Temperature TBKT Research Articles

The BKT transition and its dynamics in a spin fluid.

We study the effect of particle mobility on phase transitions in a spin fluid in two dimensions. The presence of a phase transition of the BKT universality class is shown in an off-lattice model of particles with purely repulsive interaction employing computer simulations. A critical spin wave region 0 < T < TBKT is found with a nonuniversal exponent η(T) that follows the shape suggested by BKT theory, including a critical value consistent with ηBKT = 1/4. One can observe a transition from power-law decay to exponential decay in the static correlation functions at the transition temperature TBKT, which is supported by finite-size scaling analysis. A critical temperature TBKT = 0.17(1) is suggested. Investigations into the dynamic aspects of the phase transition are carried out. The short-time behavior of the incoherent spin autocorrelation function agrees with the Nelson-Fisher prediction, whereas the long-time behavior differs from the finite-size scaling known for the static XY model. Analysis of coherent spin wave dynamics shows that the spin wave peak is a propagating mode that can be reasonably well fitted by hydrodynamic theory. The mobility of the particles strongly enhances damping of the spin waves, but the model still lies within the dynamic universality class of the standard XY model.

Flat-band superconductivity in periodically strained graphene: mean-field and Berezinskii–Kosterlitz–Thouless transition

In the search of high-temperature superconductivity one option is to focus on increasing the density of electronic states. Here we study both the normal and s-wave superconducting state properties of periodically strained graphene, which exhibits approximate flat bands with a high density of states, with the flatness tunable by the strain profile. We generalize earlier results regarding a one-dimensional harmonic strain to arbitrary periodic strain fields, and further extend the results by calculating the superfluid weight and the Berezinskii–Kosterlitz–Thouless (BKT) transition temperature TBKT to determine the true transition point. By numerically solving the self-consistency equation, we find a strongly inhomogeneous superconducting order parameter, similarly to twisted bilayer graphene. In the flat-band regime the order parameter magnitude, critical chemical potential, critical temperature, superfluid weight, and BKT transition temperature are all approximately linear in the interaction strength, which suggests that high-temperature superconductivity might be feasible in this system. We especially show that by using realistic strain strengths TBKT can be made much larger than in twisted bilayer graphene, if using similar interaction strengths. We also calculate properties such as the local density of states that could serve as experimental fingerprints for the presented model.

Strong pairing in two dimensions: pseudogaps, domes, and other implications

This paper addresses the transition from the normal to the superfluid state in strongly correlated two dimensional fermionic superconductors and Fermi gases. We arrive at the Berezinskii–Kosterlitz–Thouless (BKT) temperature TBKT as a function of attractive pairing strength by associating it with the onset of ‘quasi-condensation’ in the normal phase. Our approach builds on a criterion for determining the BKT transition temperature for atomic gases which is based on a well established quantum Monte Carlo analysis of the phase space density. This latter quantity, when derived from BCS–BEC crossover theory for fermions, leads to non-monotonic behavior for TBKT as a function of the attractive interaction or inverse scattering length. In Fermi gases, this implies a robust superconducting dome followed by a long tail from the flat BEC asymptote, rather similar to what is observed experimentally. For lattice systems we find that TBKT has an absolute maximum of the order of 0.1EF. We discuss how our results compare with those derived from the Nelson–Kosterlitz criterion based on the mean field superfluid density and the approach to the transition from below. While there is agreement in the strict mean-field BCS regime at weak coupling, we find that at moderate pairing strength bosonic excitations cause a substantial increase in TBKT followed by an often dramatic decrease before the system enters the BEC regime.

The dimensional crossover in critical behavior of layered XY-model

The study of critical properties and size transition in a diluted layered XY-model was carried out for the first time. The dimensional dependence of the temperature TBKT(p, N) of the Berezinskii-Kosterlitz-Thouless phase transition on the system thickness N is obtained for a diluted layered XY-model for a wide range of spin concentrations p. The temperature T, concentration p, and dimensional N dependencies of the vortex density v(p, N, T) in a layered XY-model are obtained.

Disorder Aggregation by Vortices in Non-Equilibrium Critical Annealing of Two-Dimensional XY-model

It is shown that the non-equilibrium vortex annealing of structural disorder in a two-dimensional XY-model leads to a non-equilibrium critical coarsening. Large clusters are separated into an individual subsystem, the relaxation dynamics of which is much slower than the relaxation dynamics of the cluster subsystem as a whole. Despite the fact that the main equilibrium critical properties, even the Berezinskii-Kosterlitz-Thouless phase transition temperature TBKT(p), of the two-dimensional XY-model with disorder thermalization do not change as compared with the system with quench disorder, the non-equilibrium critical relaxation shows significant differences.

Pairing fluctuations in a strongly interacting two-dimensional Fermi gas

We theoretically investigate strong-coupling properties of a two-dimensional Fermi gas in the normal phase. Including pairing fluctuations within the framework of a self-consistent T-matrix approximation, we calculate the single-particle density of states (DOS) near the observed Berezinskii-Kosterlitz-Thouless phase transition temperature TBKT. We show that the pseudogap phenomenon associated with strong pairing fluctuations appears as an almost fully gapped single-particle density of states in the strong-coupling regime, indicating that amplitude fluctuations of the order parameter are almost absent and the system is dominated by phase fluctuations of the order parameter, as expected in a two-dimensional system near TBKT. On the other hand, although pairing fluctuations are enhanced by the low-dimensionality of the system, they are found to be still not strong enough to open such a full gap in the intermediate coupling (crossover) regime. In this regime, a dip structure is only seen in DOS around ω = 0, indicating that amplitude of the superfluid order parameter is also fluctuating, in addition to phase fluctuations. In theoretically determining TBKT in a two-dimensional Fermi gas, it is frequently assumed that, while phase fluctuations exist, the amplitude of the superfluid order parameter is fixed. However, our results indicate the necessity of including both amplitude and phase fluctuations of the order parameter in evaluating TBKT in the crossover region. Since the BKT phase transition has recently been reported in a two-dimensional 6Li Fermi gas, our results would be useful for the theoretical study of this observed novel Fermi superfluid and effects of strong low-dimensional pairing fluctuations.

Non-equilibrium critical vortex dynamics of disordered 2D XY-model

Vortex dynamics and clustering in non-equilibrium critical relaxation of disordered 2D XY-model are investigated for different initial states. Time dependencies of vortex concentration and clusters sizes are studied for different spin concentrations. The anomalous slow down of clustering in disordered system are explained by pinning of vortices on defects. The calculated temperature dependence of transverse stiffness allows to estimate critical temperature Tbkt and applicability of spin-wave approximation for disordered system.

Pseudogap phenomena in a two-dimensional ultracold Fermi gas near the Berezinskii-Kosterlitz-Thouless transition

We investigate single-particle excitations and strong-coupling effects in a twodimensional Fermi gas. Including pairing fluctuations within a Gaussian fluctuation theory, we calculate the density of states ρ(ω) near the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature TBKT. Near TBKT, we show that superfluid fluctuations induce a pseudogap in ρ(ω). The pseudogap structure is very similar to the BCS superfluid density of states, although the superfluid order parameter is absent in the present two-dimensional case. Since a twodimensional 40K Fermi gas has recently been realized, our results would contribute to the understanding of single-particle properties near the BKT instability.

Excess conductivity and Berezinskii–Kosterlitz–Thouless transition in superconducting FeSe thin films

Temperature-dependent electronic transport in the vicinity of the superconducting transition is reported for quasi-two-dimensional textured FeSe thin films. The conspicuous rounding of the resistive transitions and large transition widths are indications of excess conductivity due to thermal Cooper-pair fluctuations, which can be well-described by the two-dimensional Aslamazov–Larkin theory. The Halperin–Nelson form of the sheet resistance between the phase-ordering temperature TBKT and the mean-field temperature TMF, and the power-law behaviour of the voltage–current characteristics, with a distinctive jump of the exponent at TBKT, are indicative of a Berezinskii–Kosterlitz–Thouless transition. The complementary results suggest a two-dimensional character of superconductivity in the FeSe films and allow a quantitative estimate of the Ginzburg number Gi.

Kosterlitz-Thouless Transition: The Diluted XY model

The effect of nonmagnetic disorder on Berezinskii-Kosterlitz-Thouless (BKT) transition in the two-dimensional ferromagnetic XY model on a square lattice, diluted by randomly placed vacancies can be an important source of information on the role played by vortexes in this transition. The transition temperature TBKT is determined as a function of vacancy density ρv by stiffness ρ and for different size of the lattice. The anomalous behavior for TBKT when ρv is close to the square lattice percolation limit is a consequence of the effect of finite size of lattice and not due the quantum fluctuations as concluded in literature. We obtain that TBKT falls to zero at ρv ≈ 0.40 close to the value 0.41 obtained for the classic model.

Finite-size scaling method for the Berezinskii–Kosterlitz–Thouless transition

We test an improved finite-size scaling method for reliably extracting the critical temperature TBKT of a Berezinskii–Kosterlitz–Thouless (BKT) transition. Using known single-parameter logarithmic corrections to the spin stiffness ρs at TBKT in combination with the Kosterlitz–Nelson relation between the transition temperature and the stiffness, ρs(TBKT) = 2TBKT/π, we define a size-dependent transition temperature TBKT(L1,L2) based on a pair of system sizes L1,L2, e.g., L2 = 2L1. We use Monte Carlo data for the standard two-dimensional classical XY model to demonstrate that this quantity is well behaved and can be reliably extrapolated to the thermodynamic limit using the next expected logarithmic correction beyond the ones included in defining TBKT(L1,L2). For the Monte Carlo calculations we use GPU (graphical processing unit) computing to obtain high-precision data for L up to 512. We find that the sub-leading logarithmic corrections have significant effects on the extrapolation. Our result TBKT = 0.8935(1) is several error bars above the previously best estimates of the transition temperature, TBKT ≈ 0.8929. If only the leading log-correction is used, the result is, however, consistent with the lower value, suggesting that previous works have underestimated TBKT because of the neglect of sub-leading logarithms. Our method is easy to implement in practice and should be applicable to generic BKT transitions.

Intrinsic superconductivity in ABA-stacked trilayer graphene

We study the phonon-mediated superconductivity in light doped ABA-stacked trilayer graphene system by means of two theoretical models. We find superconducting transition temperature TC can be greatly enlarged by tuning the Fermi energy away from neutral point. Utilizing realistic parameters, we find Tc is approximately 1 K even under weak doping condition EF = 0.1 eV. Specifically, we give out the analytical expression for superconductivity gap △ and superconducting transition temperature Tc for negative-U Hubbard model. Further, we consider the thermal fluctuation and calculate the Berezinskii-Kosterlitz-Thouless critical temperature TBKT. Besides, we consider a two-band BCS model in comparision with the negative-U Hubbard model. The results for both models are qualitatively consistent. Our study provides a promising possibility for realizing intrinsic superconductivity in multilayer graphene systems.

Magnetic field, temperature and frequency dependence of complex conductance of ultra thin YBa2Cu3O7-x films

We have studied the magnetic field, temperature and frequency dependencies of the complex sheet conductance, σ(ω,T), of 1–3 unit cell (UC) thick YBa2Cu3O7-x films sandwiched between semiconducting Pr0.6Y0.4Ba2Cu3O7-x layers. Experiments have been carried out at frequencies between 2 MHz -1 GHz, with one-spiral coil technique and at 250–500 GHz, by aid of a quasi optical spectrometer based on backward-wave oscillators. We have found a very large shift of the superconducting transition onset temperature and of the maximum Reσ(T) position to higher temperatures with increasing ω. The dependence of Hc2(T) is exponential close to Tc, with a break in a slope at the Berezinski-Kosterlitz-Thouless (BKT) temperature TBKT, due to the vortex-antivortex pair unbinding, and linear below TBKT because the Abrikosov vortex formation. We have compared our experimental results with the extended dynamic theory for the BKT transition and found that the research explored the dynamics of bound vortex-antivortex pairs with short separation lengths.

Nonlinearity of the current-voltage characteristics for YBa2Cu3O7–x single crystals and the Berezinskii-Kosterlitz-Thouless transition

The nonlinearity of the current-voltage characteristics for YBa2Cu3O7 − x single crystals is investigated in the vicinity of the superconducting transition temperature Tc, and the mechanisms responsible for the nonlinearity of the current-voltage characteristics are considered. The current-voltage characteristics and the amplitudes of the higher voltage harmonics for the YBa2Cu3O7 − x single crystals are directly measured using modulation Fourier analysis. It is shown that the positions of the maxima in the amplitudes of the higher voltage harmonics coincide with the Berezinskii-Kosterlitz-Thouless transition temperature TBKT. This coincidence can provide a means for determining the transition temperature TBKT. A number of parameters characterizing the YBa2Cu3O7 − x single crystals in the superconducting state are estimated using the experimental results and the model of a Berezinskii-Kosterlitz-Thouless transition. The parameters thus estimated are in good agreement with the data available in the literature.

Finite-temperature renormalization group analysis of interaction effects in 2D lattices of Bose–Einstein condensates

By using a renormalization group analysis, we study the effect of interparticle interactions on the critical temperature TBKT at which the Berezinskii–Kosterlitz–Thouless (BKT) transition occurs for Bose–Einstein condensates loaded at finite temperature in a 2D optical lattice. We find that TBKT decreases as the interaction energy decreases; when U/J = 36/π one has TBKT = 0, signalling the possibility of a quantum phase transition of BKT type.

Manifestation of two-dimensional behavior of YBCO films in a study of their complex susceptibility

The temperature dependence of the complex magnetic susceptibility χ′+χ″ of various YBCO films is investigated at different amplitudes of the exciting field Hac. It is found that when the temperature Tm at which the maximum is observed on the χ″(T) curve is plotted as a function of Hacα (the parameter α=1, 1/2, or 2/3, depending on the character of the coupling between crystallites), a kink appears at a certain field Hac=H1*. It is suggested that the temperature Tc1 obtained by extrapolating the Tm(Hac2/3) curve from the high-field region to zero field is the Berezinskii–Kosterlitz–Thouless transition temperature TBKT. This suggestion is based on a comparison of the present results with published data from a study of the complex susceptibility of a GdBa2Cu3O6.75 single crystal for directions of Hac parallel to the c axis of the single crystal and in its ab plane, and also on the coincidence of the calculated values of certain characteristic temperatures near the BKT transition with our experimental values.

Essential finite-size effect in the two-dimensionalXYmodel

The thermodynamics of the 2D XY model is formulated by a transfer matrix method and analyzed by a density matrix renormalization group. The finite-size scaling and the beta function of the model are studied by the Roomany-Wyld renormalization group theory. It is found that the 2D XY model has an essential finite-size effect and the Berezinskii-Kosterlitz-Thouless transition with the critical temperature TBKT = 0.892 appears in a finite system of 2000 - 3000 spins as a massless to massive transition with the effective critical temperature Tc = 1.07 " 0.01.

Quantum correction to the BKT transition for 2D easy-plane antiferromagnets

We consider the quantum antiferromagnet with easy-plane exchange anisotropy, namely, the antiferromagnetic XXZ model, on the square lattice. Its classical counterpart, compared to the planar model shows a reduction of the critical temperature TBKT of the Berezinskii–Kosterlitz–Thouless phase transition, that is a consequence of the thermal out-of-plane fluctuations. For the quantum system we use the pure-quantum self-consistent harmonic approximation to calculate how much the effective exchange interaction is weakened as an effect of the pure-quantum part of the fluctuations. One can then predict the further reduction of TBKT with respect to the corresponding classical system. The theory works well in a wide range of values of the easy-plane anisotropy. In the extreme case of the spin-1/2 model, the result is compatible with the estimate of TBKT obtained by previous quantum Monte Carlo simulations. When the anisotropy is weak the theory leads to an unphysical ‘‘isotropization’’ due to the use of the Villain spin-boson transformation.

Effect of Berezinskii-Kosterlitz-Thouless vortex fluctuations on the nuclear spin relaxation rate

In this work we examine the influence of the diffusive motion of vortices in highly anisotropic high-Tc superconductors near the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature T bkt on the spin-lattice relaxation rate T 1 −1 .We find a jump in T 1 −1 at the temperature T bkt .