Phase coherence and vortex order in a Josephson-junction array at irrational frustration are studied by extensive Monte Carlo simulations using the parallel tempering method. A scaling analysis of the correlation length of phase variables in the full equilibrated system shows that the critical temperature vanishes with a power-law divergent correlation length and critical exponent $ν_{ph}$, in agreement with recent results from resistivity scaling analysis. A similar scaling analysis for vortex variables reveals a different critical exponent $ν_{v}$, suggesting that there are two distinct correlation lengths associated with a decoupled zero-temperature phase transition.
Within the formalism of Usadel equations the Josephson effect in dirty point contacts between single-band and three-band superconductors is investigated. The general expression for the Josephson current, which is valid for arbitrary temperatures, is obtained. We calculate current-phase relations for very low temperature and in the vicinity of the critical temperature. For three-band superconductors with broken time-reversal symmetry (BTRS) point contacts undergo frustration phenomena with different current-phase relations, corresponding to ϕ-contacts. For three-band superconductors without BTR…
AC magnetoimpedance measurements performed on proximity-effect coupled Josephson junction arrays on a dice lattice reveal unconventional behaviour resulting from the interplay between the frustration f created by the applied magnetic field and the particular geometry of the system. While the inverse magnetoinductance exhibits prominent peaks at f=1/3 and at f=1/6 (and weaker structures at f=1/9,2/9,1/12,...) reflecting vortex states with a high degree of superconducting phase coherence, the deep minimum at f=1/2 points to a state in which the phase coherence is strongly suppressed. These obser…
To study the properties of frustrated two-dimensional Josephson junction arrays near incommensurability, we examine the current-voltage characteristics of a square proximity-coupled Josephson junction array at a sequence of frustrations f=3/8, 8/21, 0.382 $(\approx (3-\sqrt{5})/2)$, 2/5, and 5/12. Detailed scaling analyses of the current-voltage characteristics reveal approximately universal scaling behaviors for f=3/8, 8/21, 0.382, and 2/5. The approximately universal scaling behaviors and high superconducting transition temperatures indicate that both the nature of the superconducting transi…
We study the energy spectrum for an aperiodic Josephson junction ladder, as a function of frustration. Frustration is brought about by application of a transverse magnetic field, and aperiodicity is imposed by the arrangement of plaquettes with two incommensurate areas. We study the effect of the incommensurate plaquette areas in conjunction with that of the aperiodicity. The structure of the energy spectrum at deep minima is shown to be described by a model that treats the plaquettes independently. The energy spectrum is a quasiperiodic function of frustration; short range correlations in the…
We use a driven Monte Carlo dynamics in the phase representation to determine the linear resistivity and current-voltage scaling of a two-dimensional Josephson-junction array at an irrational flux quantum per plaquette. The results are consistent with a phase-coherence transition scenario where the critical temperature vanishes. The linear resistivity is nonzero at any finite temperatures but nonlinear behavior sets in at a temperature-dependent crossover current determined by the thermal critical exponent. From a dynamic scaling analysis we determine this critical exponent and the thermally a…
We have studied the rationally frustrated Josephson-junction array model in the square lattice through Monte Carlo simulations of $(2+1)$D XY-model. For frustration $f=1/4$, the model at zero temperature shows a continuous superfluid-insulator transition. From the measurement of the correlation function and the superfluid stiffness, we obtain the dynamical critical exponent $z=1.0$ and the correlation length critical exponent $ν=0.4 \pm 0.05$. While the dynamical critical exponent is the same as that for cases $f=0$, 1/2, and 1/3, the correlation length critical exponent is surprisingly quite …
The Josephson equations predict remarkable effects concerning the phase state of a superconducting junction with an oscillating current induced by a static voltage. Whether the paradigm can be twisted by yielding an oscillating voltage without making use of harmonic drives is a fundamentally relevant problem yet not fully settled. Here, we demonstrate that a dynamical regime with an oscillating phase evolution is a general hallmark of driven Josephson systems exhibiting sign competition in the Josephson couplings. We show that in frustrated Josephson systems an oscillating phase dynamics gets …
Using the path integral approach, we provide an explicit derivation of the equation for the phase boundary for quantum Josephson junction arrays with offset charges and non-diagonal capacitance matrix. For the model with nearest neighbor capacitance matrix and uniform offset charge $q/2e=1/2$, we determine, in the low critical temperature expansion, the most relevant contributions to the equation for the phase boundary. We explicitly construct the charge distributions on the lattice corresponding to the lowest energies. We find a reentrant behavior even with a short ranged interaction. A merit…
The scaling behavior of the current-voltage ($IV$) characteristics of a two-dimensional proximity-coupled Josephson junction array (JJA) with quenched bond disorder was investigated for frustrations $f=1/5$, 1/3, 2/5, and 1/2. For all these frustrations including 1/5 and 2/5 where a strongly first-order phase transition is expected in the absence of disorder, the $IV$ characteristics exhibited a good scaling behavior. The critical exponent $ν$ indicates that bond disorder may drive the phase transitions of frustrated JJA's to be continuous but not into the Ising universality class, contrary to…
We present analytical and numerical studies of pinned superconducting states of open-ended Josephson ladder arrays, neglecting inductances but taking edge effects into account. Treating the edge effects perturbatively, we find analytical approximations for three of these superconducting states -- the no-vortex, fully-frustrated and single-vortex states -- as functions of the dc bias current $I$ and the frustration $f$. Bifurcation theory is used to derive formulas for the depinning currents and critical frustrations at which the superconducting states disappear or lose dynamical stability as $…
The s+- state in which order parameter has different signs in different bands is a leading candidate for the superconducting state in the iron based superconductors. We investigate a Josephson junction between s and s+- superconductors within microscopic theory. Frustration, caused by interaction of the s-wave gap parameter with the opposite-sign gaps of the s+- superconductor, leads to nontrivial phase diagram. When the partial Josephson coupling energy between the s-wave superconductor and one of the s+- bands dominates, s-wave gap parameter aligns with the order parameter in this band. In t…
A novel time-reversal symmetry breaking state is found theoretically in the Josephson junction between the two-gap superconductor and the conventional s-wave superconductor. This occurs due to the frustration between the three order parameters analogous to the two antiferromagnetically coupled XY-spins put under a magnetic field. This leads to the interface states with the energies inside the superconducting gap. Possible experimental observations of this state with broken time-reversal symmetry are discussed.
We develop a model for high-Tc superconductors based on an electronic phase separation where low-and high-density domains are formed. At low temperatures this system may act as a granular superconductor forming an array of Josephson junctions. Cuprates are also known to have low superfluid densities and strong correlation effects. Both characteristics activate a negative Josephson coupling due to frustration that leads to spontaneous currents responsible for the weak ferromagnetic order. This original approach reproduces the observed onset of spontaneous magnetic signal and its dependence on t…
The ordering trend of magnetic impurities at low temperature results in the frustration of the pair-breaking effect and induces a ``recovery'' of superconducting properties. We show that this effect manifests itself in the deviation of the Josephson current amplitude from the values obtained within the Ambegaokar-Baratoff and the Abrikosov-Gor'kov models. We consider both weak and strong-coupling cases. The theory is applied to describe the experimental data obtained for the low-$T_c$ superconductor SmRh$_4$B$_4$. We further predict a ``recovery'' effect of the Josephson current in high-temper…
Fully frustrated one-dimensional diamond Josephson chains have been shown [B. Douçot and J. Vidal, Phys. Rev. Lett. {\bf 88}, 227005 (2002)] to posses a remarkable property: The superfluid phase occurs through the condensation of pairs of Cooper pairs. By means of Monte Carlo simulations we analyze quantitatively the Insulator to $4e$-Superfluid transition. We determine the location of the critical point and discuss the behaviour of the phase-phase correlators. For comparison we also present the case of a diamond chain at zero and 1/3 frustration where the standard $2e$-condensation is observe…
Equilibrium and non-equilibrium relaxation behaviors of two-dimensional superconducting arrays are investigated via numerical simulations at low temperatures in the presence of incommensurate transverse magnetic fields, with frustration parameter f= (3-\sqrt{5})/2. We find that the non-equilibrium relaxation, beginning with random initial states quenched to low temperatures, exhibits a three-stage relaxation of chirality autocorrelations. At the early stage, the relaxation is found to be described by the von Schweidler form. Then it exhibits power-law behavior in the intermediate time scale an…
Using the lumped circuit equations, we derive a stability criterion for superconducting pinned states in two-dimensional arrays of Josephson junctions. The analysis neglects quantum, thermal, and inductive effects, but allows disordered junctions, arbitrary network connectivity, and arbitrary spatial patterns of applied magnetic flux and DC current injection. We prove that a pinned state is linearly stable if and only if its corresponding stiffness matrix is positive definite. This algebraic condition can be used to predict the critical current and frustration at which depinning occurs.
We study the effect of an externally imposed rotation or magnetic field on frustrated multiband superconductors/superfluids. The frustration originates with multiple superconducting bands crossing the Fermi surface in conjunction with interband Josephson-couplings with a positive sign. These couplings tend to frustrate the phases of the various components of the superconducting order parameter. This in turn leads to an effective description in terms of a $\groupUZ$-symmetric system, where essentially only the $\groupU$-sector couples to the gauge-field representing the rotation or magnetic fie…
Transport measurements are carried out on dice Josephson-junction arrays with the frustration index $f=1/3$ and 1/2 which possess, within the limit of the $XY$ model, an accidental degeneracy of the ground states as a consequence of the formation of zero-energy domain walls. The measurements demonstrate that both the systems undergo a phase transition to a superconducting vortex-ordered state at considerably high temperatures. The experimental findings are in apparent contradiction with the theoretical expectation that frustration effects in the $f=1/3$ system are particularly strong enough to…
We show that the critical behavior of quantum systems undergoing a percolation transition is dramatically affected by their topological Berry phase $2πρ$. For irrational $ρ$, we demonstrate that the low-energy excitations of diluted Josephson-junctions arrays, quantum antiferromagnets, and interacting bosons are spinless fermions with fractal spectrum. As a result, critical properties not captured by the usual Ginzburg-Landau-Wilson description of phase transitions emerge, such as complex critical exponents, log-periodic oscillations and dynamically broken scale-invariance.
In this Letter we study the phase diagram and the approach to the equilibrium of Josephson junction arrays on a dice lattice for two different values of the magnetic frustration ($f=1/2,1/3$). In both cases the array unedrgoes a Berezinskii-Kosterlitz-Thouless like phase transition. For the fully frustrated array, $f=1/2$, we find evidence of a {\em glassy behavior} although the system has {\em no disorder}. For comparison we study dynamics of the array at a different value of frustration ($f=1/3$) and find no trace of glassy dynamics.
We classify ground states and normal modes for $n$-component superconductors with frustrated intercomponent Josephson couplings, focusing on $n = 4$. The results should be relevant not only to multiband superconductors, but also to Josephson-coupled multilayers and Josephson-junction arrays. It was recently discussed that three-component superconductors can break time-reversal symmetry as a consequence of phase frustration. We discuss how to classify frustrated superconductors with an arbitrary number of components. Although already for the four-component case there are a large number of diffe…
The nature of decoupling in the mixed phase of extremely type-II layered superconductors is studied theoretically through a duality transformation of the layered XY model with frustration. In the limit of weak coupling, we generally find that the Josephson effect is absent if and only if the phase correlations within isolated layers are short range. In the case specific to uniform frustration, we notably identify a decoupled pancake vortex liquid phase that is bounded by first-order and second-order decoupling lines in the magnetic field vs. temperature plane. These transitions potentially acc…
We carry out extensive Monte Carlo simulations on the Coulomb gas dual to the uniformly frustrated two dimensional XY model, for a sequence of frustrations f converging to the irraltional (3-sqrt 5)/2. We find in these systems a sharp first order equilibrium phase transition to an ordered vortex structure at a T_c which varies only slightly with f. This ordered vortex structure remains in general phase incoherent until a lower pinning transition T_p(f) that varies with f. We argue that the glassy behaviors reported for this model in earlier simulations are dynamic effects.
We present low temperature transport measurements in one dimensional Josephson junctions rhombi chains. We have measured the current phase relation of a chain of 8 rhombi. The junctions are either in the classical phase regime with the Josephson energy much larger than the charging energy, $E_{J}\gg E_{C}$, or in the quantum phase regime where $E_{J}/E_{C}\approx 2$. In the strong Josephson coupling regime ($E_{J}\gg E_{C} \gg k_{B}T$) we observe a sawtooth-like supercurrent as a function of the phase difference over the chain. The period of the supercurrent oscillations changes abruptly from …
We study theoretically the two Kitaev chains put in parallel, i.e., Kitaev ladder, coupled by Josephson junction. The $π$-junction between the Majorana bound states at the ends of the chains competes with the usual Josephson coupling along the chain, and this frustration leads to the modulation of the phase difference of the superconducting order parameter between the two chains. We show that this modulation gives the double degeneracy of the ground states, which can be manipulated by external electric and magnetic fields.
We report a study of overdamped Josephson junction arrays with the geometry of periodically repeated Sierpinski gaskets. These model superconductors share essential geometrical features with truly random (percolative) systems. When exposed to a perpendicular magnetic field B, their euclidian or fractal behavior depends on the relation between the intervortex distance (imposed by B) and the size of a constituent gasket, and was explored with high-resolution measurements of the sample magnetoinductance L(B). In terms of the frustration parameter f expressing (in units of the superconducting flux…
We investigate the ground state of the irrationally frustrated Josephson junction array with controlling anisotropy parameter λ that is the ratio of the longitudinal Josephson coupling to the transverse one. We find that the ground state has one dimensional periodicity whose reciprocal lattice vector depends on λ and is incommensurate with the substrate lattice. Approaching the isotropic point, λ=1 the so called hull function of the ground state exhibits analyticity breaking similar to the Aubry transition in the Frenkel-Kontorova model. We find a scaling law for the harmonic spectrum of the h…
We propose novel model system for the studies of superconductor-insulator transitions, which is a regular lattice, whose each link consists of Josephson-junction chain of $N \gg 1$ junctions in sequence. The theory of such an array is developed for the case of semiclassical junctions with the Josephson energy $E_J$ large compared to the junctions's Coulomb energy $E_C$. Exact duality transformation is derived, which transforms the Hamiltonian of the proposed model into a standard Hamiltonian of JJ array. The nature of the ground state is controlled (in the absence of random offset charges) by …
In this work, we investigate the Josephson effect between a two-band superconductor either with the $s++$ (two energy gaps have the same sign and are fully gapped) pairing symmetry or $s\pm$ (two energy gaps have $π$ phase difference and are fully gapped) pairing symmetry and a conventional s-wave superconductors. The ground state, critical current, plasma modes, flux flow dynamics, and response to external ac electric field, possible soliton solutions are investigated. For junctions with the charge neutrality breaking, we find a new plasma mode for junctions, which gives rise to new resonance…
We consider the dynamics of a two-dimensional array of underdamped Josephson junctions placed in a single-mode resonant cavity. Starting from a well-defined model Hamiltonian, which includes the effects of driving current and dissipative coupling to a heat bath, we write down the Heisenberg equations of motion for the variables of the Josephson junction and the cavity mode, extending our previous one-dimensional model. In the limit of large numbers of photons, these equations can be expressed as coupled differential equations and can be solved numerically. The numerical results show many featu…
In order to mimic the phase changes in the primordial Big Bang, several "cosmological" solid-state experiments have been conceived, during the last decade, to investigate the spontaneous symmetry breaking in superconductors and superfluids cooled through their transition temperature. In one of such experiments the number of magnetic flux quanta spontaneously trapped in a superconducting loop was measured by means of a long Josephson tunnel junction built on top of the loop itself. We have analyzed this system and found a number of interesting features not occurring in the conventional case wit…
In this paper we study the quantum phase transition between the insulating and the globally coherent superfluid phases in the Bose-Hubbard model with T_3 structure, the "dice lattice". Even in the absence of any frustration the superfluid phase is characterized by modulation of the order parameter on the different sublattices of the T_3 structure. The zero-temperature critical point as a function of a magnetic field shows the characteristic "butterfly" form. At fully frustration the superfluid region is strongly suppressed. In addition, due to the existence of the Aharonov-Bohm cages at f=1/2,…
Polar chiral active matter as a motile, disordered Josephson array: Information supercurrents and Goldstone spin waves
The European Space Agency Centre for Earth Observation（欧洲空间局地球观测中心）；Department of Physics and Engineering Physics, University of Saskatchewan（萨斯喀彻温大学物理与工程物理系）
Multi-layered Josephson junctions are modeled in the context of a field theory, and dynamics of Josephson vortices trapped inside insulators are studied. Starting from a theory consisting of complex and real scalar fields coupled to a U(1) gauge field which admit parallel $N-1$ domain-wall solutions, Josephson couplings are introduced weakly between the complex scalar fields. The $N-1$ domain walls behave as insulators separating $N$ superconductors, where one of the complex scalar fields has a gap. We construct the effective Lagrangian on the domain walls, which reduces to a coupled sine-Gord…
We study heat transport and thermoelectric effects in two-dimensional superconductors in a magnetic field. These are modeled as granular Josephson-junction arrays, forming either regular or random lattices. We employ two different models for the dynamics, relaxational model-A dynamics or resistively and capacitively shunted Josephson junction (RCSJ) dynamics. We derive expressions for the heat current in these models, which are then used in numerical simulations to calculate the heat conductivity and the Nernst coefficient for different temperatures and magnetic fields. At low temperatures and…
Cooper quartets and fractional vortices in frustrated Josephson junction dice arrays
University of Cologne（科隆大学）；Forschungszentrum Jülich GmbH, Institute of Quantum Control, Peter Grünberg Institut (PGI-8)（于利希研究中心有限公司，量子控制研究所，彼得·格林贝格研究所（PGI-8））；University of Oslo（奥斯陆大学）；Università di Pisa（比萨大学）；INFN, Sezione di Pisa（意大利国家核物理研究所，比萨分部）
The mixed phase of extremely type-II layered superconductors in perpendicular magnetic field is studied theoretically via the layered XY model with uniform frustration. A partial duality analysis is carried out in the weak-coupling limit. It consistently accounts for both intra-layer (pancake) and inter-layer (Josephson) vortex excitations. The main conclusion reached is that dislocations of the two-dimensional (2D) vortex lattices within layers drive a unique second-order melting transition at high perpendicular fields between a low-temperature superconducting phase that displays a Josephson …
Superconducting nanowires are the dual elements to Josephson junctions, with quantum phase-slip processes replacing the tunneling of Cooper pairs. When the quantum phase-slip amplitude ES is much smaller than the inductive energy EL, the nanowire responds as a superconducting inductor. When the inductive energy is small, the response is capacitive. The crossover at low temperatures as a function of ES/EL is discussed and compared with earlier experimental results. For one-dimensional and two-dimensional arrays of nanowires quantum phase transitions are expected as a function of ES/EL. They can…
