarised field emission, photo-emission and Tedrow-Meservey tunnelling. The specific material examples presented include 3d-metals, order-disorder transition alloys and zero-moment half-metals – Fe, FeAl and MnRuGa, alternative low-Z and high-Z superconductors – MgB2 and NbTi, and magnetic topological insulators, such as Cr- and V-doped (Bi1-xSbx)2Te3.

Andreev reflection spectroscopy of ferromagnet/superconductor (F/S) junctions is a sensitive probe of the junction interface as well as the spin polarization. We theoretically investigate spin-polarized transport in F/S 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. This suggests a similar control of the superconducting proximity effect and Majorana states. 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 F/S junction. This work has been supported by DFG SFB 689, the International Doctorate Program Topological Insulators of the Elite Network of Bavaria, DOE-BES Grant DE-SC0004890, and ONR N000141310754. P. H\"{o}gl, A. Matos-Abiague, Igor \v{Z}uti\'c, J. Fabian, Phys. Rev. Lett. 115, 116601 (2015)

Conventional superconductors disordered by magnetic impurities demonstrate physical properties that are drastically different from their pristine counterparts. In our previous work [D. Persson et al., Phys. Rev. B 92, 245430 (2015)], we explored the spectral and thermodynamic properties of such systems for two extreme cases: completely random and ferromagnetically aligned impurity magnetic moments. Here we consider the transport properties of these systems and show that they have a potential to be used in superconducting spintronic devices. Each magnetic impurity contributes a Yu-Shiba-Rusinov (YSR) bound state to the spectrum, residing at subgap energies. Provided the YSR states form metallic bands, we demonstrate that the tunneling current carried by these states can be highly spin polarized when the impurities are ferromagnetically ordered. The spin polarization can be switched by tuning the bias voltage. Moreover, even when the impurity spins are completely uncorrelated, one can still achieve almost 100% spin polarization of the current, if the tunnel interface is spin active. We compute electric current and noise, varying parameters of the interface between tunneling and fully transparent regimes, and analyze the relative role of single-particle and Andreev reflection processes.

We investigate the Andreev reflections in a single-dot quantum ring with one s-wave superconductor side-coupled to the quantum dot, by considering the presence of local Rashba interaction and magnetic flux. It shows that in this system, the local Rashba interaction induces apparent spin polarizations of the local Andreev reflections, with their directions depending on the Rashba interaction and the lead index, respectively. Nevertheless, the crossed Andreev reflection cannot be polarized, and its magnitude can be adjusted by the threaded local magnetic flux. We propose this structure to be the promising candidate for achieving the manipulation of Andreev reflections.

In a superconductor–normal–superconductor (SNS) structure, the effect of transverse current across the normal part on the transport through Andreev bound states (ABSs) has been examined. Here, a ballistic InAs two-dimensional electron system (2DES) is used as the N-layer to form ABSs. At the same time the 2DES has strong spin–orbit interaction, hence there should emerge the spin-Hall effect associated with the transverse current. We have observed strong reduction of characteristic oscillation in the conductance versus bias voltage, which may be attributed to spin polarization due to the spin-Hall effect.

We discuss the Andreev reflection at the interface of normal metal with spin triplet superconductor in the equal-spin pairing case. The pairing induces a net spin polarization on the normal side which should be detectable. With the presence of this polarization one can distinguish between the polarized triplet and the singlet pairings. It may also play an important role in detecting the triplet component in unconventional superconductors.

This paper theoretically analyzed Andreev reflection in the ferromagnetic metal/insulator/d-wave superconductor junctions using the Bogoliubov-de Gennes equations. We calculated the total tunneling conductance spectra and found that the conductance suppression due to the insulator depends on the relation between the exchange energy and the Fermi wave number difference. Our results showed the feasibility of the spin polarization measurement with high-Tc superconductivity using the same system of the Point-contact Andreev reflection (PCAR) measurement.

Point contact Andreev reflection spectroscopy is employed to extract the effective Fermi-level spin polarization of three distinct compositions from the (${\mathrm{Bi}}_{1\ensuremath{-}x}{\mathrm{Sb}}_{x}$)${}_{2}{\mathrm{Te}}_{3}$ topological insulator family. The end members, ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ and ${\mathrm{Sb}}_{2}{\mathrm{Te}}_{3}$, exhibit high polarization of 70(4)% and 57(3)%, respectively. High-field $({\ensuremath{\mu}}_{0}H=14\phantom{\rule{0.16em}{0ex}}\mathrm{T})$ point contact spectroscopy shows carrier depletion close to the Fermi level for these two compositions with small activation gaps of 0.40(4) and 0.28(2) meV, respectively. The almost fully suppressed bulk conductivity in the (${\mathrm{Bi}}_{0.18}{\mathrm{Sb}}_{0.82}$)${}_{2}{\mathrm{Te}}_{3}$ results in an even higher spin polarization of 83(9)%. Further, it is demonstrated that magnetic doping with Cr and V tends to reduce the spin-polarization values with respect to the ones of the pure compositions. ${\mathrm{Bi}}_{1.97}{\mathrm{Cr}}_{0.03}{\mathrm{Te}}_{3}, {\mathrm{Sb}}_{1.975}{\mathrm{Cr}}_{0.025}{\mathrm{Te}}_{3}, {\mathrm{Bi}}_{1.975}\phantom{\rule{0.16em}{0ex}}{\mathrm{V}}_{0.025}{\mathrm{Te}}_{3}$, and ${\mathrm{Sb}}_{1.97}\phantom{\rule{0.16em}{0ex}}{\mathrm{V}}_{0.03}{\mathrm{Te}}_{3}$ exhibit spin polarization of 52%, 52%, 58%, and 50%, respectively. In view of the rather high effective polarization, nonmagnetic topological insulators close to (${\mathrm{Bi}}_{0.18}{\mathrm{Sb}}_{0.82}$)${}_{2}{\mathrm{Te}}_{3}$ may provide a path towards the characterization of pair-breaking mechanisms in spin-triplet superconductors.

We demonstrate that zero-energy Majorana bound state, in the ferromagnetic insulator (FI)-superconductor (SC) junction formed on the edge of two-dimensional topological insulator, exhibits three types of spin-triplet pairing correlations and its spin polarization direction is position independent in ferromagnetic insulator. When an electron is injected with a spin (anti-)parallel to this direction, equal-spin Andreev reflection exhibits the widest (narrowest) resonance peak. Similar behaviour is found when the coupling between two Majorana bound states in a FI-SC-FI junction is invoked, though an additional weak spin-singlet pairing correlation is generated. These signatures can readily facilitate the experimental detection of spin-triplet correlations and spin polarization of Majorana bound states., Comment: 5 pages, 5 figures

In this chapter, transport properties in hybrid structures involving a superconductor are discussed. The transport quantities are expressed in terms of reflection coefficients within the framework of the Blonder-Tinkham-Klapwijk theory. These coefficients are evaluated in the scattering theory. The enhancement of conductance from Andreev reflection process is revealed, and its suppression due to the spin polarization is examined. Finally, the possible revelation of chiral Majorana modes through the tunneling differential conductance in a normal-metal-ferromagnetic insulator-s-wave superconductor junction is discussed.

We present a new device which consists of a molecular quantum dot (MQD) attached to a normal-metal, two ferromagnetic (FM), and a superconducting leads. The spin-related Andreev reflection (AR) current and the spin-dependent single-particle tunneling current through the normal-metal terminal are obtained, and it is found that the spin current exhibits the transistor-like behavior. The joint effects of the coherent spin flip and the angle between magnetic moments of the two FM leads on the spin current are also studied, these results provide the possibility to manipulate the spin current with the system parameters.

We study the tunneling magnetoresistance (TMR) effect in asymmetric ferromagnet/ferromagnet/ s -wave superconductor junctions based on the extended Blonder–Tinkham–Klapwijk theory. When the left ferromagnet (FM) is in the half-metallic limit, the low-energy charge transport in this system is governed by the so-called same-spin-band Andreev reflection, where the incident electron and the Andreev reflected hole belong to the same spin subband. It is demonstrated that the same-spin-band Andreev reflection depends sensitively on the relative orientation of the magnetizations in the two FMs leading to giant TMR effect (TMR > 10 6 % for T / T c ≪ 1). Distinctive oscillatory variation of TMR with the thickness or the spin polarization of the intermediate FM is also found.

Spin-dependent transport of holes is studied in silicon nanosandwiches on an n-Si (100) surface which are represented by ultranarrow p-Si quantum wells confined by δ-barriers heavily doped with boron. The measurement data of the longitudinal and Hall voltages as functions of the top gate voltage without an external magnetic field show the presence of edge conduction channels in the silicon nanosandwiches. An increase in the stabilized source-drain current within the range 0.25–5 nA subsequently exhibits the longitudinal conductance value 4e2/h, caused by the contribution of the multiple Andreev reflection, the value 0.7(2e2/h) corresponding to the known quantum conductance staircase feature, and displays Aharonov-Casher oscillations, which are indicative of the spin polarization of holes in the edge channels. In addition, at a low stabilized source-drain current, due to spin polarization, a nonzero Hall voltage is detected which is dependent on the top gate voltage; i. e., the quantum spin Hall effect is observed. The measured longitudinal I–V characteristics demonstrate Fiske steps and a negative differential resistance caused by the generation of electromagnetic radiation as a result of the Josephson effect. The results obtained are explained within a model of topological edge states which are a system of superconducting channels containing quantum point contacts transformable to single Josephson junctions at an increasing stabilized source-drain current.

An extended Blonder–Tinkham–Klapwijk (BTK) approach is applied to study the spin polarization and Zeeman effects in ferromagnet/ferromagnetic p -wave superconductor ( FM / F p S ) junctions. Three kinds of pairings for FpS are chosen: p x , p y , p x + i p y waves. It is found that the normalized conductance strongly depends on both kinds of pairings and the relative orientations of the effective exchange field in the FM and F p S . In triplet superconductor junctions the multiplication of zero-energy Andreev bound states (ABSs) with the Zeeman effect induces an additional peak splitting. This property may serve as a method to identify triplet symmetry of ferromagnetic superconductors.

By using the nonequilibrium Green's function technique, we study the Andreev reflection (AR) in a triangular triple quantum dot system coupled with ferromagnetic and superconducting electrodes. An expression for the AR conductance is derived at zero temperature. It is found that the AR process does not break time-reversal symmetry due to the AR coefficient as an even function of the magnetic flux. Similar to the matching condition of the Fermi velocities, the zero-bias conductance reaches its maximum provided that the matching condition is satisfied. One can observe that the spectrum of the AR conductance presents the resonant peaks, the dips or the Fano-like shape, and the spin polarization of the ferromagnetic lead and the magnetic flux strongly affect the AR process. The dependence of the AR current on the temperature is also discussed. These results provide the ways of modulating the AR process.

A modification of the Blonder–Tinkham–Klapwijk (BTK) model is proposed for the description of the ferromagnet-superconductor interface. Modelling the contact potential with a rectangular barrier, we investigate the influence of the barrier width at the interface on the value of spin polarisation measured by point contact Andreev reflection. Results suggesting that neglecting the width of the barrier at the interface can lead to an overestimation of the spin polarisation using the original BTK model are presented. This effect is particularly strong for low values of polarization and vanishes for high polarisation. The impact on analysis of the experimental data is also discussed.

An extended Blonder–Tinkham–Klapwijk (BTK) approach is applied to study the spin polarized transport in ferromagnetic semiconductor/ferromagnetic p -wave superconductor ( FS/F p S ) junctions. It is demonstrated that the normalization conductance strongly depends not only on the kinds of holes (heavy or light) in the FS and pairings for the F p S but also on the relative orientations of the effective exchange field in the FS and F p S . In triplet superconductor junctions zero-energy Andreev bound states (ABS) and proximity effect can coexist with each other. This property may serve as a method to identify the triplet symmetry of ferromagnetic superconductors.

With the fabrication of gapped graphene, interest in the tunneling spectroscopy in graphene-based FG/SG junctions in which one side consists of a gapless ferro-magnetic graphene (FG) and the other side, of a gapped superconducting graphene (SG) has arisen. The carriers in the gapless (gapped) graphene are 2D relativistic particles having an energy spectrum given by E = ℏ 2 v F 2 k 2 + ( mv F 2 ) 2 (where mv F 2 is the gap and v F is the Fermi velocity). The spin currents in this FG/SG junction are obtained within the framework of the extended Blonder–Tinkham–Klapwijk (BTK) formalism. The effects of the superconducting energy gap in SG, of the gap mv F 2 which opened in the superconducting graphene, of the exchange field in FG, of the spin-dependent specular Andreev reflection, of the effective Fermi energy ( E FF ) of FG and of the bias voltage across the junction ( V ) are simulated. It is seen that by adjusting E FF or V , the spin polarization (defined as SP(%) = 100% × ( G ↑ − G ↓ )/( G ↑ + G ↓ )) can be switched from a pure spin up (SP = +100%) state to pure spin down (SP = −100%) state.

The Andreev reflection (AR) probability and transmission of quasiparticles in ferromagnetic semiconductor/d-wave superconductor (FS/DS) ballistic junctions are studied based on an extended Blonder–Tinkham–Klapwijk (BTK) theory. It is shown that the dependence of AR probability and pair potential on the spin orientation of incident quasiparticles for the heavy holes is much different from that for light holes due to the different mismatches in the effective mass and Fermi velocity between FS and DS. The junction conductance is dominated by the quasiparticles which undergo AR processes with the largest probability, and this provides a method for measuring the spin polarization in FS.

It is investigated the possibility of controlling the electric flow through a ferromagnet–superconductor junction by spin polarization, within a simple, ideal model of a perfect ferromagnetic–superconductor junction. The ferromagnetic and superconducting properties as well as the Andreev reflection are briefly reviewed and the electrical resistance of the junction is computed both in the diffusive and ballistic regime for the ferromagnetic sample. It is shown that the resistance of the junction increases with increasing magnetization, including both positive or negative jumps on passing from the ballistic to the diffusive regime.

The Kondo effect and the Andreev reflection tunneling through a normal (ferromagnet)–double quantum dots–superconductor hybrid system is examined in the low temperature by using the nonequilibrium Green's function technique in combination with the slave-boson mean-field theory. The interplay of the Kondo physics and the Andreev bound state physics can be controlled by varying the interdot hopping strength. The Andreev differential conductance is mainly determined by the competition between Kondo states and Andreev states. The spin-polarization of the ferromagnetic electrode increases the zero-bias Kondo peak. The spin-flip scattering influences the Kondo effect and the Andreev reflection in a nontrivial way. For the ferromagnetic electrode with sufficiently large spin polarization, the negative Andreev differential conductance is found when the spin flip strength in the double quantum dots is sufficiently strong.

We theoretically investigate the spin accumulation in two parallel coupled quantum dots (QDs) with ferromagnetic and superconducting electrodes. Due to the ferromagnetic lead, the spin accumulation appears on the resonance of Andreev reflection. The spin accumulation in each of the two QDs can be controlled by the gate voltage. The sign of the spin accumulation is also controllable by tuning the bias. Furthermore, tuning the magnetic flux can exchange the amplitude of the spin accumulation in the two QDs. The Aharonov–Bohm oscillation effects also provides a way to control the spin accumulation of each QD.

Using a general expression for dc Josephson current, we study the Josephson effect in ballistic superconductor (SC)/ferromagnetic semiconductor (FS)/SC junctions, in which the mismatches of the effective mass and Fermi velocity between the FS and SC, spin polarization P in the FS, as well as strengths of potential scattering Z at the interfaces are included. It is shown that in the coherent regime, the oscillatory dependences of the maximum Josephson current on the FS layer thickness L and Josephson current on the macroscopic phase difference φ for the heavy and light holes, resulting from the spin splitting energy gained or lost by a quasiparticle Andreev-reflected at the FS/SC interface, are much different due to the different mismatches in the effective mass and Fermi velocity between the FS and the SC, which is related to the crossovers between positive (0) and negative ( π ) couplings or equivalently 0 and π junctions. Also, we find that, for the same reason, Z and P are required not to surpass different critical values for the Josephson currents of the heavy and light holes. Furthermore, it is found that, for the dependence of the Josephson current on φ , regardless of how L , Z , and P change, the Josephson junctions do not transit between 0 and π junctions for the light hole.

Spin transport properties of a mesoscopic superconductor/ferromagnetic (S/F) junctions of a quantum device are investigated. The thermoelectric voltage as a function of magnetic field oscillations for different heater currents has been calculated. The dependence shows that by increasing the heater current, the oscillation first disappears, and then remarkably reappears inverted compared to low heater current. Also, the value of the thermo-power increases with increasing value of the barrier strength. Our result shows that the degree of spin polarization of the current can be unambiguously determined using Andreev reflection. Our result agrees qualitatively with those in the literature.

Superconductors (S) can be employed to probe the spin polarization of ferromagnetic metals (F) by virtue of Andreev reflection. Using nanocontacts defined by e-beam lithography, the spin-polarization of the current across an S/F interface can be determined reliably. Via non-local Andreev reflection, an incident electron from a nanocontact is retroreflected as a hole in an adjacent contact, forming spatially separated but entangled Einstein–Podolski–Rosen pairs. Finally, the proximity-induced superconductivity can be probed by magnetization measurements.

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., Pages 6-10 contain supplemental material

An extended Blonder-Tinkham-Klapwijk (BTK) approach is applied to study the coherent spin polarized transport in an ferromagnetic semiconductor (FS)/superconductor (SC)/FS double tunelling junction, in which the Andreev reflection, mismatches in the effective mass and Fermi velocity between the FS and SC, as well as strengths of potential scattering at the interfaces are included. It is demonstrated that they have different effects on the oscillations of differential conductances with energy, which is quite different from that in an ferromanet (FM)/SC/FM double tunneling junction. A direct robust measure of the spin polarization of the FS using conductance spectroscopy, being very weakly dependent on the strengths of potential scattering and energy, is also revealed.