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Low Temperature Physics

Spontaneous currents in Josephson junctions between unconventional superconductors and d-wave qubits (Review)

Yu. A. Kolesnichenko, A. N. Omelyanchouk, Alexandre M. Zagoskin

Published Jul 1, 2004• 12 citations
Publisher

Abstract

The modern physics of superconductivity can be called the physics of unconventional superconductivity. The discovery of the d-wave symmetry of the order parameter in high-temperature superconductors and the triplet superconductivity in compound Sr2RuO4 has caused a huge stream of theoretical and experimental investigations of unconventional superconductors. In this review we discuss some novel aspects of the Josephson effect which are related to the symmetry of the order parameter. The most intriguing of them is spontaneous current generation in an unconventional weak link. The example of a Josephson junction in the form of a grain boundary between two disorientated d-wave or f-wave superconductors is considered in detail. Josephson current–phase relations and the phase dependences of the spontaneous current that flows along the interface are analyzed. The spontaneous current and spontaneous phase difference are manifestations of the time-reversal symmetry (𝒯 ) breaking states in the system. We analyzed the region of appearance of 𝒯-breaking states as function of temperature and mismatch angle. A review of the basics of superconducting qubits with emphasis on specific properties of d-wave qubits is given. Recent results in the problem of decoherence in d-wave qubits, which is the major concern for any qubit realization, are presented.

DOI
10.1063/1.1789112

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The modern physics of superconductivity can be called the physics of unconventional superconductivity. The discovery of the d-wave symmetry of the order parameter in high-temperature superconductors and the triplet superconductivity in compound Sr2RuO4 has caused a huge stream of theoretical and experimental investigations of unconventional superconductors. In this review we discuss some novel aspects of the Josephson effect which are related to the symmetry of the order parameter. The most intriguing of them is spontaneous current generation in an unconventional weak link. The example of a Josephson junction in the form of a grain boundary between two disorientated d-wave or f-wave superconductors is considered in detail. Josephson current–phase relations and the phase dependences of the spontaneous current that flows along the interface are analyzed. The spontaneous current and spontaneous phase difference are manifestations of the time-reversal symmetry (𝒯 ) breaking states in the system. We analyzed the region of appearance of 𝒯-breaking states as function of temperature and mismatch angle. A review of the basics of superconducting qubits with emphasis on specific properties of d-wave qubits is given. Recent results in the problem of decoherence in d-wave qubits, which is the major concern for any qubit realization, are presented.
Conventional tunnel Josephson junctions form the basic building blocks of superconducting electronics. Their operation is based on comparatively simple dynamics where the superconducting phases across the junctions is the only dynamical degree of freedom. The goal of the project on which this thesis is based, is to understand the physics and develop a consistent theoretical description of the quantum dynamics of unconventional Josephson structures: spin active junctions, junctions containing low energy quasiparticles, and junctions composed of ddd-wave superconductors. Spin active Josephson junctions involve the additional degree of freedom of quasiparticle spin. Here we theoretically investigate the spin-structure of the current carrying interface bound states - Andreev Bound States (ABS), and induced ground state spin polarization of a short (shorter than the superconducting coherence length) nanowire junction containing a localized magnetic moment. We show that temporal variation of the superconducting phase difference and magnetic moment induce rotations in spin polarized and unpolarized subspaces respectively, which is manifested by temporal oscillation of the Josephson current.The interlevel transitions obey a selection rule that forbids manipulations in a certain region ofexternal parameters and results from specific properties of Andreev bound states in magnetic contacts where, in a certain regime of phase bias and strength of magnetic scatterer, ABS belong to different eigenstates of the combined charge and parity inversion symmetry operator.A general framework is developed to include low energy quasiparticle states into the dynamics of Josephson junctions. Such states exist in e.g. constriction type junctions with high transparency channels or resonant states, as well as in junctions of unconventional superconductors. The existence of such states prevent the separation of energy scales which in conventional tunnel junctions freezes out the quasiparticle degrees of freedom. We show that the resonant interaction with such low energy states rather than the Josephson potential defines the nonlinear Josephson dynamics at small amplitudes.The framework is applied to high temperature Josephson junctions, whose unconventional order parameter admits ABS with energies in the middle of the superconducting gap - Mid Gap States (MGS). In addition to the non-linear dynamics induced by the MGS, we identify a reentrance effect in the transition between thermal activation and macroscopic quantum tunneling associated with the MGS, and connect this phenomenon to experimental observations.
This thesis is about unconventional superconductors out of equilibrium. More precisely, it summarizes our theoretical efforts in addressing a few questions related to the real-time evolution in models displaying unconventional superconductivity. Apart from the purely theoretical interest, the motivation for these studies comes from the recent achievement in the field of ultrafast time-resolved spectroscopy on correlated materials, such as the high-temperature copper-oxide superconductors. The task of describing such systems in nonequilibrium is a very difficult one. In this thesis we attack the problem from two different points of view: • the anisotropic unconventional d-wave symmetry, • the strong electron-electron correlations. The thesis is organized as follows: The first part introduces the basic concepts which lay at the foundation of the work presented in the other two parts. In Chapter 1, the concept of unconventional superconductivity is briefly introduced. This mainly includes the high-temperature copper-oxide superconductors and their phenomenology: d-wave symmetry of the super- conducting gap and strong electron-electron interaction. Chapter 2 is devoted to a review of the recent experimental advances in the field of ultrafast spectroscopy of high temperature superconductors and correlated materials, with a particular focus on time- and angle- resolved photoemission spectroscopy. Finally, Chapter 3 is a short review of some works in the field of cold-atom Fermi gases. In the second part we address the physics of the d-wave superconductor after a sudden excitation. First, in Chapter 4 we introduce in some detail a model of mean-field superconductor with a d-wave symmetry. The principal feature of this model is the anisotropy of the gap and the nodal lines along which the gap vanishes. The results concerning the dynamics of the gap after a “quantum quench” are exposed in Chapter 5 where we compare our model to the s-wave superconductor. This comparison allows to identify the consequences of the unconventional symmetry. In Chapter 6 we discuss the spectral features of the transient nonequilibrium state of the d-wave superconductor. This is particularly important to move a first step towards photoemission experiments. In the third part we concentrate on the attractive Hubbard model as a prototype of strongly correlated superconductor. In Chapter 8 we discuss the superconducting state at equilibrium with the use of dynamical mean-field theory. In Chapter 9 we discuss the extension of this technique to systems out of equilibrium. In particular it is described the implementation in the superconducting phase. At the end of the thesis two appendices give some details of the calculations.
A stationary Josephson effect in a weak link between misoriented nonunitary triplet superconductors is investigated theoretically. The non-self-consistent quasiclassical Eilenberger equation for this system is solved analytically. As an application of this analytical calculation, the current-phase diagrams are plotted for the junction between two nonunitary bipolar f-wave superconducting banks. A spontaneous current parallel to the interface between superconductors is observed. Also, the effect of misorientation between crystals on the Josephson and spontaneous currents is studied. Such experimental investigations of the current-phase diagrams can be used to test the pairing symmetry in the above-mentioned superconductors.
The properties of d-wave YBCO Josephson junctions and dc-SQUIDs with high misorientation angles have been\nstudied experimentally .\nThe predominant d-wave symmetry of the pairing wavefunction in high-Tc superconductors has, to a large extent, been\na hinderance in applications, but it also makes it possible to fabricate devices with novel properties that may be suitable\nfor applications in the quantum regime; one particulary interesting property is a strong second harmonic component in the current-phase relation of\njunctions with the electrodes oriented in a node-lobe arrangement; so-called 0-45 junctions.\n\nThe work has been focused on the properties of grain-boundary 0-45 dc-SQUIDs: Their dc-properties as well\nas the effects of a strong second harmonic component on the dynamics have been studied experimentally and\nmodelled numerically. The experimental results can be explained by taking into account the meandering of\nthe grain boundary which in combination with a strong orientational dependence of the transport properties due to the\nd-wave symmetry results in interfaces with properties that change dramatically over a length scale of 50-100 nm.\n\nThe properties of grain-boundary YBCO 0-45 junctions have been studied in the quantum regime. Macroscopic\nquantum tunnelling has been demonstrated in these junctions and microwave spectroscopy is here used to verify\nthe presence of discrete energy levels. The quality factor of the junction has been experimentally determined to 40+-10, a much higher value than previously believed to be possible in high-Tc structures.\n\nFinally, the possibility of using high-Tc_cc​ structures to build qubits is discussed. There is now a renewed\ninterest in this possibility, especially in light of our recent results which\ndemonstrate that the inherent dissipation mechanisms are much less detrimental to coherent phenomena than previously feared.
Abstract We propose the Josephson junctions linked by a normal metal between a d + id superconductor and another d + id superconductor, a d-wave superconductor, or a s-wave superconductor for identifying the chiral d + id superconductivity. The time-reversal breaking in the chiral d-wave superconducting state is shown to result in a Josephson φ0-junction state where the current-phase relation is shifted by a phase φ0 from the sinusoidal relation, other than 0 and π. The ground-state phase difference φ0 and the critical current can be used to definitely confirm and read the information about the d + id superconductivity. A smooth evolution from conventional 0-π transitions to tunable φ0-states can be observed by changing the relative magnitude of two types of d-wave components in the d + id pairing. On the other hand, the Josephson junction involving the d + id superconductor is also the simplest model to realize a φ0- junction, which is useful in superconducting electronics and superconducting quantum computation.
We show that superconductors have a thin spectrum associated with spontaneous symmetry breaking similar to that of antiferromagnets, while still being in full agreement with Elitzur's theorem, which forbids the spontaneous breaking of local (gauge) symmetries. This thin spectrum in the superconductors consists of in-gap states that are associated with the spontaneous breaking of a global phase symmetry. In qubits based on mesoscopic superconducting devices, the presence of the thin spectrum implies a maximum coherence time which is proportional to the number of Cooper pairs in the device. Here we present the detailed calculations leading up to these results and discuss the relation between spontaneous symmetry breaking in superconductors and the Meissner effect, the Anderson-Higgs mechanism, and the Josephson effect. Whereas for the Meissner effect a symmetry breaking of the phase of the superconductor is not required, it is essential for the Josephson effect.