Vortex Unbinding Transition Research Articles

Vortex unbinding transition in nonequilibrium photon condensates

We present a theoretical study of a Berezinskii-Kosterlitz-Thouless-like phase transition in lattices of nonequilibrium photon condensates. Starting from linearized fluctuation theory and the properties of vortices, we propose an analytical formula for the critical point containing four fitting parameters, that captures well all our numerical simulations. We find that the ordered phase becomes more stable when driving and dissipation are increased.

Topological phase transitions in four dimensions

We show that four-dimensional systems may exhibit a topological phase transition analogous to the well-known Berezinskii-Kosterlitz-Thouless vortex unbinding transition in two-dimensional systems. We study a suitable generalization of the sine-Gordon model in four dimensions and the renormalization group flow equation of its couplings, showing that the critical value of the frequency is the square of the corresponding value in 2D. The value of the anomalous dimension at the critical point is determined (η=1/32) and a conjecture for the universal jump of the superfluid stiffness (4/π2) presented.

Approaching Two-Dimensional Superconductivity in Ultrathin DyBa_{2}Cu_{3}O_{7-δ}.

The temperature dependence of the superfluid density ρ_{s}(T) has been measured for a series of ultrathin MBE-grown DyBa_{2}Cu_{3}O_{7-δ} superconducting (SC) films by submillimeter wave interferometry combined with time-domain terahertz spectroscopy and IR ellipsometry. We find that all films 10u.c. and thicker show the same universal temperature dependence of ρ_{s}(T), which follows the critical behavior characteristic of single crystal YBa_{2}Cu_{3}O_{7-δ} as T approaches T_{c}. In 7u.c. thick films, ρ_{s}(T) declines steeply upon approaching T_{c}, as expected for the Berezinskii-Kosterlitz-Thouless vortex unbinding transition. Our analysis provides evidence for a sharply defined 4u.c. non-SC interfacial layer, leaving a quasi-2D SC layer on top. We propose that the SC state in this interfacial layer is suppressed by competing (possibly charge) order.

Coupled superfluidity of binary Bose mixtures in two dimensions

We consider a two-component Bose gas in two dimensions at low temperature with short-range repulsive interaction. In the coexistence phase where both components are superfluid, inter-species interactions induce a nondissipative drag between the two superfluid flows (Andreev-Bashkin effect). We show that this behavior leads to a modification of the usual Berezinskii-Kosterlitz-Thouless (BKT) transition in two dimensions. We extend the renormalization of the superfluid densities at finite temperature using the renormalization group approach and find that the vortices of one component have a large influence on the superfluid properties of the other, mediated by the nondissipative drag. The extended BKT flow equations indicate that the occurrence of the vortex unbinding transition in one of the components can induce the breakdown of superfluidity also in the other, leading to a locking phenomenon for the critical temperatures of the two gases.

Vortices and antivortices in two-dimensional ultracold Fermi gases

Vortices are commonly observed in the context of classical hydrodynamics: from whirlpools after stirring the coffee in a cup to a violent atmospheric phenomenon such as a tornado, all classical vortices are characterized by an arbitrary circulation value of the local velocity field. On the other hand the appearance of vortices with quantized circulation represents one of the fundamental signatures of macroscopic quantum phenomena. In two-dimensional superfluids quantized vortices play a key role in determining finite-temperature properties, as the superfluid phase and the normal state are separated by a vortex unbinding transition, the Berezinskii-Kosterlitz-Thouless transition. Very recent experiments with two-dimensional superfluid fermions motivate the present work: we present theoretical results based on the renormalization group showing that the universal jump of the superfluid density and the critical temperature crucially depend on the interaction strength, providing a strong benchmark for forthcoming investigations.

Berezinskii-Kosterlitz-Thouless transition in homogeneously disordered superconducting films

We develop a theory for the vortex unbinding transition in homogeneously disordered superconducting films. This theory incorporates the effects of quantum, mesoscopic and thermal fluctuations stemming from length scales ranging from the superconducting coherence length down to the Fermi wavelength. In particular, we extend the renormalization group treatment of the diffusive nonlinear sigma model to the superconducting side of the transition. Furthermore, we explore the mesoscopic fluctuations of parameters in the Ginzburg-Landau functional. Using the developed theory, we determine the dependence of essential observables (including the vortex unbinding temperature, the superconducting density, as well as the temperature-dependent resistivity and thermal conductivity) on microscopic characteristics such as the disorder-induced scattering rate and bare interaction couplings.

Vector Chiral Phases in the Frustrated 2DXYModel and Quantum Spin Chains

The phase diagram of the frustrated 2D classical and 1D quantum XY models is calculated analytically. Four transitions are found: the vortex unbinding transitions triggered by strong fluctuations occur above and below the chiral transition temperature. Vortex interaction is short range on small and logarithmic on large scales. The chiral transition, though belonging to the Ising universality class by symmetry, has different critical exponents due to nonlocal interaction. In a narrow region close to the Lifshitz point a reentrant phase transition between paramagnetic and quasiferromagnetic phase appears. Applications to antiferromagnetic quantum spin chains and multiferroics are discussed.

Detecting classical phase transitions with Renyi mutual information

By developing a method to represent the Renyi entropies via a replica trick on classical statistical mechanical systems, we introduce a procedure to calculate the Renyi mutual information (RMI) in any Monte Carlo simulation. Through simulations on several classical models, we demonstrate that the RMI can detect finite-temperature critical points, and even identify their universality class, without knowledge of an order parameter or other thermodynamic estimators. Remarkably, in addition to critical points mediated by symmetry breaking, the RMI is able to detect topological vortex-unbinding transitions, as we explicitly demonstrate on simulations of the $XY$ model.

Berezinskii-Kosterlitz-Thouless crossover in a photonic lattice

We show that a periodic two-dimensional (2D) photonic lattice with Kerr nonlinearity exhibits a Berezinskii-Kosterlitz-Thouless (BKT) crossover associated with a vortex-unbinding transition. We find that averaging over random initial conditions is equivalent to Boltzmann thermal averaging with the discrete nonlinear Schr$\stackrel{\mathrm{\ifmmode\cdot\else\textperiodcentered\fi{}\ifmmode\cdot\else\textperiodcentered\fi{}}}{\mathrm{o}}$dinger Hamiltonian. By controlling the initial randomness we can continuously vary the effective temperature. Since this Hamiltonian is in the 2D $\mathit{XY}$ universality class, a BKT transition ensues. We verify this prediction using experimentally accessible observables and find good agreement between theory and simulations. This opens the possibility of experimental access to interesting phase transitions known in condensed matter using nonlinear optics.

CFT description of the fully frustratedXY model and phase diagram analysis

Following an earlier suggestion, we show how the symmetry of the fully frustratedXY (FFXY) model on a square lattice can be accounted for in the framework of them-reduction procedure developed for a Quantum Hall system at ‘paired states’ fillingsν = 1. The resulting twisted conformal field theory (CFT) with central chargec = 2 is shown to well describe the physical properties of theFFXY model. In particular, the whole phase diagram is recovered by analysing the flow from theZ2 degeneratevacuum of the c = 2 CFT to the infrared fixed point unique vacuum of the CFT. The last theory is known to successfully describe the critical behaviour of thesystem at the overlap temperature for the Ising and vortex-unbinding transitions.

Correlation between Superfluid Density andTCof UnderdopedYBa2Cu3O6+xNear the Superconductor-Insulator Transition

We report measurements of the ab-plane superfluid density n(s) (magnetic penetration depth lambda) of heavily underdoped films of YBa2Cu3O6+x, with T(C)'s from 6 to 50 K. We find the characteristic length for vortex unbinding transition equal to the film thickness, suggesting strongly coupled CuO2 layers. At the lowest dopings, T(C) is as much as 5 times larger than the upper limit set by the 2D Kosterlitz-Thouless-Berezinskii transition temperature calculated for individual CuO2 bilayers. Our main finding is that T(C) is not proportional to n(s)(0); instead, we find T(C) proportional to ns(1/2.3+/-0.4). This conflicts with a popular point of view that quasi-2D thermal phase fluctuations determine the transition temperature.

Vacancy effects in an easy-plane Heisenberg model: Reduction ofTcand doubly charged vortices

Magnetic vortices in thermal equilibrium in two-dimensional magnets are studied here in the presence of a low concentration of nonmagnetic impurities (spin vacancies). A nearest-neighbor Heisenberg (XXZ) spin model with easy-plane exchange anisotropy is used to determine static thermodynamic properties and vortex densities via combined cluster and over-relaxation Monte Carlo simulations. Especially at low temperatures, a large fraction of the thermally generated vortices nucleate centered on vacancies, where they have a lower energy of formation. This fact is responsible for the reduction of the vortex-unbinding transition temperature with increasing vacancy concentration, similar to that seen in the planar rotator model. Spin vacancies also present the possibility of the appearance of vortices with double topological charges ($\ifmmode\pm\else\textpm\fi{}4\ensuremath{\pi}$ change in in-plane spin angle), stable only when centered on vacancies.

Probing vortex unbinding via dipole fluctuations

We develop a numerical method for detecting a vortex-unbinding transition in a two-dimensional system by measuring large-scale fluctuations in the total vortex dipole moment $\stackrel{\ensuremath{\rightarrow}}{P}$ of the system. These are characterized by a quantity $\mathcal{F}$ that measures the number of configurations in a simulation for which either ${P}_{x}$ or ${P}_{y}$ is half the system size. It is shown that $\mathcal{F}$ tends to a nonvanishing constant for large system sizes in the unbound phase, and vanishes in the bound phase. The method is applied to the $\mathrm{XY}$ model both in the absence and in the presence of a magnetic field. In the latter case, the system size dependence of $\mathcal{F}$ suggests that there exist three distinct phases, one unbound vortex phase, a logarithmically bound phase, and a linearly bound phase.

Critical currents and vortex-unbinding transitions in quench-condensed ultrathin films of bismuth and tin

We have investigated the I-V characteristics of strongly disordered ultra-thin films of {\it Bi} and {\it Sn} produced by quench-condensation. Our results show that both these sytems can be visualized as strongly disordered arrays of Josephson junctions. The experimentally observed I-V characteristics of these films is hysteretic, when the injected current is ramped from zero to critical current and back. These are remarkably similar to the hysteretic I-V of an underdamped single junction. We show by computer simulations that hysteresis can persist in a very strongly disordered array. It is also possible to estimate the individual junction parameters ($R$, $C$ and $I_c$) from the experimental I-Vs of the film using this model. The films studied are in a regime where the Josephson-coupling energy is larger than the charging energy. We find that a simple relation $I_c(T)=I_c(0)(1-(T/T_c)^4)$ describes the temperature dependence of the critical current quite accurately for films with sheet resistance $\sim$ 500$\Omega$ or lower. We also find evidence of a vortex-unbindi

Is there a phase transition in the isotropic Heisenberg anti-ferromagnet on the triangular lattice?

The phase diagram of the classical anisotropic (XXZ) Heisenberg model on the two-dimensional triangular lattice is investigated using Monte Carlo methods. In the easy-axis limit, two finite-temperature vortex-unbinding transitions have been observed. In the easy-plane limit, there also appear to be two distinct finite-temperature phase transitions that are very close in temperature. The upper transition corresponds to an Ising-like chirality ordering and the lower temperature transition corresponds to a Kosterlitz–Thouless vortex-unbinding transition. These phase-transition lines all meet at the Heisenberg point and provide strong evidence that the isotropic model undergoes a novel finite-temperature phase transition. PACS Nos.: 75.10Hk, 75.40Mg

Is there a phase transition in the isotropic Heisenberg anti-ferromagnet on the triangular lattice?

The phase diagram of the classical anisotropic (XXZ) Heisenberg model on the 2-dimensional triangular lattice is investigated using Monte Carlo methods. In the easy-axis limit, two finite temperature vortex unbinding transitions have been observed. In the easy-plane limit, there also appear to be two distinct finite temperature phase transitions. The upper transition corresponds to an Ising-like chirality ordering and the lower temperature transition corresponds to a Kosterlitz-Thouless vortex unbinding transition. These phase transition lines all meet at the Heisenberg point and provide strong evidence that the isotropic model undergoes a novel finite temperature phase transition.

Two Dimensional Josephson Junction Arrays

Two dimensional Josephson junction arrays (JJAs) offer theopportunity to study a variety of basic physical concepts. Thepresent review focuses on recent experimental work on thedynamics of JJAs, as characterized by ac conductancemeasurements. The review starts with a discussion of basicphysics necessary to describe JJAs. Some experimentalissues, array fabrication and measurement techniques areconsidered next. In a perpendicular magnetic field, a JJA isan experimental realization of the frustrated XY model, withthe frustration parameter f, corresponding to the number offlux quanta in a unit cell of the array, adjusted by themagnetic field. It is thereby possible to investigate thenature of the ground states at arbitrary frustrations. Phasetransitions are the next topic: the vortex unbindingtransition is observed at integer f-values, while, if thejunction coupling energies are appropriately varied across thearray, at half-integer f-values the Ising transition,associated with chiral symmetry breaking, may be observed.Some aspects of vortex dynamics, a subject which is not yetcompletely understood, are then considered. Under certainconditions there is virtually no pinning in JJAs, they aretherefore ideally suited for the study of vortex dynamics. Thenext topic of this review is concerned with the influence ofdisorder on the ground states and on the phase transitions inJJAs. Site percolation in JJAs has provided some insightsinto the physics of disordered systems and allowed to verifysome theoretical predictions on percolation in two dimensions.A quick look at JJAs in the underdamped regime concludesthis review.

Effect of finite size on the Kosterlitz-Thouless transition in two-dimensional arrays of proximity-coupled junctions

We have investigated the Kosterlitz-Thouless (KT) transition in a series of proximity-coupled Josephson junction arrays of varying widths. Our results indicate that the KT transition in any experimentally realizable sample is almost always obscured by the presence of thermally generated, finite-size-induced free vortices. While the existence of these finite-size-induced free vortices has been known for some time, our work suggests that they are much more prevalent and thus have a far greater effect on the transition than had been previously thought. As a consequence of this, the vortex-unbinding transition temperature T{sub KT} may not occur when the experimentally measured current-voltage exponent a(T)=3, but in fact may occur at significantly higher temperatures. We present a detailed picture of these finite-size effects applied specifically to arrays, but which may have implications for other two-dimensional systems. {copyright} {ital 1998} {ital The American Physical Society}

First-order vortex unbinding transition in thin superconducting films.

The vortex unbinding transition in thin superconducting films is discussed within the cycle approximation, taking into account a vortex core shape. It is shown that for large core energies the universal Kosterlitz-Thouless-like behavior takes place in the vicinity of the characteristic transition temperature ${\mathit{T}}_{\mathrm{KT}}$, while for low core energies the vortex-antivortex pair unbinding occurs through a first-order transition. \textcopyright{} 1996 The American Physical Society.

Charge-vortex duality in double-layered Josephson-junction arrays.

A system of two parallel Josephson junction arrays coupled by interlayer capacitances is considered in the situation where one layer is in the vortex-dominated and the other in the charge-dominated regime. This system shows a symmetry (duality) of the relevant degrees of freedom, i.e. the vortices in one layer and the charges in the other. In contrast to single-layer arrays both contribute to the kinetic energy. The charges feel the magnetic field created by vortices, and, vice versa, the vortices feel a gauge field created by charges. For long-range interaction of the charges the system exhibits two Berezinskii-Kosterlitz-Thouless transitions, one for vortices and another one for charges. The interlayer capacitance suppresses both transition temperatures. The charge-unbinding transition is suppressed already for relatively weak coupling, while the vortex-unbinding transition is more robust. The shift of the transition temperature for vortices is calculated in the quasi-classical approximation for arbitrary relations between the capacitances (both weak and strong coupling).