Multiple Andreev-reflection in asymmetric superconducting weak-links

The present paper is a continuation of [1], where we demonstrated the occurrence of multiple Andreev-reflection (AR) in symmetric Pb/n-InSb/Pb sandwich junctions. Here we are presenting the results of our investigations for the asymmetric configuration Pb/n-InSb/Sn. We discuss the measuredI(V)- anddV/dI(V)-characteristics in comparison with numerical calculations, which we carried out in a theoretical extension of the OTBK-theory [2,3] and a formulation given by W.M. van Huffelen et al. [4]. The main features in the characteristics are thesubharmonic gap structure (SGS) and anexcess current, which show interesting deviations from the symmetric situation. These deviations can be understood in a simple physical picture.     

Multiple Andreev-reflection in superconducting weak-links in the interaction with external microwave-fields

We present calculated current-voltage characteristics (CVCs) of NS- and SNS-contacts, where the carrier transport is characterised by single and multiple Andreev-reflection (AR) in the presence of an external microwave field. Based on the Tien-Gordon model of multiphoton- assisted electron tunneling [1] we describe the microwave field by an ac-voltage potential. This additional potential is added in the time-dependent Bogoliubov-de Gennes equations (BdGE) which describe inhomogeneous superconductors and in this way NS-phase boundaries. These modified BdGE are solved by single particle wave-functions, which contain the multiphoton emission and absorption processes of the quasi-particles (QPs). With this ansatz we obtain an extension of the BTK-theory for NS-contacts [2] and the OTBK-theory for SNS-contacts [3,4]. We show, that the calculated CVCs for NS-contacts are in the case of a vanishing probability for AR identical with the characteristics obtained with the Tien-Gordon model. For SNS-contacts we show theoretically that features in the CVCs appear at voltages $V = \frac{{2\Delta }} {{ne}} + \frac{m} {n}\frac{{\hbar \omega }} {e}$ (n,m integers). This equation was initially found experimentally by Hoffmann-Soerensen et al. [5]. We are now able to explain their results and show that investigations of the interaction of multiple AR with an external microwave field give clear evidence for the occurrence of multiple AR in the junction.     

Andreev-reflection in highly doped Pb/n−InSb/Pb junctions

We studied the carrier transport through n-InSb-films sandwiched between two superconducting lead electrodes. These n-InSb-films were about 30 nm thick, polycrystalline and very highly doped (10²¹ cm^–3). TheV(I)- and dV/dI (V)-characteristics indicated all the properties of Andreev-reflection (subharmonic energygap structures (SGS) and excess current) according to the theory of Octavio et al. (OTBK-model) [1, 2]. Our measurements show the temperature dependence of these structures and also the influence of magnetic fields up to 80 mT and give a further reference to the importance of Andreev-reflection in semiconductor-coupled superconducting junctions (SSmS junctions).     

Weak links in the superconducting transition of multiphase Bi-Ca-Sr-Cu-O compounds

The ac resistivities and dc V-I characteristics have been studied in a multiphase Bi-Ca-Sr-Cu-O sample in the temperature region where the transition from the normal to the superconducting state takes place. The resistivity drops sharply between 112K and 107K and follows a tail before zero resistivity is reached near 94K. The resistivity in the tail region is current dependent, this current dependence is easily suppressed by a magnetic field. We argue that this phenomenon is due to weak links between regions of the 110K-phase material.     

Persistent currents in superconducting quantum interference devices

Starting from the reduced dynamical model of a two-junction quantum interference device, it shown that a quantum analog of the system can be exhibited. This quantum model extends the well-known properties of the device when its characteristic dimensions are of the order of mesoscopic length scales. By finding eigenvalues of the corresponding Hamiltonian operator, the persistent currents flowing in the ring have been obtained. The resulting quantum analog of the overdamped two-junction quantum interference device can be seen as a supercurrent qubit operating in the limit of negligible capacitance and finite inductance.     

Fluxon ratchet potentials in superconducting circuits

A fluxon in a Josephson-junction parallel array behaves like a single particle in a periodic pinning potential. Different configurations of critical currents and cell areas result in different profiles for the fluxon potential. We analyze the minimal conditions to achieve an effective potential in which mirror symmetry is absent, namely a fluxon ratchet potential. Following one of the configurations, we designed circular arrays and probed some of the fluxon properties. Theoretical predictions are nicely fulfilled by the experiments. Received: 20 October 2001 / Accepted: 14 January 2002 / Published online: 22 April 2002     

Subharmonic gap structure in superconducting scanning tunneling microscope junctions

We observe a subharmonic gap structure (SGS) and the Josephson effect in superconducting scanning tunneling microscope junctions with resistances below 100 kΩ. The magnitude of the n=2 SGS is shown to scale with the square of the junction normal state conductance, in agreement with theory. We show by analyzing the Josephson effect in these junctions that the superconducting phase dynamics are strongly affected by thermal fluctuations. We estimate the linewidth of the Josephson oscillations due to phase fluctuations, a quantity that may be important in modern theories of the subgap structure. While phase fluctuations may smear the SGS current onsets, we conclude that the sharpness of these onsets in our data is not limited by fluctuations.     

Andreev reflexion at nanocontacts of superconducting AuIn2 with copper

We investigated superconducting AuIn₂ by point-contact spectroscopy. Andreev reflexion was observed with nearly full excess current at contact sizes down to 0.15 nm. This implies, together with a large superconducting coherence length of 11 μm, almost ideal retroreflectivity. At the onset of lateral confinement of the ballistic electrons the Andreev-derived spectra broaden dramatically due to inelastic scattering at defects or the strain field near the contact. Lateral confinement does not suppress Andreev reflexion.     

Multiple Andreev-reflection in YBCO break-junctions

We present current-voltage characteristics of HTSC point-contacts prepared by the break-junction technique with YBCO single crystals. We compare the measured I(V)-, $\frac{{dV}} {{dI}}(V)$ (V)- and $\frac{{d^2 V}} {{dI^2 }}(V)$ (V)-characteristics to calculated characteristics of the OTBK-theory [1], which describes SINIS-junctions in which multiple Andreevreflection (AR) occurs. Taking into account systematic deviations between characteristics measured with conventional weak-links and characteristics calculated with the OTBK-theory, discussed in [2] and [3], we can demonstrate, that the characteristics of the YBCO breakjunctions clearly show all features, which indicate the occurrence of multiple AR. Thus we determine the energy gap of YBCO with a high precision to 2Δ = (42 ± 2) meV. In addition we find, that the structures in the characteristics at eV = 2Δ always show a broadening, whereas the structures at higher order subharmonic gap voltages $\left( {eV = \frac{{2\Delta }} {n}} \right)$ are not broadened. The reason for this behavior is subject for discussion. The investigation of the temperature dependence of the energy gap shows that 2Δ decreases substantially with rising temperature already at low temperatures. We confirm this result with two other independent methods. Break-junctions with very small or vanishing interface barriers at the two NIS-phase boundaries show characteristics which indicate also the occurrence of multiple Andreev-reflection, which cannot be described with the OTBK-theory. We demonstrate, that these characteristics can be explained with the relaxation time model for SNS-junctions published by Kümmel et al. [4].     

Andreev-reflection in YBCO “break-junctions”

We present measurements at break-junctions prepared of polycrystalline and textured YBCO-pellets with different resistances. The higher-ohmic junctions show the well known behaviour of HTSC-tunnel contacts with gap-like structures in their dI/dV-characteristics. Lower-ohmic junctions show the behaviour of point contacts. TheirI(VV)-and dI/dV-characteristics indicate all properties of the Andreev-reflection corresponding to the theory of Kümmel et al. [1] for BCS-superconductors. This could be an alternative method to study the energy gap in high temperature superconductors. Additionally we will show, that sharp minima in the dI/dV-characteristics could also be explained by the process of Andreev-reflection. For correcting the measured characteristics we substract the typical background to compare the characteristics directly with theoretical calculations. We studied the influence of magnetic fields up to 8 T.     

A frequency-modulated read-out system for dc SQIDs

A simple fm read-out system for dc SQUIDs is described that makes use of dc SQUIDs operated as relaxation oscillators. Measurements on system noise as well as on slew rate were performed, which demonstrate the applicability of the read-out scheme.     

Static characteristics of Josephson interferometers

This investigation deals with the range in operating currents for which a Josephson interferometer, sometimes also referred to as Superconducting QUantum Interference Device (SQUID), may remain in the zero-voltage Josephson condition. An interferometer consists of one or more inductive loops each of which contains two Josephson junctions or other weak links. Two types of current are considered. Gate currentI _gpasses the junctions in parallel. Control currentI _cgenerates magnetic flux via inductive coupling in the loops. Zero-voltage operation is possible within certain areas of theI _g,I _cplane. These areas are manifestations of flux-quantum states and their boundary lines are referred to as static characteristics. In view of the nonlinearity of the constituting equations, not all their formal solutions are physically realizable. A stability analysis yields criteria which permit the identification of realizable operating conditions. The static characteristics comprise operating conditions where the limit of stability is reached. To obtain the static characteristics, linearized equations may be utilized if theLI _o product, a measure for the size of an interferometer, is large compared to the flux quantumΦ ₀, whereL is the inductance per loop, andI _o the maximum Josephson current per junction. As a general method of solving system of transcendental equations, continuation is discussed. The utilization of continuation for obtaining interferometer characteristics is explained. It is shown that some changes in the gate-current feed arrangement are equivalent to shearing the characteristics in theI _g,I _cplane. Analytical results are given on extrema, inflexion points, and singularities in the shape of cusps which conceptually relate to the existence and connectivity of flux-quantum states. Experimental static characteristics are presented on two-and four-junction interferometers. They are in agreement with characteristics computed on the basis of simple lumped circuit models. Relevant circuit parameters are obtained from the experimental characteristics.     

Noise properties of SQUIDs with Superconductor-Semiconductor-Superconductor proximity effect Josephson junctions

SQUIDs using Superconductor-Semiconductor-Superconductor (SSmS) proximity effect Josephson junctions were prepared and noise measurements were carried out. Since SSmS junctions are basic elements of Josephson field effect transistors (JoFETs), information about dynamic properties of JoFETs can be gained in this way. A planar geometry was used for the SSmS junctions, with a single crystalline silicon wafer acting as both, substrate and proximity layer. Rf- and dc-SQUIDs could be realized. When the SQUIDs were operated in a flux locked loop, flux noise values comparable to conventional tunnel junction SQUIDs were measured.     

Measurements of the dynamic conductance on SS-and NS-point contacts

Mechanically point contacts made of Ta, Al, Ag (anvil) and of Ta, Ag (needle) were investigated in the temperature range between 4.2 K and 1.3 K and in magnetic fields up to 0.8 T. For point contacts consisting of two superconducting electrodes we measured the current voltage characteristics and also the dynamic conductance. The characteristics with a negative differential conductance and the occurrence of an excess current point to the appearance of Andreev-multiple reflection at an SNS-interface in the contact region.The investigated current voltage characteristics and the dynamic conductance of typical NS-point contacts (Ta–Ag and Ta–Al) point to a microconstriction with a barrier of arbitrary strength at the interface between the normalconductor and the superconductor. We performed theoretical calculations forT=0 and also for temperatures up to the critical temperature using the model of Blonder, Tinkham and Klapwijk (BTK model). In this model the Andreev-reflection is the main scattering mechanism at the NS-interface but also elastic scattering and transmission processes are taken into consideration. The comparison of our theoretical results with the experimental results and also the determined excess current at all investigated point contacts lead to the assumption that there exist metallic contacts with very small barrier strengths at the NS-interface where the Andreev-reflection is the dominant process and the other scattering mechanisms play a subdominant role.     

Low-field magnetic response of multi-junction superconducting quantum interference devices

The magnetic states of multi-junction superconducting quantum interference device containing 2N identical conventional Josephson junctions are studied by means of a perturbation analysis of the non-linear first-order ordinary differential equations governing the dynamics of the Josephson junctions in these devices. In the zero-voltage state, persistent currents are calculated in terms of the externally applied magnetic flux Φ_ex . The resulting d.c. susceptibility curves show that paramagnetic and diamagnetic states are present, depending on the value of Φ_ex . The stability of these states is qualitatively studied by means of the effective potential notion for the system.     

Proximity effect in ferromagnet/triplet p-wave superconductor structures

The superconducting proximity effect in normal metal/insulator/ferromagnet/triplet p  -wave superconductor (N/I/FP) structures is studied based on an extended Blonder–Tinkham–Klapwijk (BTK) theory. Three kinds of pairings for the P side are chosen: px$p_x$, py$p_y$, px+ipy$p_x+i{p}_y$ waves. The transition from the “0” to “π” state is found in the conductance spectra with increasing the thickness of F or the ferromagnetic exchange energy. The large amplitude of the normalized conductance suggests the possible coexistence of the ferromagnetism and p-wave superconductivity in a small region near the F/P interface induced by the proximity effect.     

Spin dependent Andreev reflection in ferromagnetic semiconductor/d-wave superconductor ballistic junction

The Andreev reflection (AR) probability and transmission of quasiparticles in ferromagnetic semiconductor/d-wave superconductor (FS/DS) ballistic junctions are studied based on an extended Blonder–Tinkham–Klapwijk (BTK) theory. It is shown that the dependence of AR probability and pair potential on the spin orientation of incident quasiparticles for the heavy holes is much different from that for light holes due to the different mismatches in the effective mass and Fermi velocity between FS and DS. The junction conductance is dominated by the quasiparticles which undergo AR processes with the largest probability, and this provides a method for measuring the spin polarization in FS.     

Ferromagnetic insulator effects in ferromagnetic semiconductor/ferromagnetic insulator/p-wave superconductor junctions

The effect of the ferromagnetic insulator on tunneling conductance in ferromagnetic semiconductor/ferromagnetic insulator/p-wave superconductor (FS/FI/P) junctions is studied based on a scattering theory. Three kinds of pairings for the P side are chosen: p_x, p_{y ,}p_x+ip_y waves. It is shown that the spin filtering effect originating from the exchange field in the FI strongly modifies the normalization conductance. Many novel features including the zero-bias conductance dip and splitting are exhibited for fixed spin polarization in the FS. The tunneling spectrum for the heavy holes is much different from that for the light holes due to the different mismatches in the effective mass and Fermi velocity between FS and P.     

Relaxation oscillators made of bridge-type Josephson contacts

Nb, NbN, and Nb₃Ge nanobridges on sapphire substrates with hysteretic I–V-characteristics are used as active elements in relaxation oscillators. Amplitudes of up to 350 mV and frequencies of up to 500 MHz could be generated, which make these oscillators useful for many applications. Linewidth and amplitude of the relaxation oscillations in dependence of nanobridge geometry are studied in some detail.Dedicated to Prof. Dr. Dres. h.c. A. Scharmann on the occasion of his 60^th birthday