Berezinskii-Kosterlitz-Thouless Theory Research Articles

Non-spontaneous symmetry breaking, chaos, and universality in 2D superconducting phase transition

This research paper explores the intriguing phenomenon of the superconductor-metal–insulator phase transition in thin films, examining it from a theoretical standpoint. Our study revolves around the proposition that the process of U(1) symmetry breaking in the Landau–Ginzburg theory might not be entirely spontaneous. Building on this insight, we derive critical parameters characterizing the superconducting phase transition. Our findings demonstrate that the application of an electric field can effectively control the phase transition, leading to the suppression of the supercurrent at specific electric potential values, which is consistent with recent research. Furthermore, we have developed a robust relationship for the nonlinear resistivity that accurately simulates experimental measurements below the critical temperature. This derived relation adopts the form of logistic functions, providing a systematic framework to describe the system within the realm of chaos theory. Moreover, we establish a link with the Berezinskii–Kosterlitz–Thouless theory, highlighting the universality of the topological transition. However, this universality breaks down under the influence of multiple control parameters. To delve further into the underlying reasons for the collapse of universality, we turn to the study of Markus–Lyapunov fractals, which offers a deep understanding into the system’s behavior in the presence of varying external influences..

Observation of first and second sound in a BKT superfluid.

Superfluidity in its various forms has been of interest since the observation of frictionless flow in liquid helium II1,2. In three spatial dimensions it is conceptually associated with the emergence of long-range order at a critical temperature. One of the hallmarks of superfluidity, as predicted by the two-fluid model3,4 and observed in both liquid helium5 and in ultracold atomic gases6,7, is the existence of two kinds of sound excitation-the first and second sound. In two-dimensional systems, thermal fluctuations preclude long-range order8,9; however, superfluidity nevertheless emerges at a non-zero critical temperature through the infinite-order Berezinskii-Kosterlitz-Thouless (BKT) transition10,11, which is associated with a universal jump12 in the superfluid density without any discontinuities in the thermodynamic properties of the fluid. BKT superfluids are also predicted to support two sounds, but so far this has not been observed experimentally. Here we observe first and second sound in a homogeneous two-dimensional atomic Bose gas, and use the two temperature-dependent sound speeds to determine the superfluid density of the gas13-16. Our results agree with the predictions of BKT theory, including the prediction of a universal jump in the superfluid density at the critical temperature.

Berezinskii-Kosterlitz-Thouless phase in two-dimensional ferroelectrics

The celebrated Berezinskii-Kosterlitz-Thouless (BKT) phase transition refers to a topological transition characterized, e.g., by the dissociation of vortex-antivortex pairs in two-dimensional (2D) systems. Such unusual phase has been reported in various types of materials, but never in the new class of systems made by one-unit-cell-thick (1UC) ferroelectrics (also coined as 2D ferroelectrics). Here, the use of a first-principles-based effective Hamiltonian method leads to the discovery of many fingerprints of a BKT phase existing in-between the ferroelectric and paraelectric states of 1UC tin tellurium being fully relaxed. Moreover, epitaxial strain is found to have dramatic consequences on the temperature range of such BKT phase for the 1UC SnTe. Consequently, our predictions extend the playground of BKT theory to a novel class of functional materials, and demonstrate that strain is an effective tool to alter BKT characteristics there.

Signatures of a universal jump in the superfluid density of a two-dimensional Bose gas with a finite number of particles

We study, within the classical fields approximation, a two-dimensional weakly interacting uniform Bose gas of a finite number of atoms. By using a grand canonical ensemble formalism we show that such systems exhibit, in addition to the Berezinskii-Kosterlitz-Thouless (BKT) and thermal phases, the intermediate region. This region is characterized by a decay of current-current correlations at low momenta and by an algebraic decay of the first-order correlations with an exponent being larger than the critical value predicted by the BKT theory. The density of the superfluid fraction at the temperature which separates the BKT phase from the intermediate region approaches the one found by Nelson and Kosterlitz for two-dimensional superfluids while the number of atoms is increased.

Pseudogap Regime of a Two-dimensional Uniform Fermi Gas

We investigate pseudogap phenomena in a two-dimensional Fermi gas. Including pairing fluctuations within a self-consistent $T$-matrix approximation, we determine the pseudogap temperature $T^*$ below which a dip appears in the density of states $\rho(\omega)$ around the Fermi level. Evaluating $T^*$, we identify the pseudogap region in the phase diagram of this system. We find that, while the observed BKT (Berezinskii-Kosterlitz-Thouless) transition temperature $T^{\rm exp}_{\rm BKT}$ in a $^6$Li Fermi gas is in the pseudogap regime, the detailed pseudogap structure in $\rho(\omega)$ at $T^{\rm exp}_{\rm BKT}$ still differs from a fully-gapped one, indicating the importance of amplitude fluctuations in the Cooper channel there. Since the observed $T^{\rm exp}_{\rm BKT}$ in the weak-coupling regime cannot be explained by the recent BKT theory which only includes phase fluctuations, our results may provide a hint about how to improve this BKT theory. Although $\rho(\omega)$ has not been measured in this system, we show that the assessment of our results is still possible by using the observable Tan's contact.

Duality, Gauge Symmetries, Renormalization Groups and the BKT Transition

In this chapter, I will briefly review, from my own perspective, the situation within theoretical physics at the beginning of the 1970s, and the advances that played an important role in providing a solid theoretical and experimental foundation for the Berezinskii–Kosterlitz–Thouless theory (BKT). Over this period, it became clear that the Abelian gauge symmetry of the 2D-XY model had to be preserved to get the right phase structure of the model. In previous analyses, this symmetry was broken when using low order calculational approximations. Duality transformations at that time for two-dimensional models with compact gauge symmetries were introduced by José, Kadanoff, Nelson and Kirkpatrick (JKKN). Their goal was to analyze the phase structure and excitations of XY and related models, including symmetry breaking fields which are experimentally important. In a separate context, Migdal had earlier developed an approximate Renormalization Group (RG) algorithm to implement Wilson’s RG for lattice gauge theories. Although Migdal’s RG approach, later extended by Kadanoff, did not produce a true phase transition for the XY model, it almost did asymptotically in terms of a non-perturbative expansion in the coupling constant with an essential singularity. Using these advances, including work done on instantons (vortices), JKKN analyzed the behavior of the spin–spin correlation functions of the 2D XY-model in terms of an expansion in temperature and vortex-pair fugacity. Their analysis led to a perturbative derivation of RG equations for the XY model which are the same as those first derived by Kosterlitz for the two-dimensional Coulomb gas. JKKN’s results gave a theoretical formulation foundation and justification for BKT’s sound physical assumptions and for the validity of their calculational approximations that were, in principle, strictly valid only at very low temperatures, away from the critical [Formula: see text] temperature. The theoretical predictions were soon tested successfully against experimental results on superfluid helium films. The success of the BKT theory also gave one of the first quantitative proofs of the validity of the RG theory.

Topological Superfluid in a Fermi-Bose Mixture with a High Critical Temperature.

We show that a 2D spin-polarized Fermi gas immersed in a 3D Bose-Einstein condensate constitutes a very promising system for realizing a p_{x}+ip_{y} superfluid. The fermions attract each other via an induced interaction mediated by the bosons, and the resulting pairing is analyzed with retardation effects fully taken into account. This is further combined with Berezinskii-Kosterlitz-Thouless (BKT) theory to obtain reliable results for the superfluid critical temperature. We show that both the strength and the range of the induced interaction can be tuned experimentally, which can be used to make the critical temperature approach the maximum value allowed by general BKT theory. Moreover, this is achieved while keeping the Fermi-Bose interaction weak so that three-body losses are small. Our results show that realizing a topological superfluid with atomic Fermi-Bose mixtures is within experimental reach.

Semi-phenomenological analysis of neutron scattering results for quasi-two dimensional quantum anti-ferromagnet

The available results from the inelastic neutron scattering experiment performed on the quasi-two dimensional spin 12 anti-ferromagnetic material La2CuO4 have been analysed theoretically. The formalism of ours is based on a semi-classical like treatment involving a model of an ideal gas of mobile vortices and anti-vortices built on the background of the Néel state, using the bipartite classical spin configuration corresponding to an XY-anisotropic Heisenberg anti-ferromagnet on a square lattice. The results for the integrated intensities for our spin 12 model corresponding to different temperatures, show occurrence of vigorous unphysical oscillations, when convoluted with a realistic spectral window function. These results indicate failure of the conventional semi-classical theoretical model of ideal vortex/anti-vortex gas arising in the Berezinskii–Kosterlitz–Thouless theory for the low spin magnetic systems. A full fledged quantum mechanical formalism and calculations seem crucial for the understanding of topological excitations in such low spin systems. Furthermore, a severe disagreement is found to occur at finite values of energy transfer between the integrated intensities obtained theoretically from the conventional formalism and those obtained experimentally. This further suggests strongly that the full quantum treatment should also incorporate the interaction between the fragile-magnons and the topological excitations. This is quite plausible in view of the recent work establishing such a process in XXZ quantum ferromagnet on 2D lattice. The high spin XXZ quasi-two dimensional antiferromagnet like MnPS3 however follows the conventional theory quite well.

Spatial correlation of two-dimensional bosonic multimode condensates

The Berezinskii-Kosterlitz-Thouless (BKT) theorem predicts that two-dimensional bosonic condensates exhibit quasi-long-range order which is characterized by a slow decay of the spatial coherence. However previous measurements on exciton-polariton condensates revealed that their spatial coherence can decay faster than allowed under the BKT theory, and different theoretical explanations have already been proposed. Through theoretical and experimental study of exciton-polariton condensates, we show that the fast decay of the coherence can be explained through the simultaneous presence of multiple modes in the condensate.

Effective two-dimensional thickness for the Berezinskii-Kosterlitz-Thouless-like transition in a highly underdopedLa2−xSrxCuO4

The nature of the superconducting transition in highly underdoped thick films of ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$ ($x=0.07$ and 0.08) has been investigated using the in-plane transport measurements. The contribution of superconducting fluctuations to the conductivity in zero magnetic field, or paraconductivity, was determined from the magnetoresistance measured in fields applied perpendicular to the ${\mathrm{CuO}}_{2}$ planes. Both the temperature dependence of the paraconductivity above the transition and the nonlinear current-voltage ($I\ensuremath{-}V$) characteristics measured across it exhibit the main signatures of the Berezinskii-Kosterlitz-Thouless (BKT) transition. The quantitative comparison of the superfluid stiffness, extracted from the $I\ensuremath{-}V$ data, with the renormalization-group results for the BKT theory, reveals a large value of the vortex-core energy. This finding is confirmed by the analysis of the paraconductivity obtained using different methods. The results strongly suggest that the characteristic energy scale controlling the BKT behavior in this layered system corresponds to the superfluid stiffness of a few layers.

Anisotropic properties of a single superconducting CaCuO2/SrTiO3 interface

The transport properties of CaCuO2/SrTiO3 single interfaces are studied by resistance versus temperature measurements in external magnetic fields. The superconducting anisotropy where and are the superconducting coherence lengths parallel and perpendicular to the interface, respectively, shows values higher than that previously obtained for CaCuO2/SrTiO3 superlattices deposited in the same conditions. The larger anisotropy, observed for the single interfaces, indicates that the charge carriers are confined inside a thin superconducting layer next to the interface rather than spread throughout the whole CaCuO2 block. The activation energy and the irreversibility line confirm this hypothesis, suggesting that quasi two-dimensional transport is dominant in this system. The interpretation of the experimental data in the framework of the Berezinskii–Kosterlitz–Thouless theory confirms that the thickness of the superconducting sheet layer is about 1 nm, corresponding roughly to two CaCuO2 unit cells.

Evidence for Berezinskii–Kosterlitz–Thouless transition in atomically flat two-dimensional Pb superconducting films

We report results from scanning tunneling microscopy and transport measurements on a series of crystalline lead films containing an integer number of atomic layers, and find that the observed features in sufficiently thin films are consistent with Berezinskii–Kosterlitz–Thouless (BKT) physics. Specifically, Cooper pairing and superconductivity disappear at two distinct temperatures; the current–voltage characteristics in the intermediate phase are non-Ohmic; and the temperature and current dependences of resistance agree with the expectation from the BKT theory.

Berezinskii–Kosterlitz–Thouless crossover in a trapped atomic gas

Any state of matter is classified according to its order, and the type of order that a physical system can possess is profoundly affected by its dimensionality. Conventional long-range order, as in a ferromagnet or a crystal, is common in three-dimensional systems at low temperature. However, in two-dimensional systems with a continuous symmetry, true long-range order is destroyed by thermal fluctuations at any finite temperature. Consequently, for the case of identical bosons, a uniform two-dimensional fluid cannot undergo Bose-Einstein condensation, in contrast to the three-dimensional case. However, the two-dimensional system can form a 'quasi-condensate' and become superfluid below a finite critical temperature. The Berezinskii-Kosterlitz-Thouless (BKT) theory associates this phase transition with the emergence of a topological order, resulting from the pairing of vortices with opposite circulation. Above the critical temperature, proliferation of unbound vortices is expected. Here we report the observation of a BKT-type crossover in a trapped quantum degenerate gas of rubidium atoms. Using a matter wave heterodyning technique, we observe both the long-wavelength fluctuations of the quasi-condensate phase and the free vortices. At low temperatures, the gas is quasi-coherent on the length scale set by the system size. As the temperature is increased, the loss of long-range coherence coincides with the onset of proliferation of free vortices. Our results provide direct experimental evidence for the microscopic mechanism underlying the BKT theory, and raise new questions regarding coherence and superfluidity in mesoscopic systems.

Current-induced vortex unbinding in bolometer mixers

We present a description of the current-voltage characteristics of hot electron bolometers in terms of the current-dependent intrinsic resistive transition of NbN films. We find that, by including this current dependence, we can correctly predict the complete current-voltage characteristics, showing excellent agreement with measurements for both low and high bias and for small as well as large devices. It is assumed that the current dependence is due to vortex-antivortex unbinding as described in the Berezinskii–Kosterlitz–Thouless theory. The presented approach will be useful in guiding device optimization for noise and bandwidth.