We have investigated the transmission of electrons and holes through interfaces between superconducting aluminum (Tc = 1.2 K) and various normal non-magnetic metals (copper, gold, palladium, platinum, and silver) using Andreev-reflection spectroscopy at T = 0.1 K. We analyzed the point contacts with the modified BTK theory that includes Dynes' lifetime as a fitting parameter G in addition to superconducting energy gap 2D and normal reflection described by Z. For contact areas from 1 nm^2 to 10000 nm^2 the BTK Z parameter was 0.5, corresponding to transmission coefficients of about 80 %, independent of the normal metal. The very small variation of Z indicates that the interfaces have a negligible dielectric tunneling barrier. Fermi surface mismatch does not account for the observed transmission coefficient.
The bulk microwave conductivity of a dirty d-wave superconductor is known to depend sensitively on the range of the disorder potential: long-range scattering enhances the conductivity, while short- range scattering has no effect. Here we show that the three-terminal electrical conductance of a normal-metal-d-wave superconductor-normal-metal junction has a dual behavior: short-range scattering suppresses the conductance, while long-range scattering has no effect.
We present measurements of current noise and cross-correlations in three-terminal Superconductor-Normal metal-Superconductor (S-N-S) nanostructures that are potential solid-state entanglers thanks to Andreev reflections at the N-S interfaces. The noise correlation measurements spanned from the regime where electron-electron interactions are relevant to the regime of Incoherent Multiple Andreev Reflection (IMAR). In the latter regime, negative cross-correlations are observed in samples with closely-spaced junctions.
We discuss the quasiparticle entropy and heat capacity of a dirty superconductor-normal metal-superconductor junction. In the case of short junctions, the inverse proximity effect extending in the superconducting banks plays a crucial role in determining the thermodynamic quantities. In this case, commonly used approximations can violate thermodynamic relations between supercurrent and quasiparticle entropy. We provide analytical and numerical results as a function of different geometrical parameters. Quantitative estimates for the heat capacity can be relevant for the design of caloritronic d…
Anomalous far infrared monochromatic transmission through a film of type-II superconductor in magnetic field
发现并报道了通过II型超导薄膜中Abrikosov涡旋晶格的异常远红外单色传输。透射频率对应于由Abrokosov晶格的缺陷局域化的光子模式。这些缺陷是由放置在理想Abrokosov晶格的节点之外的额外涡旋形成的。额外的涡旋可以被超导体的晶格缺陷钉扎。相应的频率作为磁场和温度的函数的狄拉克型的两个带模型的框架内进行了研究。虽然我们的方法是有效的所有II型超导体，具体的计算已经进行了YBa $_{2}$ Cu $_{3}$ O $_{7-δ}$（YBCO）。分析了通过改变磁场和/或温度来控制发射频率。指出所发现的透射局域模可用于远红外单色滤光片。
Systems of superconducting islands placed on normal metal films offer tunable realizations of two-dimensional (2D) superconductivity; they can thus elucidate open questions regarding the nature of 2D superconductors and competing states. In particular, island systems have been predicted to exhibit zero-temperature metallic states. Although evidence exists for such metallic states in some 2D systems, their character is not well understood: the conventional theory of metals cannot explain them, and their properties are difficult to tune. Here, we characterize the superconducting transitions in m…
We develop a theory of current-voltage (I-U) characteristics for superconductor-normal metal-superconductor (SNS) junctions. At small voltages and sufficiently low temperatures the I-U characteristics of the junction is controlled by the inelastic relaxation time, τ_{in}. In particular, the linear conductance is proportional to, τ_{in}. In this regime the I-U characteristics can be expressed solely in terms of dependence of the density of states in the normal region, ν(χ), on the phase difference of the order parameter across the the junction. In contrast, at large voltages the I-U characteris…
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…
We study a diffusive superconductor-normal metal-superconductor junction in an environment with intrinsic incoherent fluctuations which couple to the junction through an electromagnetic field. When the temperature of the junction differs from that of the environment, this coupling leads to an energy transfer between the two systems, taking the junction out of equilibrium. We describe this effect in the linear response regime and show that the change in the supercurrent induced by this coupling leads to qualitative changes in the current-phase relation and for a certain range of parameters, an …
We investigate electron cooling based on a clean normal-metal/spin-filter/superconductor junction. Due to the suppression of the Andreev reflection by the spin-filter effect, the cooling power of the system is found to be extremely higher than that for conventional normal-metal/nonmagnetic-insulator/superconductor coolers. Therefore we can extract large amount of heat from normal metals. Our results strongly indicate the practical usefulness of the spin-filter effect for cooling detectors, sensors, and quantum bits.
The fractional Josephson effect is known to be a characteristic phenomenon of topological Josephson junctions hosting Majorana zero modes (MZMs), where the Josephson current has a $4π$ (rather than a $2π$) periodicity in the phase difference between the two topological superconductors. We introduce a one-dimensional model of a topological superconductor/normal-metal/superconductor (SNS) junction with the normal-metal (N) region of finite length, which is intermediate regime between the short- and long-junction limits. Assuming weak tunneling at the SN interfaces, we investigate resonance and f…
The phase difference $ϕ$, between the superconducting terminals in superconductor-normal metal-superconductor tunnel junctions (SINIS), incorporates the phase differences $χ_{1,2}$ across thin interfaces of constituent $SIN$ junctions and the phase incursion $φ$ between the side faces of the central electrode of length $L$. It is demonstrated here that $χ_{1,2}$ pass through over their proximity-reduced domain twice, there and back, while $ϕ$ changes over the single period. Two corresponding solutions, that describe the double-valued order-parameter dependence on $χ_{1,2}$, jointly form the si…
We study the variation of the differential conductance $G=dj/dV$ of a normal metal wire in a Superconductor/Normal metal heterostructure with a cross geometry under external microwave radiation applied to the superconducting parts. Our theoretical treatment is based on the quasiclassical Green's functions technique in the diffusive limit. Two limiting cases are considered: first, the limit of a weak proximity effect and low microwave frequency, second, the limit of a short dimension (short normal wire) and small irradiation amplitude.
We report on nonlocal transport in superconductor hybrid structures, with ferromagnetic as well as normal-metal tunnel junctions attached to the superconductor. In the presence of a strong Zeeman splitting of the density of states, both charge and spin imbalance is injected into the superconductor. While previous experiments demonstrated spin injection from ferromagnetic electrodes, we show that spin imbalance is also created for normal-metal injector contacts. Using the combination of ferromagnetic and normal-metal detectors allows us to directly discriminate between charge and spin injection…
We propose a spin Hall device to induce a large spin Hall effect in a superconductor/normal metal (SN) junction. The side jump and skew scattering mechanisms are both taken into account to calculate the extrinsic spin Hall conductivity in the normal metal. We find that both contributions are anomalously enhanced when the voltage between the superconductor and the normal metal approaches to the superconducting gap. This enhancement is attributed to the resonant increase of the density of states in the normal metal at the Fermi level. Our results demonstrate a novel way to control and amplify th…
We report the study of ballistic transport in normal metal/graphene/superconductor junctions in edge-contact geometry. While in the normal state, we have observed Fabry-Pérot resonances suggesting that charge carriers travel ballistically, the superconducting state shows that the Andreev reflection at the graphene/superconductor interface is affected by these interferences. Our experimental results in the superconducting state have been analyzed and explained with a modified Octavio-Tinkham-Blonder-Klapwijk model taking into account the magnetic pair-breaking effects and the two different inte…
The nonlocal conductance and the current cross-correlations are investigated within scattering theory for three-terminal normal metal-superconductor-normal metal (NSN) hybrid structures. The positive cross-correlations at high transparency found by Mélin, Benjamin and Martin [Phys. Rev. B 77, 094512 (2008)] are not due to crossed Andreev reflection. On the other hand, local processes can be enhanced by reflectionless tunneling but this mechanism has little influence on nonlocal processes and on current cross-correlations. Therefore Cooper pair splitting cannot be enhanced by reflectionless tun…
We investigate the full counting statistics of a voltage-driven normal metal(N)-superconductor(S) contact. In the low-bias regime below the superconducting gap, the NS contact can be mapped onto a purely normal contact, albeit with doubled voltage and counting fields. Hence in this regime the transport characteristics can be obtained by the corresponding substitution of the normal metal results. The elementary processes are single Andreev transfers and electron- and hole-like Andreev transfers. Considering Lorentzian voltage pulses we find an optimal quantization for half-integer Levitons.
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 …
We analyze non-equilibrium states in a tunnel superconductor-normal metal (NSN) structure in the presence of a tunnel current $I$. We use an approximation of an effective temperature $T$ and calculate the current-voltage I-V characteristics. It is shown that the I-V dependence may have an S-shaped form. We determine nonuniform current $I(x)$ and temperature $T(x)$ distributions that arise as a result of instability of the uniform state with negative differential conductance ($dI/dV<0$). We discuss an analogy with equilibrium superconductors with an exchange field in which nonuniform states pre…
I derive a general set of boundary conditions for quasiclassical transport theory of metals and superconductors that is valid for equilibrium and non-equilibrium situations and includes multi-band systems, weakly and strongly spin-polarized systems, and disordered systems. The formulation is in terms of the normal state scattering matrix. Various special cases for boundary conditions are known in the literature, that are however limited to either equilibrium situations or single band systems. The present formulation unifies and extends all these results. In this paper I will present the genera…
We calculate the transmission of electrons and holes between two normal-metal electrodes (N), separated over a distance L by an impurity-free superconductor (S) with d-wave symmetry of the order parameter. Nodal lines of vanishing excitation gap form ballistic conduction channels for coupled electron-hole excitations, described by an anisotropic two-dimensional Dirac equation. We find that the transmitted electrical and thermal currents, at zero energy, both have the pseudodiffusive 1/L scaling characteristic of massless Dirac fermions - regardless of the presence of tunnel barriers at the NS …
Spin-polarized normal-metal wires coupled to a superconductor can host Majorana states at their ends. These decay into the bulk and are protected by a minigap in the spectrum. Previous studies have found that strong coupling between the superconductor and the normal-metal wire renormalizes the properties of this low-energy phase. Here, we develop a semiclassical scattering approach to explain these renormalization effects. We show that a renormalization of the propagation velocity in the normal wire originates from double Andreev reflection processes at the superconductor interface and that it…
We study the quantum transport behavior of a normal-superconductor-normal junction based on type-II Weyl semimetal, which is arranged in the tilting direction of the Weyl semimetal. We find that both the crossed Andreev reflection and normal reflection are forbidden, while there will be double Andreev reflections and double electron transmissions for the incident electron from the semimetal side. Andreev reflections and transmissions occur both in the retro and specular directions simultaneously, symmetric about the normal of the interface but with different amplitudes, depending on the angle …
Divergence at low bias and down-mixing of the current noise in a diffusive superconductor-normal metal-superconductor junction
我们目前的电流噪声测量在一个长的扩散超导正常金属超导结在低电压制度，其中运输可以部分地描述在相干多Andreev反射。我们发现，当电压降低时，电流噪声表现出强烈的发散性以及一个宽峰。我们把这个峰归因于交流约瑟夫森电流和结本身噪声之间的混合。我们表明，结噪声对应于一个非线性电阻4kBT=R，R V = I V和没有可调参数的热噪声。
The superconductor-insulator transition in two dimensions has been widely investigated as a paradigmatic quantum phase transition. The topic remains controversial, however, because many experiments exhibit a metallic regime with saturating low-temperature resistance, at odds with conventional theory. Here, we explore this transition in a novel, highly controllable system, a semiconductor heterostructure with epitaxial Al, patterned to form a regular array of superconducting islands connected by a gateable quantum well. Spanning nine orders of magnitude in resistance, the system exhibits regime…
Two-dimensional superconductors with time-reversal symmetry have a Z_2 topological invariant, that distinguishes phases with and without helical Majorana edge states. We study the topological phase transition in a class-DIII network model, and show that it is associated with a metal-insulator transition for the thermal conductance of the helical superconductor. The localization length diverges at the transition with critical exponent nu approx 2.0, about twice the known value in a chiral superconductor.
We study low temperature electron transport in p-wave superconductor-insulator-normal metal junctions. In diffusive metals the p-wave component of the order parameter decays exponentially at distances larger than the mean free path $l$. At the superconductor-normal metal boundary, due to spin-orbit interaction, there is a triplet to singlet conversion of the superconducting order parameter. The singlet component survives at distances much larger than $l$ from the boundary. It is this component that controls the low temperature resistance of the junctions. As a result, the resistance of the sys…
We analyse the possibility of the appearance of spontaneous currents in proximated superconducting/normal metal (S/N) heterostructure when Cooper pairs penetrate into the normal metal from the superconductor. In particular, we calculate the free energy of the S/N structure. We show that whereas the free energy of the N film $F_{N}$ in the presence of the proximity effect increases compared to the normal state, the total free energy, which includes the boundary term $F_{B}$, decreases. The condensate current decreases $F_{N}$, but increases the total free energy making the current-carrying stat…
