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 suppress a vortex-ordering transition down to near zero temperature. The data for $f=1/2$ are more consistent with theoretical evaluations. The agreement between the experiments and the Monte Carlo simulations of a $XY$ model for $f=1/3$ suggests that the order-from-disorder mechanism for the removal of an accidental degeneracy may still be effective in the $f=1/3$ system. The transport data also reveal that the dice arrays with zero-energy domain walls experience a much slower critical relaxation than other frustrated arrays only with finite-energy walls.
The structure and the degenracy of the ground state of a fully-frustrated XY-model are investigated for the case of a dice lattice geometry. The results are applicable for the description of Josephson junction arrays and thin superconducting wire networks in the external magnetic field providing half-integer number of flux quanta per plaquette. The mechanisms of disordering of vortex pattern in such systems are briefly discussed.
We consider the effect of positional disorder on a Josephson junction array with an applied magnetic field of f=1/2 flux quantum per unit cell. This is equivalent to the problem of random Gaussian phase shifts in the fully frustrated 2D XY model. Using simple analytical arguments and numerical simulations, we present evidence that the ground state vortex lattice of the pure model becomes disordered, in the thermodynamic limit, by any amount of positional disorder.
A highly degenerate family of states [proposed in PRB 63, 134503 (2001)] is proven to really minimize the Hamiltonian of the fully frustrated XY model on a dice lattice. The harmonic fluctuations are shown to be no consequence for the removal of the accidental degeneracy of these states, so a particular vortex pattern can be stabilized only by the anharmonic fluctuations. The structure of this pattern is found and the temperature of its disordering due to the proliferation of domain walls is estimated. The extreme smallness of the fluctuations induced free energy of domain walls leads to the a…
We study the resistive transition in Josephson-junction arrays at $f=1/2$ flux quantum per plaquette by dynamical simulations of the resistively-shunted-junction model. The current-voltage scaling and critical dynamics of the phases are found to be well described by the same critical temperature and static exponents as for the chiral (vortex-lattice) transition. Although this behavior is consistent with a single transition scenario, where phase and chiral variables order simultaneously, two different dynamic exponents result for phase coherence and chiral order.
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.
The superconducting state in a fully frustrated wire network with the dice lattice geometry is investigated in the vicinity of the transition temperature. Using Abrikosov's variational procedure, we write the Ginzburg-Landau free energy functional projected on its unstable supspace as an effective model on the triangular lattice of sixfold coordinated sites. For this latter model, we obtain a large class of degenerate equilibrium configurations in one to one correspondence with those previously constructed for the pure XY model on the maximally frustrated dice lattice. The entropy of these sta…
We study the scaling behavior and critical dynamics of the resistive transition in Josephson-junction arrays, at f=1/2 flux quantum per plaquette, by numerical simulation of an on-site dissipation model for the dynamics. The results are compared with recent simulations using the resistively-shunted-junction model. For both models, we find that the resistivity scaling and critical dynamics of the phases are well described by the same critical temperature as for the chiral (vortex-lattice) transition, with a power-law divergent correlation length. The behavior is consistent with the single trans…
It is identified numerically that the resistivity of a fully-frustrated Josephson-junction array is due to motion of domain walls in vortex lattice rather than to motion of single vortices.
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…
We consider a two-dimensional fully frustrated Josephson-junction array driven by combined direct and alternating currents. Interplay between the mode locking phenomenon, manifested by giant Shapiro steps in the current-voltage characteristics, and the dynamic phase transition is investigated at finite temperatures. Melting of Shapiro steps due to thermal fluctuations is shown to be accompanied by the dynamic phase transition, the universality class of which is also discussed.
We consider a Josephson-junction ladder in an external magnetic field with half flux quantum per plaquette. When driven by external currents, periodic in time and staggered in space, such a fully frustrated system is found to display spatiotemporal stochastic resonance under the influence of thermal noise. Such resonance behavior is investigated both numerically and analytically, which reveals significant effects of anisotropy and yields rich physics.
We study dynamical phase transitions at temperature T = 0 in a fully frustrated square Josephson junction array subject to a driving current density which has nonzero components parallel to both axes of the lattice. Our numerical results show clear evidence for three dynamical phases: a pinned vortex lattice characterized by zero time-averaged voltages, a ``plastic'' phase in which both voltages are nonzero, and a moving lattice phase in which only one of the time-average voltage components is nonzero. The last of these has a finite transverse critical current.
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…
We study the effect of thermal fluctuations in a fully frustrated Josephson junction array driven by a current I larger than the apparent critical current I_c(T). We calculate numerically the behavior of the chiral order parameter of Z_2 symmetry and the transverse helicity modulus (related to the U(1) symmetry) as a function of temperature. We find that the Z_2 transition occurs at a temperature T_{Z_2}(I) which is lower than the temperature T_{U(1)}(I) for the U(1) transition. Both transitions could be observed experimentally from measurements of the longitudinal and transverse voltages.
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 report the results of ac sheet conductance measurements performed on fully frustrated square arrays of Josephson junctions whose coupling energy is periodically modulated in one of the principal lattice directions. Such systems are predicted to exhibit two distinct transitions: a low-temperature Ising-like transition triggered by the proliferation of domain walls and a high-temperature transition driven by the vortex unbinding mechanism of the Beresinskii-Kosterlitz-Thouless (BKT) theory. Both the superfluid and dissipative components of the conductance are found to exhibit features which u…
We investigate numerically the critical current of two-dimensional fully frustrated arrays of resistively shunted Josephson junctions at zero temperature. It is shown that a domino-type mechanism is responsible for the existence of a critical current lower than the one predicted from the translationally invariant flux lattice. This domino mechanism is demonstrated for uniform-current injection as well as for various busbar conditions. It is also found that inhomogeneities close to the contacts makes it harder for the domino propagation to start, which increases the critical current towards the…
We describe the dynamics of fluxons moving in a frustrated Josephson junction with p, d, and f-wave symmetry and calculate the I-V characteristics. The behavior of fluxons is quite distinct in the long and short length junction limit. For long junctions the intrinsic flux is bound at the center and the moving integer fluxon or antifluxon interacts with it only when it approaches the junction's center. For small junctions the intrinsic flux can move as a bunched type fluxon introducing additional steps in the I-V characteristics. Possible realization in quantum computation is presented.
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）
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…
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 study a quantum Hamiltonian that models an two--dimensional array of Josephson junctions with short range Josephson couplings, (given by the Josephson energy E_J and charging energiey E_C due to the small capacitance of the junctions. We include the effects from both the self-C0 and the junction-C1 capacitances in the presence of external magnetic flux f=fi/fi0 as well as uniform background of charges q_{x}. We derive an effective quantum non--linear sigma-model for the array Hamiltonian which enables us a non mean--field treatment of the zero--temperature phase transition scenario. We calc…
The uniformly frustrated XY model with f=1/3 on a dice lattice is shown to possess a so well developed accidental degeneracy of its ground states that the difference between the free energies of fluctuations does not lead to the stabilization of a particular vortex pattern down to zero temperature. Nonetheless, at low temperatures the system is characterized by a finite helicity modulus whose vanishing (at a finite temperature) is related with the dissociation of half-vortex pairs.
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…
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…
We establish a one-to-one mapping between a model for hexagonal polyelectrolyte bundles and a model for two-dimensional, frustrated Josephson-junction arrays. We find that the T=0 insulator-to-superconductor transition of the {\it quantum} system corresponds to a continuous liquid-to-solid transition of the condensed charge in the finite temperature {\it classical} system. We find that the role of the vector potential in the quantum system is played by elastic strain in the classical system. Exploiting this correspondence we show that the transition is accompanied by a spontaneous breaking of …
We use driven Monte Carlo dynamics to study the resistive behavior of superconducting Josephson junction arrays on a honeycomb lattice in a magnetic field corresponding to $f$ flux quantum per plaquette. While for $f=1/3$ the onset of zero resistance is found at nonzero temperature, for $f=1/2$ the results are consistent with a transition scenario where the critical temperature vanishes and the linear resistivity shows thermally activated behavior. We determine the thermal critical exponent of the zero-temperature transition for $f=1/2$, from a dynamic scaling analysis of the nonlinear resisti…
We study, analytically and numerically, phase locking of driven vortex lattices in fully-frustrated Josephson junction arrays at zero temperature. We consider the case when an ac current is applied {\it perpendicular} to a dc current. We observe phase locking, steps in the current-voltage characteristics, with a dependence on external ac-drive amplitude and frequency qualitatively different from the Shapiro steps, observed when the ac and dc currents are applied in parallel. Further, the critical current increases with increasing transverse ac-drive amplitude, while it decreases for longitudin…
A square array of Josephson junctions with modulated strength in a magnetic field with half a flux quantum per plaquette is studied by analytic arguments and dynamical simulations. The modulation is such that alternate columns of junctions are of different strength to the rest. Previous work has shown that this system undergoes an XY followed by an Ising-like vortex lattice disordering transition at a lower temperature. We argue that resistance measurements are a possible probe of the vortex lattice disordering transition as the linear resistance $R_{L}(T)\sim A(T)/L$ with $ A(T) \propto (T-T_…
We review the self-consistent mean-field theory for charge-frustrated Josephson junction arrays. Using <cos(ϕ)> (ϕis the phase of the superconducting wavefunction) as order parameter and imposing the self-consistency condition, we compute the phase boundary line between the superconducting region (<cos(ϕ)> not equal to zero) and the insulating one (<cos(ϕ)> = 0). For a uniform offset charge q=e the superconducting phase increases with respect to the situation in which q=0. Here, we generalize the self-consistent mean-field theory to include the effects induced by a random distribution of offse…
We have investigated the vortex state in a superconducting dice network using the Bitter decoration technique at several magnetic frustrations f=1/2 and 1/3. In contrast to other regular network geometries where the existence of a commensurate state was previouly demonstrated, no ordered state was observed in the dice network at f=1/2 and the observed vortex-vortex correlation length is close to one lattice cell.
We present a numerical study of quasi-1D frustrated Josephson junction ladders with diagonal couplings and open boundary conditions, in the large capacitance limit. We derive a correspondence between the energy of this Josephson junction ladder and the expectation value of the Hamiltonian of an analogous tight-binding model, and show how the overall superconducting state of the chain is equivalent to the minimum energy state of the tight-binding model in the subspace of one-particle states with uniform density. To satisfy the constraint of uniform density, the superconducting state of the ladd…
Eutectic Sr$_2$RuO$_4$-Ru samples with $μ$m-sized Ru-metal inclusions support inhomogeneous superconductivity above the bulk transition of Sr$_2$RuO$_4$ in the so-called 3-Kelvin phase. In Pb/Ru/Sr$_2$RuO$_4$ Josephson junctions as realized by Maeno et al., a Pb film is indirectly coupled to the superconductor Sr$_2$RuO$_4$ mediated by the proximity-induced superconducting Ru-inclusions, yielding an extended Josephson contact through the interface between Ru and Sr$_2$RuO$_4$. Motivated by this experimental setup, we formulate a sine-Gordon model for the Josephson phase of the interface, assum…
We study a new generalized version of the square-lattice frustrated XY model where unequal ferromagnetic and antiferromagnetic couplings are arranged in a zig-zag pattern. The ratio between the couplings $ρ$ can be used to tune the system, continuously, from the isotropic square-lattice to the triangular-lattice frustrated XY model. The model can be physically realized as a Josephson-junction array with two different couplings, in a magnetic field corresponding to half-flux quanta per plaquette. Mean-field approximation, Ginzburg-Landau expansion and finite-size scaling of Monte Carlo simulati…
We introduce a fully frustrated XY model with nearest neighbor (nn) and next nearest neighbor (nnn) couplings which can be realized in Josephson junction arrays. We study the phase diagram for $0\leq x \leq 1$ ($x$ is the ratio between nnn and nn couplings). When $x < 1/\sqrt{2}$ an Ising and a Berezinskii-Kosterlitz-Thouless transitions are present. Both critical temperatures decrease with increasing $x$. For $x > 1/\sqrt{2}$ the array undergoes a sequence of two transitions. On raising the temperature first the two sublattices decouple from each other and then, at higher temperatures, each s…
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.
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 …
We found a finite temperature glass transition in the absence of quenched disorder in frustrated Josephson junction arrays (JJA) on a square lattice with anisotropic Josephson couplings by numerical simulations. The vortexes develop zigzag stripes into the direction of weaker coupling at low temperatures. The whole amorphous vortex solid can flow smoothly into the direction of stronger coupling by non-trivial soft modes. As the result the macroscopic phase coherence is destroyed being reminiscent of vortex flow in pure bulk superconductors or spin-chirality decoupling in frustrated magnets. On…
We argue that the frustrated Josephson junction arrays may support a topologically ordered superconducting ground state, characterized by a non-trivial ground state degeneracy on the torus. This superconducting quantum fluid provides an explicit example of a system in which superconductivity arises from a topological mechanism rather than from the usual Landau-Ginzburg mechanism.
We propose a CFT description for a closed one-dimensional fully frustrated ladder of quantum Josephson junctions with Mobius boundary conditions, in particular we show how such a system can develop topological order. Such a property is crucial for its implementation as a "protected" solid state qubit.
The phase diagram of the fully frustrated XY model on a honeycomb lattice is shown to incorporate three different ordered phases. In the most unusual of them, a long-range order is related not to the dominance of a particular periodic vortex pattern but to the orientation of zero-energy domain walls separating domains with different orientations of vortex stripes. The phase transition leading to the destruction of this phase can be associated with the appearance of free fractional vortices and is of the first order. The stabilization of the two other ordered phases (existing at lower temperatu…
A vortex solid with self-generated randomness is found theoretically in a frustrated Josephson junction array (JJA) under external magnetic field with anisotropic couplings. Vorticies induced by external magnetic field develop stripes parallel to the direction of weaker coupling. It is shown analytically that there is a continuous, gapless band of metastable states in which stripes are deformed randomly by transverse undulation. The vortex solid with the frozen undulation in a metastable state freely slides along the direction of stronger coupling, thereby destroying ordering of phases even at…
The modulation with magnetic field of the sheet inductance measured on proximity effect Josephson-junction arrays (JJAs) is progressively vanishing on lowering the temperature, leading to a low temperature field-independent response. This behaviour is consistent with the decrease of the two-dimensional penetration length below the lattice parameter. Low temperature data are quantitatively compared with theoretical predictions based on the XY model in absence of thermal fluctuations. The results show that the description of a JJA within the XY model is incomplete and the system is put well beyo…
We report a direct observation of the crossover of the superconductor- ferromagnet-superconductor (SFS) junctions to the π-state which manifests itself in the half-period shift of the external magnetic field dependence of the transport critical current in the triangular SFS arrays. It is associated with the appearance of spontaneous supercurrents in the array at zero external field, with the ground state degenerated with respect to the two possible current flow directions. In conventional Josephson arrays this state can be observed only by imposing frustrating external field equal to a half-in…
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 study the dynamics of fully frustrated, underdamped Josephson arrays. Experiments reveal remarkable similarities among the dc current-voltage characteristics of several kinds of square and triangular arrays, where two resonant voltages are observed. Simulations indicate that a dynamical checkerboard solution underlies these similarities. By assuming such a solution, we reduce the governing equations to three coupled pendulum equations, and thereby calculate the voltages of the intrinsic resonances analytically.
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 …
A general framework is proposed to solve the two-dimensional fully frustrated XY model for the Josephson junction arrays in a perpendicular magnetic field. The essential idea is to encode the ground-state local rules induced by frustrations in the local tensors of the partition function. The partition function is then expressed in terms of a product of one-dimensional transfer matrix operator, whose eigen-equation can be solved by an algorithm of matrix product states rigorously. The singularity of the entanglement entropy for the one-dimensional quantum analogue provides a stringent criterion…
We have used Monte Carlo simulations, combined with finite-size scaling and two different real-space renormalization group approaches, to study a fully frustrated three-dimensional XY model on a simple cubic lattice. This model corresponds to a lattice of Josephson-coupled superconducting grains in an applied magnetic field ${\bf H} = (Φ_0/a^2)(1/2,1/2,1/2)$. We find that the model has a continuous phase transition with critical temperature $T_c = 0.681 J/k_B$, where $J$ is the XY coupling constant, and critical exponents $α/ν= 0.87 \pm 0.01$, $v/ν= 0.82 \pm 0.01$, and $ν= 0.72 \pm 0.07$, wher…
