Quantum Phase Fluctuations Research Articles

Phase-resolution limit in the macroscopic interference between Bose-Einstein condensates

We study the competition between phase definition and quantum phase fluctuations in interference experiments between independently formed Bose condensates. While phase-sensitive detection of atoms makes the phase progressively better defined, interactions tend to randomize it faster as the uncertainty in the relative particle number grows. A steady state is reached when the two effects cancel each other. Then the phase resolution saturates to a value that grows with the ratio between the interaction strength and the atom detection rate, and the average phase and number begin to fluctuate classically. We discuss how our study applies to both recently performed and possible future experiments.

Phase fluctuations, dissipation, and superfluid stiffness ind-wave superconductors

We study the effect of dissipation on quantum phase fluctuations in d-wave superconductors. Dissipation, arising from a nonzero low frequency optical conductivity which has been measured in experiments below $T_c$, has two effects: (1) a reduction of zero point phase fluctuations, and (2) a reduction of the temperature at which one crosses over to classical thermal fluctuations. For parameter values relevant to the cuprates, we show that the crossover temperature is still too large for classical phase fluctuations to play a significant role at low temperature. Quasiparticles are thus crucial in determining the linear temperature dependence of the in-plane superfluid stiffness. Thermal phase fluctuations become important at higher temperatures and play a role near $T_c$.

A possible mechanism of superconductivity in high- Tc cuprates

This paper derives a generic T c formula by using the long-range phase coherence condition in quantum phase fluctuation of the order parameter. Taking the two-local-spin-mediated interaction (TLSMI) proposed by Liu and Chen [Phys. Rev. B 58 (1998) 8812] as a Cooper pair potential, and the T c formula, this paper explains five basic experimental facts in high- T c cuprates. The aim of this paper is to show that TLSMI is a possible pairing mechanism of superconductivity in high- T c cuprates.

Quantum phase fluctuation in high T c superconductors

If phase coherence determines the superconducting transition temperature T c in the cuprate oxides, it is of great interest to understand the role that dynamics of the phase fluctuation plays in bringing about depletion of the superconducting condensate. We will show that a phase correlation function can be calculated that allows us to describe depletion of superconducting condensate as a result of the quantum fluctuation. The vanishing of Andreev conductivity at a critical votage below the superconducting gap will be shown as resulting from voltage induced phase excitation and dephasing.

Unified theory of superconductivity inLa2-xSrxCuO4 and Nd2-xCexCuO4

Taking the two-local-spin-mediated interaction as a Cooper pairinteraction, using the BCS (Bardeen-Cooper-Schrieffer) gap equationand the phase-coherence condition for quantum phase fluctuation,this paper explains basic experimental findings concerning bothp-type La2-xSrxCuO4 (LSCO) and n-typeNd2-xCexCuO4 (NCCO) at the same time, and predicts thatthe pseudogap should be clearly observed for underdoped NCCO.

Influence of phase quantum fluctuations on superconducting proximity correction in normal-metal wire conductance

The influence of the charging effect on the proximity correction in the conductance of a mesoscopic $\mathrm{superconductor}(S)/\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}\ensuremath{-}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{a}\mathrm{l}(N)$ coupled system is theoretically investigated. The most important contribution of the proximity correction in the conductance of a diffusive normal metal comes from the correction in the local conductivity $\ensuremath{\delta}\ensuremath{\sigma}(r).$ The correction in the conductance is given by $\ensuremath{\delta}{G=(1/L}_{N}^{2}){\ensuremath{\int}}_{\mathrm{vol}.}\ensuremath{\delta}\ensuremath{\sigma}(r)\mathrm{dr}.$ Because of the retro property of Andreev reflection and the long rangeness of the Cooperon (particle-particle ladder), Andreev reflection at the $S/N$ interface affects the local conductivity at a point in the normal region far from the interface (within the phase coherence length ${L}_{\ensuremath{\varphi}}).$ If the $S/N$ interface is very small and has a low transparency, single Andreev reflection is strongly suppressed by the Coulomb blockade at a low temperature ${(k}_{B}T<{E}_{C},$ ${E}_{C}{=e}^{2}/2C)$ in an exponential manner $\mathrm{exp}{\ensuremath{-}{4E}_{C}{/(k}_{B}T)},$ where C is the capacitance of the $S/N$ junction. Nevertheless, the proximity correction in the conductance is only suppressed with power law ${k}_{B}{T/(4E}_{C})$ because the charged state is an intermediate state in the process of the proximity correction in the conductivity. This is quite different from the charging effect on the proximity correction of the current flowing through the $S/N$ interface, which is strongly suppressed by the charging effect.

Carrier-concentration-driven superconductor-to-insulator transition in YBa 2Cu 3O 6+ x

We have succeeded in controlling carrier concentration near the superconductor-to-insulator transition by sample annealing under the equilibrium oxygen pressure of YBa 2Cu 3O 6+ x . Near the critical doping, below 60 K, we observed carrier-concentration-driven resistivity scaling of the pulsed-laser-deposited thin film of YBa 2Cu 3O 6+ x indicating the large energy scale of the quantum phase fluctuation. This demonstrates that a considerable area in the phase diagram of the pseudo-gapped underdoped YBa 2Cu 3O 6+ x is in the critical region of the quantum phase transition.

Fluctuations of the Order Parameter's Phase in Layered Superconductors

The influence of the quantum fluctuations of the order parameter's phase on the critical temperature Tc is studied for a Josephson coupled layered superconductor. Two characteristic critical temperatures exist for a system, namely the superconducting critical temperature T(2)c for a single layer estimated by the mean-field theory and the transition temperature for the outset or the superconducting phase coherence T*c. The true critical temperature Tc is shown to vary inside the intervals T*c ≤ Tc ≤ T(2)c. For a strong quantum phase fluctuation limit, the superconducting layers become decoupled.

A POSSIBLE PAIRING MECHANISM FOR HTSC: TWO-DIMENSIONAL CONFINEMENT AND COULOMB OVER-SCREENING

Among all the common properties of HTCS cuprates, we build our model on two of them: their high anisotropy, and their extremely low density of charge carriers. The intra-layer pairing mechanism is provided by the two-dimensional over-screening of Coulomb repulsion.1,2 The c-axis zero point energy restricts this pairing to a low carrier density region. Below a critical density, the system behaves as a two-dimensional confined jellium where the energy gain due to charge pairing is larger than the c-axis localization energy. In the high density region, where the pairing energy cannot compensate the localization energy, the system delocalizes and crosses over to a three-dimensional regime. This competition between binding and confinement energies implies a monotonic decrease of mass anisotropy with doping. Pre-formed pairs which exist below a Mean Field (MF) temperature defined by the binding energy, account for pseudo-gap observations.3,4 The superconducting critical temperature T c is given by the Beresinskii–Kosterlitz–Thouless (BKT) transition of the two-dimensional layer, renormalized by quantum phase fluctuations (QPF).5 QPF account for the metal-insulator transition at very low doping.

Existence of a Bose metal atT=0

This paper aims to justify the existence of a two-dimensional Bose metal, i.e., a metallic phase made out of Cooper pairs at $T=0.$ To this end, we consider the physics of quantum phase fluctuations in (granular) superconductors in the absence of disorder and emphasize the role of two order parameters in the problem, viz. phase order and charge order. We focus on the two-dimensional (2D) Bose Hubbard model in the limit of very large fillings, i.e., a 2D array of Josephson junctions. We find that the algebra of phase fluctuations is that of the Euclidean group ${E}_{2}$ in this limit, and show that the model is equivalent to two coupled $\mathrm{XY}$ models in $(2+1)$ dimensions, one corresponding to the phase degrees of freedom, and the other to the charge degrees of freedom. The Bose metal, then, is the phase in which both these degrees of freedom are disordered (as a result of quantum frustration). We analyze the model in terms of its topological excitations and suggest that there is a strong indication that this state represents a surface of critical points, akin to the gapless spin liquid states. We find a remarkable consistency of this scenario with certain low-${T}_{c}$ thin film experiments.

Quantum dynamics of superconducting point contacts: chiral anomaly, Landau–Zener transitions, and all that

Quantum effects in the dynamics of the Josephson phase difference in Josephson junctions with large electron transparency D are studied in the adiabatic regime, when the characteristic charging energyEC of the junction is much smaller than the superconducting energy gap Δ. In isolated junctions, quantum phase fluctuations are large and manifest themselves as Coulomb blockade of Cooper pair tunneling. The amplitude of the Coulomb blockade oscillations is calculated for single-mode junctions with arbitrary D. In particular, it is shown that the chiral anomaly completely suppresses Coulomb blockade in ballistic junctions with D= 1, and the suppression process at D→ 1 can be described as the Landau–Zener transition in imaginary time. In the regime when quantum phase fluctuations are small, they lead to quantum decay of supercurrent states due to macroscopic quantum tunneling of phase through the Josephson potential barrier. The decay rate is found in the nearly-ballistic junctions.

Quasi 1 and 2d dilute Bose gas in magnetic traps : Existence of off-diagonal order and anomalous quantum fluctuations

Current magnetic traps can be made so anisotropic that dilute Bose gases confined in these traps will occupy the lowest quantum state in the tightly confining direction, while still in the Thomas-Fermi limit in the loosely confining direction. As a result, the trapped Bose gas behaves like a quasi one or two dimensional systems. Unlike the homogeneous case, quantum phase fluctuations do not destroy macroscopic off-diagonal order of trapped Bose gases in d≤2 because they are suppressed by the the trapping potential. In the dilute limit, quantum fluctuations increase, remain constant, and decrease with size for 3, 2, 1 d respectively. These behaviors are due to the combination of a finite gap and the universal spectrum of the collective mode.

PSEUDOGAP, QUANTUM PHASE FLUCTUATIONS AND SPECTROSCOPY OF HTCS CUPRATES

Superconducting critical temperatures T c are calculated as a function of the doping parameter x for generic layered Cu oxide superconductors, within the framework of a 2D-XY model with quantum phase fluctuations. The model accounts for the lower doping threshold observed at x=0.05, and allows for a simple interpretation of the “pseudogap” in terms of condensation of pre-formed pairs. On the other hand, a novel pairing mechanism, based on the 2D confinement of carriers and on the in-plane overscreening of long-range Coulomb repulsion, is proposed. A 2–3D dimensional crossover which suppresses 2D pairing is considered in the overdoped regime.

The phase diagram of a two-dimensional array of mesoscopic granules

A lattice boson model is used to study ordering phenomena in regular 2D arrays of superconductive mesoscopic granules, Josephson junctions and pores filled with superfluid helium. The phase diagram of the system, for when quantum fluctuations of both the phase and the local superfluid density are essential, is analysed both analytically and by the quantum Monte Carlo technique. For the system of strongly interacting bosons it is found that as the boson density is increased the boundary of the ordered superconducting state shifts to lower temperatures and at approaches its limiting position corresponding to negligible relative fluctuations of the moduli of the order parameter (as in an array of `macroscopic' granules). In the region of weak quantum fluctuations of phases, mesoscopic phenomena manifest themselves up to . The mean-field theory and functional integral -expansion results are shown to agree with those of quantum Monte Carlo calculations of the boson Hubbard model and its quasiclassical limit, the quantum XY-model.

Charging effects on the critical temperature of the Josephson-coupled layered superconductors

Effects of quantum phase fluctuations on the critical temperature T c of Josephson-coupled layered superconductors are considered. T c is shown to decrease nonlinearly with increasing charge fluctuations. The results obtained for the critical temperature by applying the self-consistent mean field method reveal no phase transition from superconducting state to normal metal for a finite value of charging energy. The destruction of the long range phase coherence appeared to occur at asymptotically large values of self-capacitance charging. For the weak quantum phase fluctuations limit, T c is obtained to be vary in the interval of T c *< T c< T c (2), where T c (2) is the critical temperature for a single superconducting layer evaluated by the mean field theory, and T c * is the temperature when the phase coherence between the nearest neighboring layers is lost. Since T c approaches T c * with vanishing interlayer tunneling integral J ⊥. Calculation of the dependence of the transverse stiffness on the charging energy is carried out at T=0. The reentrance found can in principle occur at a sufficiently large value of the interlayer tunneling integral J ⊥> J ⊥ cr= k T c (2), where J ⊥ cr≈ k T c (2) is the value of J ⊥ when the superconductor normal metal phase transition takes place. However, the condition J ⊥≥ k T c (2) contradicts to the existence of the Josephson coupling between superconducting layers.

Quantum phase fluctuations in an array of mesoscopic Josephson junctions

The effects of macroscopic ordering in a system of mesoscopic Josephson junctions are investigated by the quantum Monte Carlo simulation technique (using path integrals). The phase diagram of the system in the T-q plane (q is the dimensionless quantum parameter \(q = 2{e \mathord{\left/ {\vphantom {e {\sqrt {JC_0 } }}} \right. \kern-\nulldelimiterspace} {\sqrt {JC_0 } }}\), where J is the Josephson coupling constant and C0 is the self-capacitance of the granules) is investigated in detail. An analysis of the behavior of the relative root-mean-square phase shifts, as well as the helicity and vorticity moduli, demonstrates the need to employ these two quantities as the parameters which most completely reflect the character of the topological phase transition in the quantum system under consideration. Two methods are proposed for calculating the vorticity modulus: 1) a modification of the Gibbs-Bogolyubov variational principle for calculating the free energy change in response to alteration of the type of boundary conditions; 2) calculation of the response to the introduction of an infinitesimal magnetic flux at some point in the system. The calculations confirm the absence of reentrant melting and phase transitions of a non-Kosterlitz-Thouless type in the region of strong quantum phase fluctuations q>1.

Superconductivity in bad metals.

We introduce a model of the superconducting transition in a bad metal, and show that quantum and classical phase fluctuations prevent long-range order unless the resistivity $\ensuremath{\rho}(T)$ falls below a critical value. Application of these ideas to high temperature superconductors accounts for the variation of $\ensuremath{\rho}({T}_{c})$ in radiation-damaged films; gives an upper bound on ${T}_{c}\ensuremath{\propto}{n}_{s}$, where ${n}_{s}$ is the zero-temperature superfluid density; and shows that, with screening, phase fluctuations give a linear temperature dependence of ${n}_{s}$ at low temperatures.

Superconducting-insulating transition in two-dimensional a-MoGe thin films.

A zero-temperature magnetic-field-tuned superconducting-insulating transition is observed in two-dimensional $a$-MoGe films. The low temperature transport properties of these films show scaling behavior consistent with a transition driven by long-range Coulomb interactions and quantum phase fluctuations in a two-dimensional superconductor. However, contrary to the theoretical predictions we find the critical resistance to be sample dependent. We suggest that the apparent lack of universality in the critical resistance is due to the finite contribution of fermionic excitations to the resistance.

Depression of the zero-temperature superfluid density in YBa 2Cu 3O 7/PrBa 2Cu 3O 7 heterostructures

Heterostructures made of thick (15 unit cells) insulating PrBa 2Cu 3O 7(PBCO) and thin superconducting YBa 2Cu 3O 7(YBCO), such as [PBCO] 15/[YBCO] n/[PBCO] 15 trilayers and decoupled [YBCO] n/[PBCO] 15 superlattices [n=1,2… unit cells (UC)], were prepared by an in-situ laser ablation technique. Both T c and the inverse kinetic inductance L k −1(T), which is proportional to the effective superfluid density, are found to be depressed with respect to the corresponding values in bulk YBCO. This behaviour is attributed to quantum phase fluctuations induced by charging effects in the CuO 2 planes.

Nonadiabatic analysis of the Josephson critical current influenced by quantum phase fluctuations.

The influence of the electromagnetic environment on the dc Josephson current is studied allowing for nonadiabatic motion of the phase difference across a junction. The critical current is evaluated nonperturbatively within mean-field theory, fully taking into account the nonlocal kernels in the Ambegaokar-Eckern-Schoen effective action. It turns out that the adiabatic approximation, which can be justified when the superconducting energy gap exceeds the charging energy, yields [ital qualitatively] correct results even for the opposite case, although [ital quantitative] deviations from the adiabatic approximation are found to be substantial in some experimentally accessible regions.