Andreev Levels Research Articles

Critical charge and spin Josephson currents through a precessing spin

We present a theoretical study of two superconductors coupled over a spin. The spin is treated classically and is assumed to precess with the Larmor frequency due to an external magnetic field. The precession results in spin-dependent Andreev scattering and a non-equilibrium population of the Andreev levels. Charge and spin currents at zero temperature were studied previously [1]. Here, we focus on the critical current as well as the corresponding spin currents at finite temperatures. At finite temperatures, the spin precession can enhance the supercurrent by a population redistribution. The enhancement leads to a modified current-phase relation and a non-monotonous critical current as function of temperature. This non-monotonous behavior is accompanied by a corresponding change in spin-transfer torques acting on the precessing spin and leads to the possibility of using temperature as a means to tune the back-action on the spin.

Spin-precession-assisted supercurrent in a superconducting quantum point contact coupled to a single-molecule magnet

The supercurrent of a quantum point contact coupled to a nanomagnet strongly depends on the dynamics of the nanomagnet's spin. We employ a fully microscopic model to calculate the transport properties of a junction coupled to a spin whose dynamics is modeled as Larmor precession brought about by an external magnetic field and find that the dynamics affects the charge and spin currents by inducing transitions between the continuum states below the superconducting gap edge and the Andreev levels. This redistribution of the quasiparticles leads to a non-equilibrium population of the Andreev levels and an enhancement of the supercurrent which is visible as a modified current-phase relation as well as a non-monotonous critical current as function of temperature. The non-monotonous behavior is accompanied by a corresponding change in spin-transfer torques acting on the precessing spin and leads to the possibility of using temperature as a means to tune the back-action on the spin.

Superconducting phase-dependent force in SNS junctions with mobile scatterers

We calculate the quantum (Casimir-like) superconducting phase-dependent force acting on mobile scatterers in superconductor–normal metal–superconductor (SNS) junctions. Repulsive Casimir forces are predicted in short SNS junctions with nonequilibrium (inverse) Andreev level populations. An anomalous (nonmonotonic) temperature dependence of the quantum force is found in long SNS junctions.

Josephson effect in S/F/S junctions: Spin bandwidth asymmetry versus Stoner exchange

We analyze the dc Josephson effect in a ballistic superconductor/ferromagnet/superconductor junction by means of the Bogoliubov--de Gennes equations in the quasiclassical Andreev approximation. We consider the possibility of ferromagnetism originating from a mass renormalization of carriers of opposite spin, i.e., a spin bandwidth asymmetry. We provide a general formula for Andreev levels that is valid for arbitrary interface transparency, exchange interaction, and bandwidth asymmetry, and we analyze the current-phase relation, free energy, and critical current in the short junction regime. We compare the phase diagrams and the critical current magnitudes of two identical junctions differing only in the mechanism by which the midlayer becomes magnetic. We show that a larger number of $0\ensuremath{-}\ensuremath{\pi}$ transitions caused by a change in junction width or polarization magnitude is expected when ferromagnetism is driven by spin bandwidth asymmetry compared to Stoner magnetism. Moreover, we show that these features can be present also for ferromagnets of the Stoner type having only a partial bandwidth asymmetry.

Coherent quantum phenomena in mesoscopic metallic conductors (Review Article)

Quantum coherent phenomena in mesoscopic cylindrical metallic conductors are examined. When pure doubly- and singly-connected normal samples are placed in a longitudinal magnetic field, interference phenomena occur which depend on the magnetic flux through the cross-section of the conductor. The period of the induced oscillations is given by the quantum of flux, hc∕e, of the normal metal. Quantum states are formed in these structures by electron collisions with the dielectric boundary of the sample. The magnetic flux is included in the expression for the quasiparticle spectrum. The proximity effect and its influence on the spectrum of quantum coherent phenomena is investigated. The behavior of cylindrical samples consisting of a superconducting (S) metal with a deposited thin pure normal (N) metal layer is analyzed. In these structures, electrons are localized in a well bounded by a dielectric on one side and by a superconductor on the other. The resulting quantized Andreev levels have the feature that in a varying field H (or temperature T) each of the levels in the well can coincide periodically with the chemical potential of the metal. As a result, the state of the system has a strong degeneracy and the density of states exhibits resonance spikes as a function of the energy of the NS sample. This makes a significant contribution to the magnetic moment. A theory of the reentrant effect for NS structures has been developed for interpreting the anomalous behavior of the magnetic susceptibility of these structures as a function of magnetic field and temperature.

Coulomb-enhanced resonance transmission of quantum SINIS junctions

Coherent charge transfer through a ballistic gated SINIS junction is mediated by the resonant tunneling via the Andreev states. Extra charge accommodated on the Andreev levels partially compensates the charge induced by the gate voltage preserving the electron wavelength and maintaining the resonance conditions in a broad range of gate voltages. As a result, the transparency of the junction as well as the supercurrent trough it can be substantially increased as compared to the zero-Coulomb case.

Doppler shift in Andreev reflection from a moving superconducting condensate in Nb/InAs Josephson junctions

We study narrow ballistic Josephson weak links in a InAs quantum wells contacted by Nb electrodes and find a dramatic magnetic-field suppression of the Andreev reflection amplitude, which occurs even for in-plane field orientation with essentially no magnetic flux through the junction. Our observations demonstrate the presence of a Doppler shift in the energy of the Andreev levels, which results from diamagnetic screening currents in the hybrid Nb/InAs-banks. The data for conductance, excess and critical currents can be consistently explained in terms of the sample geometry and the McMillan energy, characterizing the transparency of the Nb/InAs-interface.

Control of Josephson current by Aharonov-Casher phase in a Rashba ring

We study the interference effect induced by the Aharonov-Casher phase on the Josephson current through a semiconducting ring attached to superconducting leads. Using a 1D model that incorporates spin-orbit coupling in the semiconducting ring, we calculate the Andreev levels analytically and numerically, and predict oscillations of the Josephson current due to the AC phase. This result is valid from the point contact limit to the long channel length limit, as defined by the ratio of the junction length and the BCS healing length. We show in the long channel length limit that the impurity scattering has no effect on the oscillation of the Josephson current, in contrast to the case of conductivity oscillations in a spin-orbit coupled ring system attached to normal leads where impurity scattering reduces the amplitude of oscillations. Our results suggest a new scheme to measure the AC phase with, in principle, higher sensitivity. In addition, this effect allows for control of the Josephson current through the gate voltage tuned AC phase.

Nonadiabatic transitions between adiabatic surfaces: Phase diffusion in superconducting atomic point contacts

Motivated by experiments with current-biased superconducting atomic point contacts the general problem of nonadiabatic transitions between adiabatic surfaces in presence of strong dissipation is studied. For a single-channel device the supercurrent is determined by the diffusive motion of the superconducting phase difference on two Andreev levels. These surfaces are uncoupled only in the adiabatic limit of low to moderate transmissions while for high transmissions curve crossings are important. Starting from a general master equation of the full density matrix an approximate time evolution equation for the populations on the adiabatic surfaces in the overdamped limit is derived from which the relevant observables can be obtained. Specific results for the case of atomic point contacts are in agreement with experimental observations that cannot be explained by conventional theory.

Andreev levels in a graphene–superconductor surface

In order to consider the Dirac-like spectrum of graphene we employ the Bogoliubov de Gennes–Dirac formalism to determine the quasiparticle Andreev levels in an NS surface (normal–superconductor). The normal region is characterized by a width L while the superconducting region is semi-infinite and both regions are made of doped graphene. The quasiparticle energy spectrum is originated by the Andreev reflections that occur in the NS interface. It is shown that this spectrum depends on the width of the normal region and the Fermi energy in each region. When the Fermi energy in the normal metal is lower than the gap of the superconductor region, the spectrum is affected by specular Andreev reflections. The equation that is obtained to find the spectrum is very general and we solve it for some particular cases. We find that the energy spectrum oscillates when the Fermi energy in graphene is changed. Finally we obtain under some approximations an equation for the energy spectrum which is similar in structure as those obtained for an INS conventional junction.

Single-walled carbon nanotube weak links in Kondo regime with zero-field splitting

We have investigated proximity-induced supercurrents in single-walled carbon nanotubes in the Kondo regime and compared them with supercurrents obtained on the same tube with Fabry-P\'erot resonances. Our data display a wide distribution of Kondo temperatures ${T}_{K}=1--14\text{ }\text{K}$, and the measured critical current ${I}_{\text{CM}}$ vs ${T}_{K}$ displays two distinct branches; these branches, distinguished by zero-field splitting of the normal-state Kondo conductance peak, differ by an order of magnitude at large values of ${T}_{K}$. Evidence for renormalization of Andreev levels in Kondo regime is also found.

Neutron reflection from the surfaces of liquid 4He and a Dilute 3He—4He solution

We report and discuss the first neutron reflection measurements from the free surfaces of normal and superfluid 4He and of a liquid 3He-4He mixture. In case of liquid 4He the surface roughness is different above and below the lambda transition, being smoother in the superfluid state. For the superfluid, we also observe the formation of a surface layer ∼ 200 Å thick which has a subtly different neutron scattering cross-section. The results can be interpreted as an enhancement of the Bose-Einstein condensate fraction close to the helium surface. We find that the addition of 3He isotopic impurities leads to the formation of Andreev levels at low temperatures.

Josephson current in ballistic heterostructures with spin-active interfaces

We develop a general microscopic theory of dc Josephson effect in hybrid superconductor--normal-metal--superconductor structures with ballistic electrodes and spin-active normal-metal--superconductor (NS) interfaces. We establish a direct relation between the spectrum of Andreev levels and the Josephson current which contains complete information about nontrivial interplay between Andreev reflection and spin-dependent interface scattering. The system exhibits a rich structure of properties sensitive to spin-dependent barrier transmissions, spin-mixing angles, relative magnetization orientation of interfaces, and the kinematic phase of scattered electrons. We analyze the current-phase relations and identify the conditions for the presence of a $\ensuremath{\pi}$-junction state in the systems under consideration. We also analyze resonant enhancement of the supercurrent in gate-voltage-driven nanojunctions. As compared to the nonmagnetic case, this effect can be strongly modified by spin-dependent scattering at NS interfaces.

Josephson effect in superconducting hybrid S/F structures with parallel and antiparallel magnetizations of the ferromagnetic layers

The Josephson effect in S-MB-S, S/F-MB-S, and S/F-MB-F′/S superconducting hybrid structures with the parallel or antiparallel orientation of exchange fields in the layers of metal ferromagnets (F and F′) and in the magnetic barrier (MB) with arbitrary transparency has been investigated. It has been shown that the properties of the studied structures depend strongly on the orientation of the exchange fields: the exchange-field-induced stimulation of the critical current is possible for one orientation, whereas the critical current is suppressed at the opposite orientation of the exchange fields. A change in the orientation of the exchange fields can lead to the switching of the Josephson structures between 0 and π states. The effect of the pair-breaking mechanisms on the Josephson effect and on the spectrum of the Andreev levels in the S-MB-S structures has been analyzed. The results indicate the possibility of stimulating the critical current by the external magnetic field in the S-MB-S structures with thin-film superconducting banks.

Josephson Effect through an Isotropic Magnetic Molecule

We study the Josephson effect through a quantum dot magnet whose spin is isotropic and which is coupled to the dot electron spin via exchange coupling. We calculate the Andreev levels and the supercurrent and examine the intertwined effect of the exchange coupling, Kondo correlation, and superconductivity. The former suppresses Kondo correlations, which triggers phase transitions from the 0 to the pi state, but strong antiferromagnetic coupling restores the 0 state. The asymmetric phase diagram in the exchange coupling suggests that the coupling sign could be determined in experiments.

Crossover in the local density of states of mesoscopic superconductor/normal-metal/superconductor junctions

Andreev levels deplete energy states above the superconductive gap, which leads to the peculiar nonmonotonous crossover in the local density of states of mesoscopic superconductor/normal-metal/superconductor junctions. This effect is especially pronounced in the case when the normal metal bridge length $L$ is small compared to the superconductive coherence length $\ensuremath{\xi}$. A remarkable property of the crossover function is that it vanishes not only at the proximity induced gap ${ϵ}_{g}$ but also at the superconductive gap $\ensuremath{\Delta}$. Analytical expressions for the density of states at both gap edges, as well as the general structure of the crossover are discussed.

Manipulation with Andreev states in spin active mesoscopic Josephson junctions

We investigate manipulation with Andreev bound states in Josephson quantum point contacts with magnetic scattering. The Rabi oscillations in the two-level Andreev subsystems are excited by resonant driving the direction of magnetic moment of the scatterer and by modulating the superconducting phase difference across the contact. The Andreev level dynamics is manifested by the temporal oscillation of the Josephson current, which is accompanied, in the case of magnetic manipulation, also by the oscillation of the Andreev states spin polarization. The interlevel transitions obey a selection rule that forbids manipulations in a certain region of external parameters and results from specific properties of Andreev bound states in magnetic contacts: $4\ensuremath{\pi}$ periodicity with respect to the superconducting phase and strong spontaneous spin polarization.

Superconductivity-Induced Macroscopic Resonant Tunneling

We show analytically and by numerical simulations that the conductance through pi-biased chaotic Josephson junctions is enhanced by several orders of magnitude in the short-wavelength regime. We identify the mechanism behind this effect as macroscopic resonant tunneling through a macroscopic number of low-energy quasidegenerate Andreev levels.

Splitting of Andreev levels in a Josephson junction by spin-orbit coupling

We consider the effect of spin-orbit coupling on the energy levels of a single-channel Josephson junction below the superconducting gap. We investigate quantitatively the level splitting arising from the combined effect of spin-orbit coupling and the time-reversal symmetry breaking by the phase difference between the superconductors. Using the scattering matrix approach, we establish a simple connection between the quantum mechanical time delay matrix and the effective Hamiltonian for the level splitting. As an application, we calculate the distribution of level splittings for an ensemble of chaotic Josephson junctions. The distribution falls off as a power law for large splittings, unlike the exponentially decaying splitting distribution given by the Wigner surmise---which applies for normal chaotic quantum dots with spin-orbit coupling in the case that the time-reversal symmetry breaking is due to a magnetic field.

Excitation gap of a graphene channel with superconducting boundaries

We calculate the density of states of electron-hole excitations in a superconductor--normal-metal--superconductor (SNS) junction in graphene, in the long-junction regime that the superconducting gap ${\ensuremath{\Delta}}_{0}$ is much larger than the Thouless energy ${E}_{T}=\ensuremath{\hbar}v∕d$ (with $v$ the carrier velocity in graphene and $d$ the separation of the NS boundaries). If the normal region is undoped, the excitation spectrum consists of neutral modes that propagate along the boundaries---transporting energy but no charge. These ``Andreev modes'' are a coherent superposition of electron states from the conduction band and hole states from the valence band, coupled by specular Andreev reflection at the superconductor. The lowest Andreev mode has an excitation gap of ${E}_{0}=\frac{1}{2}(\ensuremath{\pi}\ensuremath{-}\ensuremath{\mid}\ensuremath{\phi}\ensuremath{\mid}){E}_{T}$, with $\ensuremath{\phi}∊(\ensuremath{-}\ensuremath{\pi},\ensuremath{\pi})$ the superconducting phase difference. At high doping (Fermi energy $\ensuremath{\mu}⪢{E}_{T}$) the excitation gap vanishes $\ensuremath{\propto}{E}_{0}{({E}_{T}∕\ensuremath{\mu})}^{2}$, and the usual gapless density of states of Andreev levels is recovered. We use our results to calculate the $\ensuremath{\phi}$ dependence of the thermal conductance of the graphene channel.