On the use of STM superconducting tips at very low temperatures

We report on high quality local tunnel spectroscopy measurements in superconductors using in-situ fabricated superconducting tips as counterelectrode. The experiments were made at very low temperatures using a dilution refrigerator and a ³He cryostat. Spectra obtained with superconducting tip and sample of Al show that the spectroscopic resolution of our set-up is of 15 eV. Following the observation of Josephson current in tunnelling regime (with tips of Pb and of Al), we discuss the feasibility of Scanning Josephson Spectroscopy with atomic size resolution. Experiments showing new applications of these superconducting tips under applied external magnetic fields are also reported.Received: 12 May 2004, Published online: 7 September 2004PACS: 73.63.Rt Nanoscale contacts - 74.25.Fy Transport properties (electric and thermal conductivity, thermoelectric effects, etc.) - 74.25.Ha Magnetic properties - 74.50. + r Tunnelling phenomena; point contacts, weak links, Josephson effects - 74.78.Na Mesoscopic and nanoscale systems - 74.80.Fp Point contacts; SN and SNS junctions     

Ferromagnet–superconductor hybrids

The new class of phenomena described in this review is based on the interaction between spatially separated, but closely located ferromagnets and superconductors, the so-called ferromagnet–superconductor hybrids (FSH). Typical FSH are: coupled uniform and textured ferromagnetic and superconducting films, magnetic dots over a superconducting film, magnetic nanowires in a superconducting matrix, etc. The interaction is provided by the magnetic field generated by magnetic textures and supercurrents. The magnetic flux from magnetic structures or topological defects can pin vortices or create them, changing the transport properties and transition temperature of the superconductor. On the other hand, the magnetic field from supercurrents (vortices) strongly interacts with the magnetic subsystem, leading to formation of coupled magnetic–superconducting topological defects.

The proximity of ferromagnetic layer dramatically changes the properties of the superconducting film. The exchange field in ferromagnets not only suppresses the Cooper-pair wavefunction, but also leads to its oscillations, which in turn leads to oscillations of observable values: the transition temperature and Josephson current. In particular, in the ground state of the Josephson junction the relative phase of two superconductors separated by a layer of ferromagnetic metal is equal to?π?instead of the usual zero (the so-called π-junction). Such a junction carries a spontaneous supercurrent and possesses other unusual properties. Theory predicts that rotation of magnetization transforms s-pairing into p-pairing. The latter is not suppressed by the exchange field and serves as a carrier of long-range interaction between superconductors.     

Nanoscale superconducting quantum bits

Various physical systems were proposed for quantum information processing. Among those nanoscale devices appear most promising for integration in electronic circuits and large-scale applications. We discuss Josephson junction circuits in two regimes where they can be used for quantum computing. These systems combine intrinsic coherence of the superconducting state with control possibilities of single-charge circuits. In the regime where the typical charging energy dominates over the Josephson coupling, the low-temperature dynamics is limited to two states differing by a Cooper-pair charge on a superconducting island. In the opposite regime of prevailing Josephson energy, the phase (or flux) degree of freedom can be used to store and process quantum information. Under suitable conditions the system reduces to two states with different flux configurations. Several qubits can be joined together into a register. The quantum state of a qubit register can be manipulated by voltage and magnetic field pulses. The qubits are inevitably coupled to the environment. However, estimates of the phase coherence time show that many elementary quantum logic operations can be performed before the phase coherence is lost. In addition to manipulations, the final state of the qubits has to be read out. This quantum measurement process can be accomplished using a single-electron transistor for charge Josephson qubits, and a d.c.-SQUID for flux qubits. Recent successful experiments with superconducting qubits demonstrate for the first time quantum coherence in macroscopic systems.     

Coulomb-blockade-induced bound quasiparticle states in a double-island structure

We determine the low temperature shape of the Coulomb-blockade staircase in a superconducting double-island device. For an odd number of electrons, in the ground state the intrinsic quasiparticle is bound to the tunneling contact. For a single channel contact the gap between the ground state and the continuum of excited states is of the order of the Josephson energy E(J). The temperature dependence of the Coulomb-blockade step width is nonmonotonic, with the minimal width occurring at T(i) approximately E(J)/ln(square root DeltaE(J)/delta), where Delta and delta are, respectively, the superconducting gap and mean level spacing in the island. For an even number of electrons, the Coulomb enhancement of the Josephson energy is shown to be significantly stronger than that for a single grain coupled to a lead. If the electrostatic energy favors a single broken Cooper pair, the resulting quasiparticles are bound to the contact at T=0.     

Electrically tunable macroscopic quantum tunneling in a graphene-based Josephson junction

Stochastic switching-current distribution in a graphene-based Josephson junction exhibits a crossover from the classical to quantum regime, revealing the macroscopic quantum tunneling of a Josephson phase particle at low temperatures. Microwave spectroscopy measurements indicate a multiphoton absorption process occurring via discrete energy levels in washboard potential well. The crossover temperature for macroscopic quantum tunneling and the quantized level spacing are controlled with the gate voltage, implying its potential application to gate-tunable superconducting quantum bits.     

A model for layered high-temperature superconductors with two CuO2 layers per unit cell

We extend a model for layered high-temperature superconductors to systems with two CuO₂ layers per unit cell and two interlayer spacings with different physical properties. The carriers are assumed to occupy Fermi liquid states, forming narrow tight-binding bands. The layers are coupled by weak interlayer-hopping matrix elements between adjacent sheets, as well as by an attractive interaction between carriers in neighboring layers in addition to an on-site intralayer coupling. We solve the Gorkov equations for this model to obtain the critical temperature and the density of states of the oneparticle excitations from the superconducting condensate, and discuss various parameter regimes concerning the coupling between the two layers. We compare our results with current experimental findings for high-temperature superconductors. The presence of two CuO₂ layers leads to multi-peak features in the superconducting density of states, as has been observed in recent tunneling measurements.     

On the mechanism of dissipation in the internal Josephson effect in layered superconductors at low temperatures

The current-voltage characteristics (IVCs) of a layered superconductor with singlet d pairing at low temperatures are calculated in the internal Josephson effect (IJE) regime. Coherent electron tunneling between layers is assumed. A finite resistance of the superconductor in the resistive state arises because of quasiparticle transitions through the superconducting gap near nodes. Because of charge effects the interaction of the Josephson junctions formed by the layers does not lead to substantial differences in the shapes of different branches of the IVCs. The model describes the basic qualitative features of the effect in high-temperature superconductors for voltages which are low compared with the amplitude of the superconducting gap. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 8, 516–521 (25 October 1999)     

Experimental test of a superconducting digital interface for vortex qubits

We have developed and tested a classical superconducting logic interface to a qubit prototype based on two macroscopically distinct quantum states of a vortex in a long Josephson junction. The initial state preparation as well as the readout of a qubit is demonstrated by using a relatively simple Rapid Single Flux Quantum (RSFQ) circuit. RSFQ logic appears as a very feasible choice for constructing an interface between superconducting qubits and room-temperature electronics.Received: 16 January 2004, Published online: 20 April 2004PACS: 74.40. + k Fluctuations (noise, chaos, nonequilibrium superconductivity, localization, etc.) - 74.50. + r Tunneling phenomena; point contacts, weak links, Josephson effects - 74.78.-w Superconducting films and low-dimensional structures     

Macroscopic quantum interference effects in superconducting multiterminal microstructures

We review the macroscopic quantum phenomena in superconducting microstructures based on multiterminal junctions. The multiterminal Josephson junction presents a system in which the weak coupling takes place between several massive superconducting banks (terminals). Compared with the conventional (two-terminal) junctions such systems have additional degrees of freedom and a corresponding set of control parameters, preset transport currents and (or) applied magnetic fluxes. The general phenomenological theory of multiterminal Josephson junctions is presented. The specific multichannel interference effects (studied theoretically and experimentally) are described for two microstructures: the four-terminal SQUID and a system consisting of two weakly coupled superconducting rings.     

超导体中库珀对的SU(2)与Glauber相干态——库珀对与约瑟夫森超流性的量子特性研究

本文利用类自旋算符证明BCS超导基态波函数是单个库珀对SU(2)相干态波函数的直积、且在一定条件下为库珀对体系的SU(2)相干态波函数。若两块处在BCS超导基态的超导体耦合在一起,则体系仍处在SU(2)相干态,且在一定条件下为定态超辐射态。在SU(2)群到谐振子群的收缩下,库珀对的SU(2)相干态变为Glauber相干态。讨论了两种情形下库珀对与约瑟夫森超流性的量子噪声、分布及二阶相关特性。     

Ground-state cooling of a suspended nanowire through inelastic macroscopic quantum tunneling in a current-biased Josephson junction

We demonstrate that a suspended nanowire forming a weak link between two superconductors can be cooled to its motional ground state by a supercurrent flow. The predicted cooling mechanism has its origins in magnetic field induced inelastic tunneling of the macroscopic superconducting phase associated with the junction. Furthermore, we show that the voltage drop over the junction is proportional to the average population of the vibrational modes in the stationary regime, a phenomenon which can be used to probe the level of cooling.     

Discrete-lattice model approach to the tunneling between d-wave superconductors: Interference of tunnel bonds

The Josephson current between d-wave superconductors is investigated in the framework of the tight-binding lattice model. The junction is modeled by a small number of connecting bonds. It is found that the Josephson current through one bond vanishes when at least one of the superconductors has the (110) interface-to-crystal orientation. Interference between the nearest bonds appears to be very important. In particular, it is the interference term that leads to the nonzero Josephson current for the (110) orientation. Also, interference of two connecting bonds manifests itself in nonmonotonic behavior of the critical Josephson current in a dependence on the distance between the bonds. The text was submitted by the author in English.     

Effect of transparency on Josephson junction between s+g-wave superconductors

In this paper, a dc Josephson junction between borocarbide superconductors has been studied theoretically. The s+g-wave pairing symmetry which is observed in rare earth complex of borocarbides has a huge anisotropy and is an interesting form of unconventional superconductivity. We calculate the Josephson current in a superconductor--insulator--superconductor (SIS) Josephson junction with s+g-wave superconducting pairing symmetry. In our planar junction c-axis is parallel to an interface with finite transparency but ab-planes of two tetragonal superconductors are misorientated by angle α. We obtain that the Josephson current is strongly dependent on mis-orientation between the left and the right ab-planes. An insulator sandwiched between two superconductors which acts as a potential barrier is demonstrated by a transparency coefficient. The effects of the potential barrier and the mis-orientation on the current are studied analytically and numerically. Occurrence of 0--π transition in this s+g-wave junction is investigated in this paper. A comparison between d-wave Josephson junction and s+g-wave one is also made in the present paper.     

Effective boundary field theory for a Josephson junction chain with a weak link

We show that a finite Josephson junction (JJ) chain, ending with two bulk superconductors, and with a weak link at its center, may be regarded as a condensed matter realization of a two-boundary sine-Gordon model. Computing the partition function yields a remarkable analytic expression for the DC Josephson current as a function of the phase difference across the chain. We show that, in a suitable range of the chain parameters, there is a crossover of the DC Josephson current from a sinusoidal to a sawtooth behavior, which signals a transition from a regime where the boundary term is an irrelevant operator to a regime where it becomes relevant.     

拓扑绝缘体/超导体异质结中的近邻效应

拓扑超导体自身具有对量子退相干天然的免疫性以及可编织性,这使得它在现代量子计算领域中受到了越来越多的重视,并且成为了下一代计算技术中最有希望的候选者之一。由于拓扑超导态在固有拓扑超导体中相当罕见,因此,当前大部分实验上的工作主要集中在由 s 波超导体与拓扑绝缘体之间通过近邻效应所诱导的拓扑超导体上。本论文中,我们回顾了基于拓扑绝缘体/超导体异质结的拓扑超导体的研究进展。在理论上,Fu 和 Kane 提出,通过近邻效应将 s 波超导体的能隙引入到拓扑绝缘体,可以诱导出拓扑超导电性。在实验上,我们也回顾了一些不同体系中的拓扑超导近邻效应的研究进展。文章的第一部分,我们介绍了一些异质结,包括：三维拓扑绝缘体 Bi2Se3和 Bi2Se3 与 s 波超导体NbSe2 以及 d 波超导体 Bi2Sr2CaCu2O8+δ 的异质结,拓扑绝缘体 Sn1−xPbxTe 与 Pb 的异质结,二维拓扑绝缘体 WTe2 与NbSe2 的异质结。此外,还介绍了 TiBiSe2 在 Pb 上的拓扑绝缘近邻效应。另一部分中,我们对基于拓扑绝缘体的约瑟夫森结进行了回顾,包括著名的基于 Fu-Kane 体系的拓扑绝缘体约瑟夫森结,以及基于约瑟夫森结的超导量子干涉器件。     

Very high frequency spectroscopy and tuning of a single-cooper-pair transistor with an on-chip generator

A single-Cooper-pair transistor (SCPT) is coupled capacitively to a voltage biased Josephson junction, used as a high-frequency generator. Thanks to the high energy of photons generated by the Josephson junction, transitions between energy levels, not limited to the first two levels, were induced and the effect of this irradiation on the dc Josephson current of the SCPT was measured. The phase and gate bias dependence of energy levels of the SCPT at high energy is probed. Because the energies of photons can be higher than the superconducting gap we can induce not only transfer of Cooper pairs but also transfer of quasiparticles through the island of the SCPT, thus controlling the poisoning of the SCPT. This can both decrease and increase the average Josephson energy of the SCPT: its supercurrent is then controlled by high-frequency irradiation.     

Condensation energy of the superconducting bilayer cuprates

In the present work, we report the interplay of single particle and Cooper pair tunnelings on the superconducting state of layered high-T _c cuprate superconductors. For this we have considered a model Hamiltonian incorporating the intra-planar interactions and the contributions arising due to the coupling between the planes. The interplanar interactions include the single particle tunneling as well as the Josephson tunneling of Cooper pairs between the two layers. The expression of the out-of-plane correlation parameter which describes the hopping of a particle from one layer to another layer in the superconducting state is obtained within a Bardeen-Cooper-Schriefer (BCS) formalism using the Green’s function technique. This correlation is found to be sensitive to the various parameter of the model Hamiltonian. We have calculated the out-of-plane contribution to the superconducting condensation energy. The calculated values of condensation energy are in agreement with those obtained from the specific heat and the c-axis penetration depth measurements on bilayer cuprates.     

Intrinsic Josephson tunneling for basic studies of high-temperature superconductors

High-temperature superconductors (HTS) are highly anisotropic with layers of CuO₂ separated by layers of charge reservoirs. The superconducting CuO₂ planes are weakly coupled by Josephson tunneling of Cooper pairs in the c-axis direction. It may be possible to use the intrinsic tunneling to realize a stack of intrinsic Josephson junctions at the surface of a single crystal (or epitaxial film) of HTS. These will form excellent tools in the study of superconducting properties of HTS.     

On possibility of the spontaneous magnetic flux in a Josephson junction containing magnetic impurities

The Josephson junction containing localized magnetic moments in a dielectric layer between two superconductors is considered. Conditions are studied under which the phase difference between superconductors in the state with energy minimum is equal to π (such a junction we call π-junction). In addition we consider “one-dimensional” Josephson junction one part (2) of which is π-junction, the other (1) being the usual Josephson junction ( 0 - junction). Conditions are found under which in such a system there is a spontaneous vortex with the centre at the boundary between the parts 1 and 2 and magnetic flux associated with this vortex. The vortex appears by second order phase transition as temperature decreases for T_c.     

Gate Tunable Supercurrent in Josephson Junctions Based on Bi_2Te_3 Topological Insulator Thin Films

We report transport measurements on Josephson junctions consisting of Bi_2Te_3 topological insulator(TI) thin films contacted by superconducting Nb electrodes.For a device with junction length L=134 nm,the critical supercurrent I_c can be modulated by an electrical gate which tunes the carrier type and density of the TI film.I_c can reach a minimum when the TI is near the charge neutrality regime with the Fermi energy lying close to the Dirac point of the surface state.In the p-type regime the Josephson current can be well described by a short ballistic junction model.In the n-type regime the junction is ballistic at 0.7 K T 3.8 K while for T 0.7 K the diffusive bulk modes emerge and contribute a larger I_c than the ballistic model.We attribute the lack of diffusive bulk modes in the p-type regime to the formation of p-n junctions.Our work provides new clues for search of Majorana zero mode in TI-based superconducting devices.