Andreev States Research Articles

Phase-dependent Andreev spectrum in a diffusive SNS junction: Static and dynamic current response

A long phase coherent normal (N) wire between superconductors (S) is characterized by a dense phase dependent Andreev spectrum. We investigate the current response of Andreev states of an NS ring to a time dependent Aharonov Bohm flux superimposed to a dc one. The ring is modeled with a tight binding Hamiltonian including a superconducting region with a BCS coupling between electron and hole states, in contact with a normal region with on site disorder. Both dc and ac currents are determined from the computed eigenstates and energies using a Kubo formula approach. Beside the well known Josephson current we identify different contributions to the ac response. A low frequency one related to the dynamics of the thermal occupations of the Andreev states and a higher frequency one related to microwave induced transitions between levels. Both are characterized by strongly anharmonic phase dependencies which are nearly opposite to one another. Our findings are successfully compared to the results of recent experiments.

Josephson current through a quantum dot coupled to a molecular magnet

Josephson currents are carried by sharp Andreev states within the superconducting energy gap. We theoretically study the electronic transport of a magnetically tunable nanoscale junction consisting of a quantum dot connected to two superconducting leads and coupled to the spin of a molecular magnet. The exchange interaction between the molecular magnet and the quantum dot modifies the Andreev states due to a spin-dependent renormalization of the quantum dot's energy level and the induction of spin flips. A magnetic field applied to the central region of the quantum dot and the molecular magnet further tunes the Josephson current and starts a precession of the molecular magnet's spin. We use a nonequilibrium Green's function approach to evaluate the transport properties of the junction. Our calculations reveal that the energy level of the dot, the magnetic field, and the exchange interaction between the molecular magnet and the electrons occupying the energy level of the quantum dot can trigger transitions from a 0 to a $\ensuremath{\pi}$ state of the Josephson junction. The redistribution of the occupied states induced by the magnetic field strongly modifies the current-phase relation. The critical current exhibits a sharp increase as a function of either the energy level of the dot, the magnetic field, or the exchange interaction.

Andreev states taken to the next level

The Andreev bound states are a hallmark of the theory of superconducting weak links. Using the versatile Josephson effect as source, device and detector, these spin-1/2 states have been directly observed. See Letter p.312 Brian Josephson proposed in 1962 that a dissipationless 'supercurrent' should flow between two superconductors separated by a weak link such as a tunnel junction. He was right, and the Josephson effect launched a new field of research with applications to magnetometry, medicine and astronomy. This paper describes an aspect of the Josephson effect that has previously been overlooked. Existing Josephson junction applications are based on properties of just the ground state, in which the electron pairs that carry the supercurrent localize at the weak link and form so-called Andreev doublets of ground and excited pair states. Bretheau et al. establish the existence of excited Andreev pair states through spectroscopic measurements of superconducting atomic contacts. This previously overlooked degree of freedom for tunneling electron pairs is a new quantum resource that could be exploited in novel types of superconducting qubits.

Frequency-dependent admittance of a short superconducting weak link

We consider the linear and nonlinear electromagnetic responses of a nanowire connecting two bulk superconductors. The Andreev states appearing at a finite phase bias substantially affect the finite-frequency admittance of such a wire junction. Electron transitions involving the Andreev levels are easily saturated, leading to the nonlinear effects in photon absorption for the subgap photon energies. We evaluate the complex admittance analytically at an arbitrary frequency and arbitrary, possibly nonequilibrium, occupation of the Andreev levels. Special care is given to the limits of a single-channel contact and a disordered metallic weak link. We also evaluate the quasistatic fluctuations of admittance induced by fluctuations of the occupation factors of the Andreev levels. In view of possible qubit applications, we compare properties of a weak link with those of a tunnel Josephson junction. Compared to the latter, a weak link has smaller low-frequency dissipation. However, because of the deeper Andreev levels, the low-temperature quasistatic fluctuations of the inductance of a weak link are exponentially larger than of a tunnel junction. These fluctuations limit the applicability of nanowire junctions in superconducting qubits.

Dissipation and Supercurrent Fluctuations in a Diffusive Normal-Metal–Superconductor Ring

A mesoscopic hybrid normal-metal-superconductor ring is characterized by a dense Andreev spectrum with a flux dependent minigap. To probe the dynamics of such a ring, we measure its linear response to a high frequency flux, in a wide frequency range, with a multimode superconducting resonator. We find that the current response contains, besides the well-known dissipationless Josephson contribution, a large dissipative component. At high frequency compared to the minigap and low temperature, we find that the dissipation is due to transitions across the minigap. In contrast, at lower frequency there is a range of temperature for which dissipation is caused predominantly by the relaxation of the Andreev states' population. This dissipative response, related via the fluctuation dissipation theorem to a nonintuitive zero frequency thermal noise of supercurrent, is characterized by a phase dependence dominated by its second harmonic, as predicted long ago but never observed thus far.

Tunneling conductance due to a discrete spectrum of Andreev states

We study tunneling spectroscopy of subgap Andreev states in a superconducting system and discuss the general situation when the discrete nature of these levels is relevant and thus the standard semiclassical result for tunneling conductance being proportional to the density of states is not applicable. If the tunneling coupling is weak, individual levels are resolved and the conductance G(V ) at low temperatures is composed of a set of resonant Lorentz peaks which cannot be described within perturbation theory over tunneling strength. We establish a general formula for the peak widths and heights and show that the width of any peak scales as normal-state tunnel conductance, while its height is ≲2e2 h−1 and depends only on contact geometry and the spatial profile of the resonant Andreev level. We also establish an exact formula for the single-channel conductance that takes the whole Andreev spectrum into account, and use it to study the interference of Andreev reflection processes through different levels. We study tunneling conductance at finite bias G(eV >0) for a system with a pair of almost decoupled Majorana fermions and derive the conditions for the ‘universal’ zero-bias peak with the height 2e2/h to be observed in a realistic system which always hosts an even number of Majorana fermions.

Spin-orbit-induced chirality of Andreev states in Josephson junctions

We study Josephson junctions (JJs) in which the region between the two superconductors is a multichannel system with Rashba spin-orbit coupling (SOC) where a barrier or a quantum point contact (QPC) is present. These systems might present unconventional Josephson effects such as Josephson currents for zero phase difference or critical currents that depend on the current direction. Here, we discuss how the spin polarizing properties of the system in the normal state affect the spin characteristics of the Andreev bound states inside the junction. This results in a strong correlation between the spin of the Andreev states and the direction in which they transport Cooper pairs. While the current-phase relation for the JJ at zero magnetic field is qualitatively unchanged by SOC, in the presence of a weak magnetic field, a strongly anisotropic behavior and the mentioned anomalous Josephson effects follow. We show that the situation is not restricted to barriers based on constrictions such as QPCs and should generically arise if in the normal system the direction of the carrier's spin is linked to its direction of motion.

Neutron reflection from the surface of a liquid 4He-3He mixture

We have used neutron reflection from the liquid surface at ultra-low temperatures to study the surface properties of liquid helium. We measured neutron scattering from the free surfaces of commercially pure 4He (0.3 ppm of 3He impurities) and of a 3He-4He mixture with a 3He concentration of 0.5% for temperatures in the range from 340mK to 2.2K We compare the reflected neutron intensity for different temperatures and we fit a model that describes the collected data. The data are described well by a diffusive 3He layer of a few hundred Angstrom thickness on the bulk 4He liquid surface. Even at high temperatures (∼2K) there is an increased concentration of 3He atoms near the liquid surface. The distribution does not change very much with temperature. At low temperatures the neutron absorption increases significantly, which might be an indication of the formation of Andreev states. However, the shapes of the curves do not change very much which seems to suggest that the layer formed by the 3He atoms in Andreev states is very thin ∼ 10Å. The experimental method, based on neutron reflectometry, opens up new opportunities for the study of the surfaces and interfaces of quantum fluids and solids.

Spin-Transfer and Exchange Torques in Ferromagnetic Superconductors

We consider how superconducting correlations influence spin-transfer torques in ferromagnetic superconductors. It is demonstrated that there is a novel torque arising from particle-hole interference that depends on the U(1) phase associated with the superconducting order parameter. We also show that there is an equilibrium exchange torque between two ferromagnetic superconductors in contact via a normal metal mediated by Andreev states. The latter equilibrium magnetic torque is also sensitive to spin-resolved phase differences in the superconducting order parameters as well as to an externally applied phase difference.

Topological Superconducting State of Lead Nanowires in an External Magnetic Field

Superconductors with an odd number of bands crossing the Fermi energy have topologically protected Andreev states at interfaces, including Majorana states in one-dimensional geometries. We propose here that repeated indentation of a Pb tip on a Pb substrate can lead to nanowires such that the resulting superconducting system has novel topological properties. We have analyzed a number of conductance curves obtained in different nanowires, and observe, in a few cases, very peculiar dependence of the critical current on magnetic field. In these cases, the form of multiple Andreev reflections observed at finite voltages are compatible with topological superconductivity. The nanowires give a low number of 1D channels, large spin orbit coupling, and a sizable Zeeman energy, provided that the applied magnetic field is higher than the Pb bulk critical field.

Decoherence of superconducting qubits caused by quasiparticle tunneling

In superconducting qubits, the interaction of the qubit degree of freedom with quasiparticles defines a fundamental limitation for the qubit coherence. We develop a theory of the pure dephasing rate \Gamma_{\phi} caused by quasiparticles tunneling through a Josephson junction and of the inhomogeneous broadening due to changes in the occupations of Andreev states in the junction. To estimate \Gamma_{\phi}, we derive a master equation for the qubit dynamics. The tunneling rate of free quasiparticles is enhanced by their large density of states at energies close to the superconducting gap. Nevertheless, we find that \Gamma_{\phi} is small compared to the rates determined by extrinsic factors in most of the current qubit designs (phase and flux qubits, transmon, fluxonium). The split transmon, in which a single junction is replaced by a SQUID loop, represents an exception that could make possible the measurement of \Gamma_{\phi}. Fluctuations of the qubit frequency leading to inhomogeneous broadening may be caused by the fluctuations in the occupation numbers of the Andreev states associated with a phase-biased Josephson junction. This mechanism may be revealed in qubits with small-area junctions, since the smallest relative change in frequency it causes is of the order of the inverse number of transmission channels in the junction.

Phenomenology and dynamics of a Majorana Josephson junction

We derive a generic phenomenological model of a Majorana Josephson junction that accounts for avoided crossing of Andreev states, and investigate its dynamics at constant bias voltage to reveal an unexpected pattern of any-\pi\ Josephson effect in the limit of slow decoherence.

Triplet Pair Correlations ins-Wave Superfluids as a Signature of the Fulde-Ferrell-Larkin-Ovchinnikov State

We show that antiparallel triplet pairing correlations are generated in superfluids with purely s-wave interactions whenever population imbalance enforces anisotropic Fulde-Ferrell (FF) or inhomogeneous Larkin-Ovchinikov (LO) states. These triplet correlations appear in the Cooper pair wave function, while the triplet part of the gap remains zero. The same set of quasiparticle states contributes to the triplet component and to the polarization, thus spatially correlating them. In the LO case, this set forms a narrow band of Andreev states centered on the nodes of the s-wave order parameter. This picture naturally provides a unifying explanation of previous findings that attractive p-wave interaction stabilizes FFLO states. We also study a similar triplet mixing which occurs when a balanced two-component system displays FFLO-type oscillations due to a spin-dependent optical lattice. We discuss how this triplet component can be measured in systems of ultracold atoms using a rapid ramp across a p-wave Feshbach resonance. This should provide a smoking gun signature of FFLO states.

The Andreev states of a superconducting quantum dot: mean field versus exact numerical results

We analyze the spectral density of a single level quantum dot coupled to superconducting leads focusing on the Andreev states appearing within the superconducting gap. We use two complementary approaches: the numerical renormalization group and the Hartree–Fock approximation. Our results show the existence of up to four bound states within the gap when the ground state is a spin doublet (π phase). Furthermore the results demonstrate the reliability of the mean field description within this phase. This is understood from a complete correspondence that can be established between the exact and the mean field quasiparticle excitation spectrum within the gap.

Generalized London theory of the mixed state of high-κ superconductors as a projection of the quasiclassical Eilenberger approach

The generalized London equation in the mixed state of high-κ s-wave pairing superconductors with impurities is considered as a projection of the quasiclassical nonlocal nonlinear Eilenberger theory. Only one fitting parameter – the cutoff parameter ξh – is used in the theory. The distribution of the magnetic field is calculated self-consistently. Both nonlocal effects originated from extended states between the vortices and bound Andreev states in the vortex are taken into account. Comparison with different analytical nonlocal linear approaches (the Kogan–Gurevich, Amin–Franz–Affleck, Kogan–Zhelezina models) including only extended states is done. The importance of the Kramer–Pesch nonlinear effect and the field dependence of the cutoff parameter is emphasized and their strong influence on the variance of the magnetic field is found. The influence of the impurities on the ratio of the cutoff parameter ξh and the Ginzburg–Landau coherence length ξc2 is considered. Quasiparticle scattering by impurities and lowering of the temperature reduces the value of ξh to the values much less than ξc2. This is different from the prediction of the local Ginzburg–Landau theory where ξh is scaled by ξc2. It is found that impurities influence by different way on the cutoff parameter ξh and the order parameter coherence length ξ1. The ξh decreases monotonously with the impurity scattering time in contrast to the nonmonotonous behavior of ξ1. The results can be used for analysis of the μSR experimental data.

Supercurrent and Andreev bound state dynamics in superconducting quantum point contacts under microwave irradiation

We present here an extensive theoretical analysis of the supercurrent of a superconducting point contact of arbitrary transparency in the presence of a microwave field. Our study is mainly based on two different approaches: a two-level model that describes the dynamics of the Andreev bound states in these systems and a fully microscopic method based on the Keldysh-Green function technique. This combination provides both a deep insight into the physics of irradiated Josephson junctions and quantitative predictions for arbitrary range of parameters. The main predictions of our analysis are: (i) for weak fields and low temperatures, the microwaves can induce transitions between the Andreev states leading to a large suppression of the supercurrent at certain values of the phase, (ii) at strong fields, the current-phase relation is strongly distorted and the corresponding critical current does not follow a simple Bessel-function-like behavior, and (iii) at finite temperature, the microwave field can enhance the critical current by means of transitions connecting the continuum of states outside the gap region and the Andreev states inside the gap. Our study is of relevance for a large variety of superconducting weak links as well as for the proposals of using the Andreev bound states of a point contact for quantum computing applications.

Probing the dynamics of Andreev states in a coherent Normal/Superconducting ring

The supercurrent that establishes between two superconductors connected through a normal N mesoscopic link is carried by quasiparticule states localized within the link, the “Andreev bound states (ABS)”. Whereas the dc properties of this supercurrent in SNS junctions are now well understood, its dynamical properties are still an unresolved issue. In this letter we probe this dynamics by inductively coupling an NS ring to a multimode superconducting resonator, thereby implementing both a phase bias and current detection at high frequency. Whereas at very low temperatures we essentially measure the phase derivative of the supercurrent, at higher temperature we find a surprisingly strong frequency dependence in the current response of the ring: the ABS do not follow adiabatically the phase modulation. This experiment also illustrates a new tool to probe the fundamental time scales of phase coherent systems that are decoupled from macroscopic normal contacts and thermal baths.

Nonequilibrium effects in a Josephson junction coupled to a precessing spin

We present a theoretical study of a Josephson junction consisting of two s-wave superconducting leads coupled over a classical spin. When an external magnetic field is applied, the classical spin will precess with the Larmor frequency. This magnetically active interface results in a time-dependent boundary condition with different tunneling amplitudes for spin-up and spin-down quasiparticles and where the precession produces spin-flip scattering processes. We show that as a result, the Andreev states develop sidebands and a non-equilibrium population which depend on the precession frequency and the angle between the classical spin and the external magnetic field. The Andreev states lead to a steady-state Josephson current whose current-phase relation could be used for characterizing the precessing spin. In addition to the charge transport, a magnetization current is also generated.This spin current is time-dependent and its polarization axis rotates with the same precession frequency as the classical spin.

Nonlocal conductance via overlapping Andreev bound states in ferromagnet-superconductor heterostructures

In a setup where two ferromagnetic electrodes are attached to a superconductor, Andreev bound states are induced at both ferromagnet/superconductor (FM/SC) interfaces. We study how these states propagate through the SC and interact with each other. As a result of this interaction, the energetic positions of the Andreev states are not anymore determined solely by the magnetic properties of a single interface, but also depend on the interface distance and the relative magnetization orientation of the FM contacts. We discuss how these bound states show up as distinct peaks in the nonlocal conductance signal, and lead to marked asymmetries with respect to the applied voltage. We relate our results to nonlocal crossed Andreev and elastic co-tunneling processes.

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.