We explore charge imbalance in mesoscopic normal-metal/superconductor multiterminal structures at very low temperatures. The investigated samples, fabricated by e-beam lithography and shadow evaporation, consist of a superconducting aluminum bar with several copper wires forming tunnel contacts at different distances from each other. We have measured in detail the local and non-local conductance of these structures as a function of the applied bias voltage V, the applied magnetic field B, the temperature T and the contact distance d. From these data the charge-imbalance relaxation length lambda_Q* is derived. The bias-resolved measurements show a transition from dominant elastic scattering close to the energy gap to an inelastic two-stage relaxation at higher bias. We observe a strong suppression of charge imbalance with magnetic field, which can be directly linked to the pair-breaking parameter. In contrast, practically no temperature dependence of the charge-imbalance signal was observed below 0.5 K. These results are relevant for the investigation of other non-local effects such as crossed Andreev reflexion and spin diffusion.
We consider quasiparticle charge and energy imbalances in a thin superconductor weakly coupled with two normal-metal electrodes via tunnel junctions at low temperatures. Charge and energy imbalances, which can be created by injecting quasiparticles at one junction, induce excess tunneling current $I_{\rm ex}$ at the other junction. We numerically obtain $I_{\rm ex}$ as a function of the bias voltage $V_{\rm det}$ across the detection junction. We show that $I_{\rm ex}$ at the zero bias voltage is purely determined by the charge imbalance, while the energy imbalance causes a nontrivial $V_{\rm …
What happens to spin-polarised electrons when they enter a superconductor? Superconductors at equilibrium and at finite temperature contain both paired particles (of opposite spin) in the condensate phase as well as unpaired, spin-randomised quasiparticles. Injecting spin-polarised electrons into a superconductor thus creates both spin and charge imbalances [1, 2, 3, 4, 5, 6, 7] (respectively Q* and S*, cf. Ref. [4]). These must relax when the injection stops, but not necessarily over the same time (or length) scale as spin relaxation requires spin-dependent interactions while charge relaxatio…
We analysed the electron-hole or, in another words, branch imbalance (BI) and the related electric potential $V_{imb}$ which may arise in a mesoscopic superconductor/normal metal (S/N) structure under non-equilibrium conditions in the presence of a supercurrent. Non-equilibrium conditions can be created in different ways: a) a quasiparticle current flowing between the N reservoirs; b) a temperature gradient between the N reservoirs and no quasiparticle current. It is shown that the voltage $V_{imb}$ oscillates with the phase difference $ϕ$. In a cross-geometry structure the voltage $V_{imb}$ a…
We develop a theory of spin relaxation in Zeeman-splitted superconducting films at low temperatures. A new mechanism of spin relaxation, specific only for Zeeman-splitted superconductors is proposed. It can explain the extremely high spin relaxation lengths, experimentally observed in Zeeman-splitted superconductors, and their strong growth with the magnetic field. In the framework of this mechanism the observed spin signal is formed by the spin-independent nonequilibrium quasiparticle distribution weighted by the spin-split DOS. We demonstrate that the relaxation length of such a spin signal …
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…
In superconductors spin-split by an exchange field, thermal effects are coupled to spin transport. We show how an oscillating electromagnetic field in such systems creates spin imbalance, that can be detected with a spin-polarized probe. The sign and magnitude of the probe signal result from a competition between processes converting field induced spin energy imbalance to spin imbalance, dominant at low frequencies, and microwave-driven pair breaking at high frequencies. In the presence of spin-flip scattering, we show that ac excitation also leads to multistabilities in the superconducting st…
In a superconductor coupled with a ferromagnetic metal, spin and charge imbalances can be induced by injecting spin-polarized electron current from the ferromagnetic metal. We theoretically study a nonequilibrium distribution of quasiparticles in the presence of spin and charge imbalances. We show that four distribution functions are needed to characterize such a nonequilibrium situation, and derive a set of linearized Boltzmann equations for them by extending the argument by Schmid and Schön based on the quasiclassical Green's function method. Using the Boltzmann equations, we analyze the spi…
A theory of spin transport and spin detection in Zeeman-split superconducting films at low temperatures is developed. It is shown that an injection of spin-unpolarized quasiparticles into a Zeeman-split superconductor gives rise to a spin imbalance. The relaxation length of such a spin signal is determined by the energy relaxation length and can be extremely large as compared to the relaxation length of spin-polarized quasiparticles. There can exist two types of signals: due to nonthermalized quasiparticle distribution and due to thermalized overheated electron distribution. They have differen…
We have measured the lifetime of spin imbalances in the quasiparticle population of a superconductor ($τ_s$) in the frequency domain. A time-dependent spin imbalance is created by injecting spin-polarised electrons at finite excitation frequencies into a thin-film mesoscopic superconductor (Al) in an in-plane magnetic field (in the Pauli limit). The time-averaged value of the spin imbalance signal as a function of excitation frequency, $f_{RF}$ shows a cut-off at $f_{RF} \approx 1/(2πτ_s)$. The spin imbalance lifetime is relatively constant in the accessible ranges of temperatures, with perhap…
We consider a $SBS$ Josephson junction the superconducting electrodes $S$ of which are in contact with normal metal reservoirs ($B$ means a barrier). For temperatures near $T_{c}$ we calculate an effective critical current $% I_{c}^{\ast}$ and the resistance of the system at the currents $I<$ $% I_{c}^{\ast}$ and $I>>I_{c}^{\ast}$. It is found that the charge imbalance, which arises due to injection of quasiparticles from the $N$ reservoirs into the $S$ wire, affects essentially the characteristics of the structure. The effective critical current $I_{c}^{\ast}$ is always larger than the critic…
We present a numerical model of local and nonlocal transport properties in a lateral spin valve structure consisting of two magnetic electrodes in contact with a third perpendicular superconducting electrode. By considering the transport paths for a single electron incident at the local F/S interface - in terms of probabilities of crossed or local Andreev reflection, elastic cotunneling or quasiparticle transport - we show that this leads to nonlocal charge imbalance. We compare this model with experimental data from an aluminum-permalloy (Al/Py) lateral spin valve geometry device and demonstr…
Recently thermally created pure spin currents were predicted for Zeeman-split superconductor/normal metal heterostructures. Here it is shown that this "thermospin" current can lead to an accumulation of a pure spin imbalance in a system. The thermally induced spin imbalance can reach the value of Zeeman splitting of the superconducting DOS and strongly influences superconductivity in the heterostructure. Depending on the temperature difference between the superconductor and the normal reservoir it can enhance the critical temperature of the superconductor or additionally suppress the zero-temp…
Crossed Andreev reflection in a lateral spin valve geometry device is an aspect of considerable recent interest, particularly with regards to Cooper pair splitting experiments to realize solid state quantum entanglement. In this work, devices are fabricated consisting of two ferromagnetic permalloy (Py) electrodes contacted by a overlaid perpendicular superconducting Ta electrode, of variable lateral in-plane offset within the expected BCS superconducting coherence length $ξ_0$. Experimental electrical transport measurements are presented of local and nonlocal conduction, showing characteristi…
Crossed Andreev reflection (CAR) in metallic nanostructures, a possible basis for solid-state electron entangler devices, is usually investigated by detecting non-local voltages in multi-terminal superconductor/normal metal devices. This task is difficult because other subgap processes may mask the effects of CAR. One of these processes is the generation of charge imbalance (CI) and the diffusion of non-equilibrium quasi-particles in the superconductor. Here we demonstrate a characteristic dependence of non-local CI on a magnetic field applied parallel to the superconducting wire, which can be…
We formulate a microscopic theory of non-local electron transport in three-terminal diffusive normal-superconducting-normal (NSN) structures with arbitrary interface transmissions. At low energies $\varepsilon$ we predict strong enhancement of non-local spectral conductance $g_{12} \propto 1/\varepsilon$ due to quantum interference of electrons in disordered N-terminals. In contrast, non-local resistance $R_{12}$ remains smooth at small $\varepsilon$ and, furthermore, is found to depend neither on parameters of NS interfaces nor on those of N-terminals. At higher temperatures $R_{12}$ exhibits…
We present a comprehensive theoretical framework for the Andreev bound state population dynamics in superconducting weak links. Contrary to previous works, our approach takes into account the generated nonequilibrium distribution of the continuum quasiparticle states in a self-consistent way. As application of our theory, we show that the coupling of the superconducting contact to environmental phase fluctuations induces a charge imbalance of the continuum quasiparticle population. This imbalance is due to the breaking of the left-right symmetry in the rates connecting continuum quasiparticles…
We investigate theoretically the non-local conductance through a superconducting wire in tunnel contact with normal and ferromagnetic leads. In the presence of an in-plane magnetic field, the superconducting density of states is spin-split, and the current injected from the normal lead is spin-polarized. A non-local conductance that is antisymmetric with the applied voltage can be measured with a ferromagnetic lead. It persists for a distance between the contacts that is larger than both the charge-imbalance relaxation length and the normal-state spin relaxation length. We determine its amplit…
The excitations in conventional superconductors, Bogoliubov quasiparticles, are spin-1/2 fermions but their charge is energy-dependent and, in fact, zero at the gap edge. Therefore, in superconductors (unlike normal metals) the spin and charge degrees of freedom may be separated. In this article, we review spin injection into conventional superconductors and focus on recent experiments on mesoscopic superconductors. We show how quasiparticle spin transport and out-of-equilibrium spin dependent superconductivity can be triggered using the Zeeman splitting of the quasiparticle density of states …
We consider a heterostructure consisting of a normal metal and a superconductor separated by a spin-active interface. At finite-bias voltages, spin-filtering and spin-mixing effects at the interface allow for an induced magnetization (spin imbalance) on the superconducting side of the junction, which relaxes to zero in the bulk. Such interfaces are also known to host a pair of in-gap Andreev bound states which were recently observed experimentally. We show that these states are responsible for the dominant contribution to the induced spin imbalance close to the interface. Motivated by recent e…
Results of theoretical study of spin-polarized tunneling in ferromagnet/superconductor junctions are presented. Spin and charge currents are calculated as a function of applied voltage and spin polarization in a ferromagnet. The model takes into account the splitting of different spin subbands in a ferromagnet and impurity scattering in the contact. The excess resistance of an FS contact due to the charge-imbalance in a superconductor is calculated for the first time. The results have implications for spin-coupled magnetoresistance in ferromagnet/superconductor contacts and for measuring spin …
We investigate charge pumping in ferromagnet/triplet superconductor junctions where the magnetization of the ferromagnet is inhomogeneous and dynamical. It is shown that charge current is pumped due to the coupling of the localized spin with triplet vector spin chirality, vector spin chirality formed by the triplet vector of Cooper pairing. Physical mechanism of the charge pumping is also discussed.
Nonequilibrium charge transport in superconductors has been investigated intensely in the 1970s and 80s, mostly in the vicinity of the critical temperature. Much less attention has been focussed on low temperatures, and the role of the quasiparticle spin. We report here on nonlocal transport in superconductor hybrid structures at very low temperatures. By comparing the nonlocal conductance obtained using ferromagnetic and normal-metal detectors, we discriminate charge and spin degrees of freedom. We observe spin injection and long-range transport of pure, chargeless spin currents in the regime…
We have found experimentally that the noise of ballistic electron transport in a superconductor/semiconductor/superconductor junction is enhanced relative to the value given by the general relation, S_V=2eIR^2coth(eV/2kT), for two voltage regions in which this expression reduces to its thermal and shot noise limits. The noise enhancement is explained by the presence of large charge quanta, with effective charge q*=(1+2Delta/eV)e, that generate a noise spectrum S_V=2q*IR^2, as predicted in Phys. Rev. Lett. 76, 3814 (1996). These charge quanta result from multiple Andreev reflections at each jun…
The electric charge density in mesoscopic superconductors with circular symmetry, i.e. disks and cylinders, is studied within the phenomenological Ginzburg-Landau approach. We found that even in the Meissner state there is a charge redistribution in the sample which makes the sample edge become negatively charged. In the vortex state there is a competition between this Meissner charge and the vortex charge which may change the polarity of the charge at the sample edge with increasing magnetic field. It is shown analytically that in spite of the charge redistribution the mesoscopic sample as a …
We use a quasi-Corbino sample geometry with independent contacts to different edge states in the quantum Hall effect regime to investigate a charge redistribution between cyclotron-split edge states at high imbalance. We also modify Buttiker formalism by introducing local transport characteristics in it and use this modified Buttiker picture to describe the experimental results. We find that charge transfer between cyclotron-split edge states at high imbalance can be described by a single parameter, which is a transferred between edge states portion of the available for transfer part of the el…
By performing experiments with thin-film resonators of NbSi, we elucidate a decoherence mechanism at work in disordered superconductors. This decoherence is caused by charged Two Level Systems (TLS) which couple to the conduction electrons in the BCS ground state; it does not involve any out-of-equilibrium quasiparticles, vortices, etc. Standard theories of mesoscopic disordered conductors enable making predictions regarding this mechanism, notably that decoherence should increase as the superconductor cross section decreases. Given the omnipresence of charged TLS in solid-state systems, this …
An in-plane magnetic field applied to an Ising superconductor converts spin-singlet Cooper pairs to spin-triplet ones. In this work, we study a Josephson junction formed by two Ising superconductors that are proximitized by ferromagnetic layers. This leads to highly tunable spin-triplet pairing correlations which allow to modulate the charge and spin supercurrents through the in-plane magnetic exchange fields. For a junction with a nonmagnetic barrier, the charge current is switchable by changing the relative alignment of the in-plane exchange fields, and a $π$-state can be realized. Furthermo…
We present a formalism to study adiabatic pumping through a superconductor - normal - superconductor weak link. At zero temperature, the pumped charge is related to the Berry phase accumulated, in a pumping cycle, by the Andreev bound states. We analyze in detail the case when the normal region is short compared to the superconducting coherence length. The pumped charge turns out to be an even function of the superconducting phase difference. Hence, it can be distinguished from the charge transferred due to the standard Josephson effect.
We use high-mobility bilayer hole systems with negligible tunneling to examine how the bilayer nu = 1 quantum Hall state evolves as charge is transferred from one layer to the other at constant total density. We map bilayer nu = 1 state stability versus imbalance for five total densities spanning the range from strongly interlayer coherent to incoherent. We observe competition between single-layer correlations and interlayer coherence. Most significantly, we find that bilayer systems that are incoherent at balance can develop spontaneous interlayer coherence with imbalance, in agreement with r…
We use interlayer tunneling to study bilayer 2D electron systems at $ν_T = 1$ over a wide range of charge density imbalance, $Δν=ν_1-ν_2$, between the two layers. We find that the strongly enhanced tunneling associated with the coherent excitonic $ν_T = 1$ phase at small layer separation can survive at least up to an imbalance of $Δν$ = 0.5, i.e $(ν_1, ν_2)$ = (3/4, 1/4). Phase transitions between the excitonic $ν_T = 1$ state and bilayer states which lack significant interlayer correlations can be induced in three different ways: by increasing the effective interlayer spacing $d/\ell$, the te…
Spin transfer torques (STT) occur when electric currents travel through inhomogeneously magnetized systems and are important for the motion of magnetic textures such as domain walls. Since superconductors are easy-plane ferromagnets in particle-hole (charge) space, it is natural to ask whether any charge duals of STT phenomena exist therein. We find that the superconducting analogue of the adiabatic STT vanishes in a bulk superconductor with a momentum-independent order parameter, while the superconducting counterpart of the nonadiabatic STT does not vanish. This nonvanishing superconducting t…
We analyze the contribution of the inhomogeneous magnetic field induced by an electrical current to the spin Hall effect in metals. The Zeeman coupling between the field and the electron spin leads to a spin dependent force, and to spin accumulation at the edges. We compare the effect of this relativistic correction to the electron dynamics to the features induced by the spin-orbit interaction. The effect of current induced magnetic fields on the spin Hall effect can be comparable to the extrinsic contribution from the spin-orbit interaction, although it does not require the presence of heavy …
We study transport in ferromagnetic-superconductor/normal-metal systems. It is shown that charge and spin currents are pumped from ferromagnetic superconductors into adjacent normal metals by adiabatic changes in the order parameters induced by external electromagnetic fields. Spin and charge pumping identify the symmetry of the superconducting order parameter, e.g., singlet pairing or triplet pairing with opposite or equal spin pairing. Consequences for ferromagnetic-resonance experiments are discussed.
Graphene grown epitaxially on SiC, close to the charge neutrality point (CNP), in an orthogonal magnetic field shows an ambipolar behavior of the transverse resistance accompanied by a puzzling longitudinal magnetoresistance. When injecting a transverse current at one end of the Hall bar, a sizeable non local transverse magnetoresistance is measured at low temperature. While Zeeman spin effect seems not to be able to justify these phenomena, some dissipation involving edge states at the boundaries could explain the order of magnitude of the non local transverse magnetoresistance, but not the a…
We identify a signature of chirality in the electrical conduction along magnetic vortices in a Weyl superconductor: The conductance depends on whether the magnetic field is parallel or antiparallel to the vector in the Brillouin zone that separates Weyl points of opposite chirality.
Transport studies of Andreev bound states (ABSs) are complicated by the interplay of charging effects and superconductivity. Here, we compare transport approaches to ABS spectroscopy in a semiconductor-superconductor island to a charge-sensing approach based on an integrated radio-frequency single-electron transistor. Consistency of the methods demonstrates that fast, non-invasive charge sensing allows accurate quantitative measurement of ABSs while eluding some complexities of transport.
Two-component fractional quantum Hall systems are providing a major motivation for a large section of the physics community. Here we study two-component fractional quantum Hall systems in the spin-polarized half-filled lowest Landau level (filling factor 1/2) and second Landau level (filling factor 5/2) with exact diagonalization utilizing both the spherical and torus geometries. The two distinct two-component systems we consider are the true bilayer and effective bilayers (wide-quantum-well). In each model (bilayer and wide-quantum-well) we completely take into account inter-layer tunneling a…
Topological Charge-2ne Superconductivity and Clustering Hierarchy
University of California, Berkeley（加州大学伯克利分校）；University of Maryland, College Park（马里兰大学帕克分校）；Johns Hopkins University（约翰斯·霍普金斯大学）；University of Pittsburgh（匹兹堡大学）；Westlake University（西湖大学）；Westlake Institute for Advanced Study（西湖高等研究院）
We develop a theoretical proposal for the charge Kondo effect in mesoscopic normal-superconductor-normal heterostructures, where the superconducting gap exceeds the electrostatic charging energy. Charge-Kondo correlations in these devices alter the conventional temperature-dependence of Andreev reflection and electron cotunneling. We predict typical Kondo temperatures of $\gtrsim 10 {\rm mK}$, and suggest experimental architectures that combine superconducting charge-qubits with semiconducting nanowires at cryogenic temperatures.
In topological semimetals and nodal superconductors, band crossings between occupied and unoccupied bands form stable nodal points/lines/surfaces carrying quantized topological charges. In particular, in centrosymmetric systems, some nodal structures at the Fermi energy $E_F$ carry two distinct topological charges, and thus they are called doubly charged nodes. Here we show that doubly charged nodal surfaces of centrosymmetric superconductors in three-dimensions always develop peculiar linking structures with nodal points or lines formed between occupied bands below $E_F$. Such linking structu…
The Majorana fermions propagating along the edge of a topological superconductor with $p_x+ip_y$ pairing deliver a shot noise power of $\frac{1}{2}\times e^2/h$ per eV of voltage bias. We calculate the full counting statistics of the transferred charge and find that it becomes trinomial in the low-temperature limit, distinct from the binomial statistics of charge-$e$ transfer in a single-mode nanowire or charge-$2e$ transfer through a normal-superconductor interface. All even-order correlators of current fluctuations have a universal quantized value, insensitive to disorder and decoherence. Th…
We use linear response theory to study the transverse force generated by an external electric field and hence possible charge Hall effect in spin-orbit coupled systems. In addition to the Lorentz force that is parallel to the electric field, we find that the transverse force perpendicular to the applied electric field may not vanish in a system with an anisotropic energy dispersion. Surprisingly, in contrast to the previous results, the transverse force generated by the electric field does not depend on the spin current, but in general, it is related to the second derivative of energy dispersi…
We develop a theory of the low-temperature charge transfer between a superconductor and a hopping insulator. We show that the charge transfer is governed by the coherent two-electron -- Cooper pair conversion process, time reversal reflection, where electrons tunnel into superconductor from the localized states in the hopping insulator located near the interface, and calculate the corresponding interface resistance. This process is an analog to conventional Andreev reflection process. We show that the time reversal interface resistance is accessible experimentally, and that in mesoscopic struc…
