Dissipative electron transport through Andreev interferometers

Superlattices and Microstructures, 1999

Journal of Computational and Theoretical Nanoscience, 2008

We have investigated the quantum transport through the Superconductor-Semiconductor mesoscopic interface in the presence of an external radiation field. The current spectrum is analyzed as a function of the frequency and the temperature. The current-voltage (I-V) characteristics were found to be very sensitive to the photon frequency. Additionally, photon-assisted transport in our system is very robust: The one-photon channel remains up to low temperature, which implies that these structures support gain at THz frequencies even at 9 K. The resonances sit on a background current which it is deeply modified, as a result of photon assisted multiple Andreev reflections. The results render rigid support for the full quantum theory of transport between two superconductors based on the idea of Andreev bound states.

Physical Review B, 2009

We study quantum transport in ballistic s±-wave superconductors where coupling between the two bands is included, and apply our model to three possible probes for detecting the internal phase shift of such a pairing state: tunneling spectroscopy in a N|s±-wave junction, crossed Andreev reflection in a two-lead N|s±-wave|N system, and Josephson current in a s-wave|I|s±-wave Josephson junction. Whereas the first two probes are insensitive to the superconducting phase in the absence of interband coupling, the Josephson effect is intrinsically phase-dependent, and is moreover shown to be relatively insensitive to the strength of the interband coupling. Focusing on the Josephson current, we find a 0-π transition as a function of the ratio of effective barrier transparency for the two bands, as well as a similar phase-shift effect as a function of temperature. An essential feature of this s±-wave model is non-sinusoidality of the current-phase relation, and we compute the dependence of the critical current on an external magnetic field, showing how this feature may be experimentally observable for this system. We also comment on the possible experimental detection of the phase shift effects in s±-wave superconductors.

Physica C: Superconductivity, 2001

We observed superconductivity-induced conductance oscillations, arising from quasiparticle interference eects in a single normal-metallic (N) electrode of ®nite width in contact with a superconductor (S). A 10 Â 10 lm 2 Al patch was overlaid on a pre-evaporated 0.5-lm-wide mesoscopic silver wire. A phase gradient along the N/S interface was induced by applying a magnetic ®eld perpendicular to the plane of the superconducting Al patch. The conductance across the N/S interface showed Fraunhofer-like oscillations with amplitudes of a small fraction of 2e 2 =h per conducting channel, for ®elds up to 450 G. For suciently low ®elds and temperatures the interfacial diraction eect of quasiparticles is more complicated due to the ®eld-induced electron±hole dephasing eect. None the less, the overall feature of the oscillatory magnetoconductance from the N/S interface appears to con®rm the diraction of Andreev-re¯ected quasiparticles proposed theoretically for a single N/S interface with a phase gradient.

Physical Review Letters, 2000

We have measured the supercurrent in aluminum atomic point contacts containing a small number of well characterized conduction channels. For most contacts, the measured supercurrent is adequately described by the opposite contributions of two thermally populated Andreev bound states per conduction channel. However, for contacts containing an almost perfectly transmitted channel 0.9 # t # 1 the measured supercurrent is higher than expected, a fact that we attribute to nonadiabatic transitions between bound states. PACS numbers: 73.40.Jn, 73.20.Dx, 74.50. + r In 1962, Josephson predicted that a surprisingly large supercurrent could flow between two weakly coupled superconducting electrodes when a phase difference d is applied across the whole structure. This phasedriven supercurrent I͑d͒ has subsequently been observed in a variety of weak coupling configurations such as thin insulating barriers, narrow diffusive wires, and ballistic point contacts between large electrodes. However, a theoretical framework powerful enough to predict the current-phase relation I͑d͒ in all configurations has emerged only during the last decade [1]. It applies in the mesoscopic regime, when electron transport between the electrodes is a quantum coherent process. Such transport is described by a set of N transmission coefficients ͕t i ͖ corresponding to N independent conduction channels. In the normal state, the conductance is given by G 0 P N i1 t i where G 0 2e 2 ͞h is the conductance quantum. In the superconducting state, electrons (holes) transmitted in one channel are Andreev reflected at the electrodes into holes (electrons) in the same channel. After a cycle involving two reflections at the electrodes, they acquire at the Fermi energy an overall phase factor p 1 d . In a "short" coupling structure, these cycles give rise to two electron-hole resonances per channel, called Andreev bound states (AS) [2] with energies E 6 ͑d, t i ͒ 6D͓1 2 t i sin 2 ͑d͞2͔͒ 1͞2 (D is the energy gap in the electrodes). These two AS carry current in opposite directions, I 6 ͑d, t͒ w 21 0 dE 6 ͑d, t i ͒͞dd (where w 0 h͞2e), and the net supercurrent results from the imbalance of their populations. A quantitative comparison of the predictions of this "mesoscopic superconductivity" picture of the Josephson effect with experimental results is usually hindered by the fact that in most devices the current flows through a very large number of channels with unknown t i . However, an atomic-size constriction between two electrodes, referred to hereafter simply as an atomic contact , is an extreme type of weak coupling structure which accommodates just a few channels. Because their set ͕t i ͖ is amenable to a complete experimental determination and because it can be controlled in a certain range [4], atomic contacts are ideal systems on which to test quantitatively the concepts of mesoscopic physics. The knowledge of ͕t i ͖ allows in principle the calculation of all transport quantities. In particular, the phase-driven supercurrent is given by

1995

Analytic predictions for resonant transport in three generic structures are presented. For a structure comprising a normal (N) contact - normal dot (NDOT) - superconducting (S) contact, we predict that finite voltage, differential conductance resonances are destroyed by the switching on of superconductivity in the S-contact. In the weak coupling limit, the surviving resonances have a double-peaked line-shape. Secondly, we demonstrate that resonant Andreev interferometers can provide galvonometric magnetic flux detectors, with a sensitivity in excess of the flux quantum. Finally, for a superconducting dot (SDOT) connected to normal contacts (N), we show that the onset of superconductivity can increase the sub-gap conductance, in contrast with the usual behaviour of a tunnel junction.

Physical Review B, 2002

Andreev reflection between a normal metal and a superconductor whose order parameter exhibits quantum phase fluctuations is examined. The approach chosen is non perturbative in the tunneling Hamiltonian, and enables to probe the whole range of voltage biases up to the gap amplitude. Results are illustrated using the one-dimensional Josephson junction array model previously introduced in the linear response regime. Phase fluctuations are shown to affect the differential conductance and are compared to the result of Blonder, Tinkham and Klapwijk for a rigid BCS superconductor. The noise spectrum of the Andreev current is also obtained and its second derivative with respect to frequency is proposed as a direct tool to analyze the phase fluctuations.

Nature Physics, 2012

Conventional superconductivity is incompatible with ferromagnetism, because the magnetic exchange field tends to spinpolarize electrons and breaks apart the opposite-spin singlet Cooper pairs 1 . Yet, the possibility of a long-range penetration of superconducting correlations into strong ferromagnets has been evinced by experiments that found Josephson coupling between superconducting electrodes separated afar by a ferromagnetic spacer 2-7 . This is considered a proof of the emergence at the superconductor/ferromagnetic (S/F) interfaces of equalspin triplet pairing, which is immune to the exchange field and can therefore propagate over long distances into the F (ref. 8). This effect bears much fundamental interest and potential for spintronic applications 9 . However, a spectroscopic signature of the underlying microscopic mechanisms has remained elusive. Here we do show this type of evidence, notably in a S/F system for which the possible appearance of equal-spin triplet pairing is controversial 10-12 : heterostructures that combine a half-metallic F (La 0.7 Ca 0.3 MnO 3 ) with a d-wave S (YBa 2 Cu 3 O 7 ). We found quasiparticle and electron interference effects in the conductance across the S/F interfaces that directly demonstrate the long-range propagation across La 0.7 Ca 0.3 MnO 3 of superconducting correlations, and imply the occurrence of unconventional equal-spin Andreev reflection. This allows for an understanding of the unusual proximity behaviour observed in this type of heterostructures 12,13 .

Journal of Physics: Condensed Matter, 1993

After presenting an intuitive picture of quasi-panicle UanspOrf in m e s m p i c superconductors, which emphasizes the intimate relation behueen Andreev scauering and m resistivity. we develop a general Wry of oc transport in mesoscopic.normal~uperconducting shuctures. Generalized multi-pmte conductance formulae are derived, which fake into aCFoun1 MK only Ihe effect of Andreev rcatte~ng on transpon coeffidents. but also the nonsonservation of quasi-panicle charge which arises in the presence of a superconducting mndensate. Experiments on quari-panicl& charge imbalance are described naturally by this approach. ~. 1. Introduction At.a low enough temperature, or for small enough systems, a quasi-particle such as an electron or hole can pass through a sample without scattering inelastically. In this mesoscopic limit, the phase coherence of quasi-particles is preserved and transport pmperties depend in detail on the diffraction pattern produced by elastic scattering from inhomogeneities and boundaries. During the past decade, the study of normal mesoscopic systems has Jed to the .discovery of a range of .new phenomena, including universal conductance fluctuations [1,2], quantized conductance of point contacts [3,4] and the detection of macroscopic changes in transpoa coefficients arising from tunnelling within a single atomic two-level system [5]. Until recently, these advances had centred almost exclusively on normal mesoscopic systems. However during the past few years, the hitherto distinct fields of mesoscopic physics and superconductivity have come together, leading to the possibility of a range of new developments involving hybrid normal-superconducting structures. One class of such systems is typified by mesoscopic Josephson junctions, which arise when a mesoscopic weak link is~fofied between two non-mesoscopic superconducting contacts. For such structures, the critical current I, is predicted to exhibit a range of new quantum phenomena Recent examples are the discretization of the'critical c-nt through a ballistic point contact [SI, the appearance of a universal resonant Josephson current through quantum dots [7] and the prediction of universal supercurrent fluctuations in diffusive point contacts [SI. Another class of hybrid systems arises when the superconductor itself is mesoscopic. This irises when a small superconducting sample is connected to the outside world through normal extemal leads, or when superconducting islands are immersed in a normal mesoscopic background. In such systems, transpon propetties such as electrical or thermal conductances exhibit new effects which are absent from their normal counterparts. For

Journal of Physics: Condensed Matter, 1993

After presenting an intuitive picture of quasi-panicle UanspOrf in m e s m p i c superconductors, which emphasizes the intimate relation behueen Andreev scauering and m resistivity. we develop a general Wry of oc transport in mesoscopic.normal~uperconducting shuctures. Generalized multi-pmte conductance formulae are derived, which fake into aCFoun1 MK only Ihe effect of Andreev rcatte~ng on transpon coeffidents. but also the nonsonservation of quasi-panicle charge which arises in the presence of a superconducting mndensate. Experiments on quari-panicl& charge imbalance are described naturally by this approach. ~. 1. Introduction At.a low enough temperature, or for small enough systems, a quasi-particle such as an electron or hole can pass through a sample without scattering inelastically. In this mesoscopic limit, the phase coherence of quasi-particles is preserved and transport pmperties depend in detail on the diffraction pattern produced by elastic scattering from inhomogeneities and boundaries. During the past decade, the study of normal mesoscopic systems has Jed to the .discovery of a range of .new phenomena, including universal conductance fluctuations [1,2], quantized conductance of point contacts [3,4] and the detection of macroscopic changes in transpoa coefficients arising from tunnelling within a single atomic two-level system [5]. Until recently, these advances had centred almost exclusively on normal mesoscopic systems. However during the past few years, the hitherto distinct fields of mesoscopic physics and superconductivity have come together, leading to the possibility of a range of new developments involving hybrid normal-superconducting structures. One class of such systems is typified by mesoscopic Josephson junctions, which arise when a mesoscopic weak link is~fofied between two non-mesoscopic superconducting contacts. For such structures, the critical current I, is predicted to exhibit a range of new quantum phenomena Recent examples are the discretization of the'critical c-nt through a ballistic point contact [SI, the appearance of a universal resonant Josephson current through quantum dots [7] and the prediction of universal supercurrent fluctuations in diffusive point contacts [SI. Another class of hybrid systems arises when the superconductor itself is mesoscopic. This irises when a small superconducting sample is connected to the outside world through normal extemal leads, or when superconducting islands are immersed in a normal mesoscopic background. In such systems, transpon propetties such as electrical or thermal conductances exhibit new effects which are absent from their normal counterparts. For

Physical Review B - PHYS REV B, 1999

We measure the resistance of a normal mesoscopic sample with two superconducting mirrors and find two regimes with qualitatively different behavior. At temperatures below 90 mK peaks in the conductance were found when the phase difference between the two superconductors is an odd multiple of pi. The peak heights increase with decreasing temperature. Above 100 mK the observed peaks give way to dips in the conductance. While the high-temperature behavior can be explained in terms of the thermal effect [Phys. Rev. Lett. 76, 823 (1996)], we propose that the low-temperature behavior is a manifestation of resonant transmission of low-energy quasiparticles through Andreev states.

Physica C: Superconductivity, 2001

We present a simple scattering approach to the charge transport across a realistic superconductor±normal injector interface of a ®nite transmittance that is modeled by a double-barrier mesoscopic junction. For a d-wave pairing symmetry, our calculations combine a fully quantum-mechanical scattering formalism with a self-consistent estimation of Andreev re¯ection coecients within the quasi-classical Eilenberger equation scheme for a free specular superconducting surface. Numerical simulations con®rm experimental criteria of Cucolo for the unconventional superconducting origin of conductance anomalies in high-temperature oxides. A discussion of dephasing eects caused by inelastic scattering processes in the interlayer and their impact on the conductance spectra is given. Ó 2001 Published by Elsevier Science B.V.

Journal of Physics: Condensed Matter, 2001

In this letter, we examine the effect of Coulomb interactions in the normal region of a normal-superconducting (N/S) mesoscopic structure; here the change from an attractive to a repulsive Coulombic interaction, at the N/S interface, causes a shift in the order parameter phase. We show that this shift has a pronounced effect on the Andreev bound states and demonstrate that the effect on Andreev scattering of non-zero order parameter tails can be used to probe the sign of the interaction in the normal region.

Physical Review B, 2009

We analyze the non-local transport properties of a d-wave superconductor coupled to metallic electrodes at nanoscale distances. We show that the non-local conductance exhibits an algebraical decay with distance rather than the exponential behavior which is found in conventional superconductors. Crossed Andreev processes, associated with electronic entanglement, are favored for certain orientations of the symmetry axes of the superconductor with respect to the leads. These properties would allow its experimental detection using present technologies.

Physical Review B, 1997

We have generalized the scattering-matrix theory of multiple Andreev reflections in mesoscopic Josephson junctions to the multi-mode case, and applied it to short superconductor/normal metal/superconductor junctions with diffusive electron transport. Both the dc and ac current-voltage characteristics are analyzed for a wide range of bias voltages V. For voltages smaller than the supeconducting gap the dc differential conductance of the junction diverges as 1/ √ V .