The newly discovered oxypnictide family of superconductors show very high critical temperatures of up to 55K. Whilst there is growing evidence that suggests a nodal order parameter, point contact Andreev reflection spectroscopy can provide crucial information such as the gap value and possibly the number of energy gaps involved. For the oxygen deficient NdFeAsO0.85 with a Tc of 45.5K, we show that there is clearly a gap value at 4.2K that is of the order of 7meV, consistent with previous studies on oxypnictides with lower Tc. Additionally, taking the spectra as a function of gold tip contact pressure reveals important changes in the spectra which may be indicative of more complex physics underlying this structure.
Using intrinsic multiple Andreev reflections effect (IMARE) spectroscopy, we studied ballistic superconductor - normal metal - superconductor (SnS) contacts in layered oxypnictide superconductors NdFeAsO$_{0.6}$H$_{0.36}$ with critical temperatures $T_c = 45-48$ K. We directly determined the magnitude of two bulk superconducting order parameters, the large gap $Δ_L \approx 10.4$ meV, and a possible small gap $Δ_S \approx 1.8$ meV, and their temperature dependence. Additionally, a resonant coupling with a characteristic bosonic mode was observed. The boson energy at 4.2 K, $\varepsilon_0 = 10.5…
Andreev reflection in ferromagnet-superconductor junctions is derived in a regime in which Zeeman splitting dominates the response of the superconductor to an applied magnetic field. Spin-up and spin-down Andreev reflections are shown to be resolved as voltage is increased. In the metallic limit, the transition from Andreev to tunnel conductivity in the spin-up channels has a non trivial behavior when spin polarization is increased. The conductance is asymmetric in a voltage reversal.
We have investigated Andreev-reflection processes occurring at a clean interface between a $p$-type semiconductor and a conventional superconductor. Our calculations are performed within a generalized Bogoliubov-de Gennes formalism where the details of the semiconductor band structure are described by a $6\times 6$ Kane model. It is found that Andreev reflection of light-hole and heavy-hole valence-band carriers is generally possible and that the two valence-band hole types can be converted into each other in the process. The normal-reflection and Andreev-reflection amplitudes depend strongly …
Understanding the subgap behavior of Normal-Insulator-Superconductor (NIS) tunnel junctions is important in order to be able to accurately model the thermal properties of the junctions. Hekking and Nazarov developed a theory in which NIS subgap current in thin-film structures can be modeled by multiple Andreev reflections. In their theory, the current due to Andreev reflections depends on the junction area and the junction resistance area product. We have measured the current due to Andreev reflections in NIS tunnel junctions for various junction sizes and junction resistance area products and…
We theoretically study the electronic transport through a ferromagnet-Ising superconductor junction. A tight-binding Hamiltonian describing the Ising superconductor is presented. Then by combing the non-equilibrium Green's function method, the expressions of Andreev reflection coefficient and conductance are obtained. A strong magnetoanisotropic spin-triplet Andreev reflection is shown, and the magnetoanisotropic period is $π$ instead of $2π$ as in the conventional magnetoanisotropic system. We demonstrate a significant increase of the spin-triplet Andreev reflection for the single-band Ising …
We consider a process of the Andreev reflection between a normal metal and the s-wave superconductor in the FFLO state. It is shown that the process takes place if the energy of the incoming electron is bound within the finite interval called the Andreev window. The position of the window determines the value of the non-zero total momentum of Cooper pairs and the value of the gap.
We study systematically the scattering processes and the conductance spectra in nodal-line semimetalsuperconductor junctions using the extended Blonder-Tinkham-Klapwijk theory. The coexistence of peculiar quadruple reflections are found, which are the specular normal reflection, the retro-normal reflection, the specular Andreev reflection and the retro-Andreev reflection. The incident angle dependence and the quasiparticle energy dependence of the double normal reflections and the double Andreev reflections are investigated under various values of parameters such as the interfacial barrier hei…
The electron-hole conversion at the normal-metal superconductor interface in inversion-symmetric Weyl semimetals is investigated with an effective two-band model. We find that the specular Andreev reflection of Weyl fermions has two unusual features. The Andreev conductance for s-wave BCS pairing states is anisotropic, depending on the angle between the line connecting a pair of Weyl points and the normal of the junction, due to opposite chirality carried by the paired electrons. For the Fulde-Ferrell-Larkin-Ovchinnikov pairing states, the Andreev reflection spectrum is isotropic and is indepe…
We study unconventional superconductivity in thin exfoliated single crystals of a promising 3D topological superconductor candidate, Nb-doped Bi$_2$Se$_3$ through Andreev reflection spectroscopy and magneto-transport. Measurements of Andreev reflection in low and high resistance samples both show enhanced conductance around zero bias and conductance dips at the superconducting energy gap. Such behavior is inconsistent with conventional Blonder-Tinkham-Klapwijk theory of Andreev reflection. We discuss how our results are consistent with $p$-wave pairing symmetry, supporting the possibility of t…
Point contact Andreev reflection studies have been conducted on FeSe single crystals by lowering the temperatures down to 0.5 K. The point contact Andreev reflection spectra were analyzed in the framework of the two-band model. As a result, the presence of two anisotropic superconducting gaps in FeSe were certainly established and their BCS-like temperature dependencies were obtained. The weights of each gap have been determined and the anisotropy parameter has been calculated. It is shown, that sub-kelvin temperatures are necessary to ascertain details of the superconducting gap structure, es…
Point contacts (PC) Andreev reflection dV/dI spectra for the antiferromagnetic (T_N =6K) superconductor (Tc=11K) ErNi2B2C have been measured for the two main crystallographic directions. Observed retention of the Andreev reflection minima in dV/dI up to Tc directly points to unusual superconducting order parameter (OP) vanishing at Tc. Temperature dependence of OP was obtained from dV/dI using recent theory of Andreev reflection including pair-breaking effect. For the first time existence of a two superconducting OPs in ErNi2B2C is shown. A distinct decrease of both OPs as temperature is lower…
A theoretical formalism of Andreev reflection is employed to provide theoretical support for distinguishing between the singlet pairing and the triplet pairing by the point contact Andreev reflection (PCAR) experiments. We utilize our theoretical curves to fit the data of the PCAR experiment on unconventional superconductivity in the Bi/Ni bilayer [arXiv:1810.10403] and find the Anderson-Brinkman-Morel (ABM) state satisfies the main characteristics of the experimental data. The chiral cross-section of the ABM state might explain well the broken time-reversal symmetry determined by the polar Ke…
We review application of point-contact Andreev-reflection spectroscopy to study elemental superconductors, where theoretical conditions for the smallness of the point-contact size with respect to the characteristic lengths in the superconductor can be satisfied. We discuss existing theoretical models and identify new issues that have to be solved, especially when applying this method to investigate more complex superconductors. We will also demonstrate that some aspects of point-contact Andreev-reflection spectroscopy still need to be addressed even when investigating ordinary metals.
We have experimentally investigated the quasiparticle shot noise in NbN/MgO/NbN superconductor - insulator - superconductor tunnel junctions. The observed shot noise is significantly larger than theoretically expected. We attribute this to the occurrence of multiple Andreev reflection processes in pinholes present in the MgO barrier. This mechanism causes the current to flow in large charge quanta (Andreev clusters), with a voltage dependent average value of m = 1+ 2 Delta/eV times the electron charge. Because of this charge enhancement effect, the shot noise is increased by the factor m.
We report tunable crossed Andreev reflection (CAR) in a superconductor sandwiched between two antiferromagnetic layers. We consider recent examples of two-dimensional magnets with hexagonal lattices, where gate voltages control the carrier type and density, and predict a robust signature of perfect CAR in the nonlocal differential conductance with one electron-doped and one hole-doped antiferromagnetic lead. The magnetic field-free and spin-degenerate CAR signal is electrically controlled and visible over a large voltage range, showing promise for solid-state quantum entanglement applications.
We study Andreev reflection and the Josephson effect in a ballistic monolayer of black phosphorous, known as phosphorene. Due to the anisotropic band structure of this system, the supercurrent changes with an order of magnitude when comparing tunneling along two perpendicular directions in the monolayer. We show that the main reason for this effect is a large difference in the number of transverse modes in Andreev bound states. The oscillatory behavior of the supercurrent as a function of the length and chemical potential of the junction also differs substantially depending on the orientation …
The quasiparticle reflection and transmission properties at normal conductor-superconductor interfaces are discussed for unitary and non-unitary spin triplet pairing states recently proposed for Sr_2RuO_4. We find resonance peaks in the Andreev reflection amplitude, which are related to surface bound states in the superconductor. They lead to conductance peak features below the quasiparticle gap in the superconductor. The position of the peaks depends on the angle of the incident quasiparticles in a different way for unitary and non-unitary states. Based on this observation we propose a possib…
We analyze non-local effects in electron transport across three-terminal normal-superconducting-normal (NSN) structures. Subgap electrons entering S-electrode from one N-metal may form Cooper pairs with their counterparts penetrating from another N-metal. This phenomenon of crossed Andreev reflection -- combined with normal scattering at SN interfaces -- yields two different contributions to non-local conductance which we evaluate non-perturbatively at arbitrary interface transmissions. Both these contributions reach their maximum values at fully transmitting interfaces and demonstrate interes…
We have measured Andreev reflections between an Au tip and Y_{1-x}Ca_{x}Ba_{2}Cu_{3}O_{7 - δ} thin films in the in-plane orientation. The conductance spectra are best fitted with a pair potential having the "d_{x^{2}-y^{2}+is" symmetry. We find that the amplitude of the "is" component is enhanced as the contact transparency is increased. This is an indication for an unusual proximity effect that modifies the pair potential in the superconductor near the surface with the normal metal.
Scanning tunneling spectroscopy measurements on thin epitaxial SrRuO3/(100)YBCO ferromagnet/superconductor bilayers, reveal localized regions in which the superconductor order parameter penetrates the ferromagnet to more than 26 nm, an order of magnitude larger than the coherence length in the ferromagnetic layer. These regions consist of narrow (< 10 nm) and long strips, separated by at least 200 nm, consistent with the known magnetic domain wall structure in SrRuO3. We attributed this behavior to Crossed Andreev Reflections, taking place in the vicinity of the magnetic domain walls.
We present a theoretical analysis of the shot noise in d-wave/d-wave contacts with arbitrary transparency, including the contribution of multiple Andreev reflections. The multiple charge quanta transferred in these processes are revealed as a huge enhancement of the noise-current ratio at low voltages, which survives for all crystal misorientations. We also show how different ingredients like non-magnetic impurities or a magnetic field produce very characteristic hallmarks in the shot noise, which can be used as a further test of the d-wave scenario in superconducting cuprates.
We present a theory of the current-voltage characteristics in diffusive superconductor-normal-metal-superconductor junctions. By solving the time-dependent Usadel equations we are able to describe the phase-coherent transport for arbitrary length of the normal wire. We show how the interplay between proximity effect and multiple Andreev reflections gives rise to a rich subgap structure in the conductance and how it is revealed in the non-equilibrium distribution function.
Layered oxypnictide Sm$_{1-x}$Th$_x$OFeAs (Sm-1111) is an ideal candidate to be probed by intrinsic multiple Andreev reflections effect (IMARE) spectroscopy. Using the classical "break-junction" technique, we formed ballistic Andreev arrays of identical S--n--S-contacts, where $S$ is superconductor, and $n$ is a layer of normal metal. For $T < T_C$, the I(V) curve shows an excess-current and a subharmonic gap structure (SGS): a set of sharp dI(V)/dV-dips at positions which depend on the superconducting gap value, the number of junctions in the array, and the natural subharmonic order, thus man…
When the $d_{x^2-y^2}$-wave pairing is suppressed by Zn-doping in $YBa_2Cu_3O_{7-δ}$ some of the Andreev reflection spectra were found to be similar to the s-wave spectra of conventional superconductors. The energy gap is rather reproducible (2.3-3.0meV). It is suppressed by low magnetic field ($H_C^{PC}=120-270mT$) in great contrast to the d-wave spectra ($H_C^{PC}>3T$) with the similar order of the gap value. We suppose that the s-wave pairing occurs near the Zn-impurities.
We calculate the current-pressure characteristics of a ballistic pinhole aperture between two volumes of B-phase superfluid 3He. The most important mechanism contributing to dissipative currents in weak links of this type is the process of multiple Andreev reflections. At low biases this process is significantly affected by relaxation due to inelastic quasiparticle-quasiparticle collisions. In the numerical calculations, suppression of the superfluid order parameter at surfaces is taken into account self-consistently. When this effect is neglected, the theory may be developed analytically like…
We construct a theory for low-energy quantum transport in normal$\mid$superconductor junctions involving the recently discovered iron-based high-$T_c$ superconductors. We properly take into account both Andreev bound surface states and the complex Fermi surface topology in our approach, and investigate the signatures of the possible order parameter symmetries for the FeAs-lattice. Our results could be helpful in determining the symmetry of the superconducting state in the iron-pnicitide superconductors.
We report on transport measurements on Nb/Al/Gd/Al/Nb junctions.Bulk Gadolinium is a weakly polarized ferromagnet (5-7%), and is present in the junction in granular form (superparamagnet). We show that Andreev reflection is strongly enhanced by a weak polarization, obtained by applying an external magnetic field. A new model is proposed that accounts for this effect. The transport is described in terms of ``hot'' carriers that experience Zeeman splitting due to the spin polarized background. The Landauer formula is $G=(4e^2)/h A(h_b)$, $h_b$ being the exchange field at the grain boundary, and …
Systematic studies of the NdFeAsOF superconducting energy gap via the point-contact Andreev-reflection (PCAR) spectroscopy are presented. The PCAR conductance spectra show at low temperatures a pair of gap-like peaks at about 4 - 7 mV indicating the superconducting energy gap and in most cases also a pair of humps at around 10 mV. Fits to the s-wave two-gap model of the PCAR conductance allowed to determine two superconducting energy gaps in the system. The energy-gap features however disappear already at T* = 15 to 20 K, much below the particular Tc of the junction under study. At T* a zero-b…
A theory of coherent multiple Andreev reflections (MAR) is developed for superconductor-normal metal-superconductor (SNS) interferometers. We consider a Y-shape normal electron beam splitter connecting two superconducting reservoirs, where the two connection points to the same superconductor can have different phase. The current is calculated in the quantum transport regime as a function of applied voltage and phase difference, $I(V,ϕ)$. MAR in interferometers incorporates two features: interference in the arms of the splitter, and interplay with Andreev resonances. The latter feature yields e…
Andreev reflection at the interface between a half-metallic ferromagnet and a spin-singlet superconductor is possible only if it is accompanied by a spin flip. Here we calculate the Andreev reflection amplitudes for the case that the spin flip originates from a spatially non-uniform magnetization direction in the half metal. We calculate both the microscopic Andreev reflection amplitude for a single reflection event and an effective Andreev reflection amplitude describing the effect of multiple Andreev reflections in a ballistic thin film geometry. It is shown that the angle and energy depende…
In the framework of Bogoliubov-de Gennes equation, we theoretically study the Andreev reflection in normal-superconducting junctions based on semi-Dirac materials. Owing to the intrinsic anisotropy of semi-Dirac materials, the configuration of Andreev reflection and differential conductance are strongly orientation-dependent. For the transport along the linear dispersion direction, the differential conductance exhibits a clear crossover from retro Andreev reflection to specular Andreev reflection with an increasing bias-voltage, and the differential conductance oscillates without a decaying pr…
We theoretically study the crossed Andreev reflection in a hybrid nanostructure which comprises a d-wave superconductor and two normal-metal quantum wires. When the superconductor of the (110) oriented surface is in contact with the wires parallel and placed close to each other, the Andreev bound state is formed by the crossed Andreev reflection. When the contact barrier potential is sufficiently large, two sharp peaks appear in the conductance well below the gap structure, which originate from the bonding and antibonding Andreev bound states. We propose that these Andreev bound states form a …
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 fiel…
We study Andreev reflection in a normal conductor-molecule-superconductor junction using a first principles approach. In particular, we focus on a family of molecules consisting of a molecular backbone and a weakly coupled side group. We show that the presence of the side group can lead to a Fano resonance in the Andreev reflection. We use a simple theoretical model to explain the results of the numerical calculations and to make predictions about the possible sub-gap resonance structures in the Andreev reflection coefficient.
We calculate the full transport counting statistics in a three-terminal tunnel device with one superconducting source and two normal-metal or ferromagnet drains. We obtain the transport probability distribution from direct Andreev reflection, crossed Andreev reflection, and electron transfer which reveals how these processes' statistics are determined by the device conductances. The cross-correlation noise is a result of competing contributions from crossed Andreev reflection and electron transfer, as well as antibunching due to the Pauli exclusion principle. For spin-active tunnel barriers th…
Andreev reflection at the interface between a ferromagnet and a superconductor has become a foundation of a versatile new technique of measuring the spin polarization of magnetic materials. In this paper we will briefly outline a general theory of Andreev reflection for spin-polarized systems and arbitrary Fermi surface in two limiting cases of ballistic and diffusive transport
The crossed Andreev reflection in a hybrid nanostructure consisting of a d-wave superconductor and two quantum wires is theoretically studied. When the (110) oriented surface of the superconductor is in contact with the wires parallel and placed close to each other, the Andreev bound state is formed by the crossed Andreev reflection. The conductance has two resonance peaks well below the gap structure in the case of tunnel contacts. These peaks originate from the bonding and antibonding Andreev bound states of hole wave functions.
We investigate the crossed Andreev reflections between two graphene leads connected by a narrow superconductor. When the leads are respectively of the n-and p- type, we find that electron elastic cotunneling and local Andreev reflection are both eliminated even in the absence of any valley-isospin or spin polarizations. We further predict oscillations of both diagonal and cross conductances as a function of the distance between the graphene-superconductor interfaces.
Nonlocal currents, in devices where two normal metal terminals are contacted to a superconductor, are determined using the circuit theory of mesoscopic superconductivity. We calculate the conductance associated with crossed Andreev reflection and electron transfer between the two normal metal terminals, in addition to the conductance from direct Andreev reflection and quasiparticle tunneling. Dephasing and proximity effect are taken into account.
We investigate theoretically charge transport in hybrid multiterminal junctions with superconducting leads kept at different voltages. It is found that multiple Andreev reflections involving several superconducting leads give rise to rich subharmonic gap structures in the current-voltage characteristics. The structures are evidenced numerically in junctions in the incoherent regime.
We study Andreev reflection at an interface between a half metal and a superconductor with spin-orbit interaction. While the absence of minority carriers in the half metal makes singlet Andreev reflection impossible, the spin-orbit interaction gives rise to triplet Andreev reflection, i.e., the reflection of a majority electron into a majority hole or vice versa. As an application of our calculation, we consider a thin half metal film or wire laterally attached to a superconducting contact. If the half metal is disorder free, an excitation gap is opened that is proportional to the spin-orbit i…
The Andreev reflection amplitude at a clean interface between a half-metallic ferromagnet (H) and a superconductor (S) for which the half metal's magnetization has a gradient perpendicular to the interface is proportional to the excitation energy $\varepsilon$ and vanishes at $\varepsilon=0$ [Béri {\em et al.}, Phys.\ Rev.\ B {\bf 79}, 024517 (2009)]. Here we show that the presence of impurities at or in the immediate vicinity of the HS interface leads to a finite Andreev reflection amplitude at $\varepsilon=0$. This impurity-assisted Andreev reflection dominates the low-bias conductance of a …
Crossed Andreev reflection in multiterminal structures in the diffusive regime is addressed within the quasiclassical Keldysh-Usadel formalism. The elastic cotunneling and crossed Andreev reflection of quasiparticles give nonlocal currents and voltages (depending on the actual biasing of the devices) by virtue of the induced proximity effect in the normal metal electrodes. The magnitude of the nonlocal processes is found to scale with the square of the barrier transparency and to decay exponentially with interface spacing. Nonlocal cotunneling and crossed Andreev conductances are found to cont…
We derive the full distribution of transmitted particles through a superconducting point contact of arbitrary transparency under voltage bias. The charge transport is dominated by multiple Andreev reflections. The counting statistics is a multinomial distribution of processes, in which multiple charges ne (n=1,2,3,...) are transferred through the contact. For zero temperature we obtain analytical expressions for the probabilities of the multiple Andreev reflections. The current, shot noise and high current cumulants in a variety of situations can be obtained from our result.
Hybrid superconductor/graphene (SC/g) junctions are excellent candidates for investigating correlations between Cooper pairs and quantum Hall (QH) edge modes. Experimental studies are challenging as Andreev reflections are extremely sensitive to junction disorder and high magnetic fields are required to form QH edge states. We fabricated low-resistance SC/g interfaces, composed of graphene edge contacted with NbN with a barrier strength of $Z\approx 0.4$, that remain superconducting under magnetic fields larger than $18$ T. We establish the role of graphene's Dirac band structure on zero-field…
The Andreev reflection of narrow ferromagnet/superconductor point contacts is theoretically studied. We show that the conductance quantization depends on whether the contact region is superconducting or ferromagnetic as well as on the strength of the exchange field in the ferromagnet. The Andreev reflection of the ferromagnetic contact is more suppressed than that of the superconducting contact. We also show that the conductance-voltage curve has a bump at zero bias-voltage if there is no interfacial-scattering. On the contrary, the conductance-voltage curve shows a dip if the system has an in…
A theory of crossed Andreev reflection in structures consisting of a superconductor with two ferromagnetic leads is presented. The electric current due to the crossed Andreev reflection strongly depends on the relative orientation of the magnetization of two ferromagnetic leads. It is shown that the dependence of the electric current and the magnetoresistance on the distance between two ferromagnetic leads is understood by considering the interference between the wave functions in ferromagnets. The current and the magnetoresistance are calculated as functions of the exchange field and the heig…
Using the tight binding model and the non-equilibrium Green function method, we study Andreev reflection in graphene-superconductor junction, where graphene has two nonequal Dirac Cones split in energy and therefore time reversal symmetry is broken. Due to the anti-chiral edge states of the current graphene model, an incident electron travelling along the edges makes distinct contribution to Andreev reflections. In a two-terminal device, because Andreev retro-reflection is not allowed for just the anti-chiral edges, in this case the mutual scattering between edge and bulk states is necessary, …
Andreev reflection is investigated in layered anisotropic normal metal / superconductor (N/S) systems in the case of an energy gap Δin S not negligible with respect to the Fermi energy E_F, as it probably occurs with high critical temperature superconductors (HTS). We find that in these limits retro-reflectivity, which is a fundamental feature of Andreev reflection, is broken modifying sensitively transport across S/N interfaces. We discuss the consequences for supercurrents in HTS Josephson junctions and for the midgap states in S-N contacts
We study Multiple Andreev Reflections in long diffusive superconductor(S)-normal metal(N)-superconductor junctions with low-transparency interfaces. Assuming strong thermalization in the weak link we calculate the current-voltage dependence $I(V)$. At intermediate temperatures, $E_\mathrm{Th}\ll T\llΔ$, the current is dominated by noncoherent multiple Andreev reflections and is obtained analytically. The results are generalized to a ferromagnetic junction. We find that the exchange field produces a non-trivial splitting of the subharmonic gap structure. This effect relies on thermalization and…
We formulate a minimal model of point contact Andreev reflection spectroscopy of a normal- metal/multiband superconductor interface. The theory generalizes the Blonder-Tinkham-Klapwijk (BTK) formulation to a multiband superconductor and it is based on the quantum waveguides theory. The proposed approach allows an analytic evaluation of the Andreev and normal reflection coefficients and thus is suitable for a data fitting of point contact experiments. The obtained differential conductance curves present distinctive features similar to the ones measured in the experiments on multiband systems, l…
We investigate Andreev reflection at the interface between a superconductor and a two--dimensional electron system (2DES) in an external magnetic field such that cyclotron motion is important in the latter. A finite Zeeman splitting in the 2DES and the presence of diamagnetic screening currents in the superconductor are incorporated into a microscopic theory of Andreev edge states, which is based on the Bogoliubov--de Gennes formalism. The Andreev--reflection contribution to the interface conductance is calculated. The effect of Zeeman splitting is most visible as a double--step feature in the…
We study the Josephson effect in a clean Superconductor-Ferromagnet-Superconductor junction for arbitrarily large spin polarizations. The Andreev reflection at a clean Ferromagnet-Superconductor interface is incomplete, and Andreev channels with a large incidence angle are progressively suppressed with increasing exchange energy. As a result, the critical current exhibits oscillations as a function of the exchange energy and of the length of the ferromagnet and has a temperature dependence which deviates from the one predicted by the quasiclassical theory.
The energy-dependent Andreev reflection eigenvalues determine the transport properties of normal-superconducting systems. We evaluate the eigenvalue density to get an insight into formation of resonant electron-hole transport channels. The circuit-theory-like method developed can be applied to any generic mesoscopic conductor or combinations thereof. We present the results for experimentally relevant cases of a diffusive wire and a double tunnel junction.
