Berezinskii-Kosterlitz-Thouless Research Articles

Flux-flow instability across Berezinskii Kosterlitz Thouless phase transition in KTaO3 (111) based superconductor

The nature of energy dissipation in 2D superconductors under perpendicular magnetic field at small current excitations has been extensively studied over the past two decades. However, dissipation mechanisms at high current drives remain largely unexplored. Here we report on the distinct behavior of energy dissipation in the AlOx/KTaO3 (111) system hosting 2D superconductivity in the intermediate disorder regime. The results show that below the Berezinskii Kosterlitz Thouless (BKT) phase transition temperature (TBKT), hot-spots and Larkin Ovchinnikov type flux-flow instability (FFI) are the major channels of dissipation, leading to pronounced voltage instability at large currents. Furthermore, such FFI leads to a rare observation of clockwise hysteresis in current-voltage characteristics within the temperature range TBKT < T < TC (TC is superconducting transition temperature). These findings deepen our understanding of how a BKT system ultimately transforms to a normal state under increasing current.

Anisotropic deformation of the 6-state clock model: Tricritical-point classification

The two-dimensional q-state clock models exhibit the Berezinskii–Kosterlitz–Thouless (BKT) transition for q≥5 since they are a subset of the isotropic XY model. We examine the 6-state clock model with an anisotropic deformation. Selecting the 6-state Potts model as a source of the deformation, the model naturally violates the discrete rotational symmetry of the clock model. We introduce the anisotropic deformation parameter α in the clock model interpolating the clock (α=1) and the Potts (α=0) models. We employ the corner transfer matrix renormalization group method to analyze the phase transitions on the square lattice in the thermodynamic limit. Three different phases and phase transitions are identified. The phase diagram is constructed, and we determine a tricritical point at αc=0.21405(4) and Tc=0.834017(5). Analyzing the latent heat and the entanglement entropy in the vicinity of the Tc(αc), we observe a single discontinuous phase transition and two BKT phase transitions meeting in the tricritical point. The tricritical point exhibits a phase transition of the second order with the critical exponents β≈1/10 and δ≈14. We conjecture that an infinitesimal surrounding of the tricritical point consists of the three fundamental phase transitions, in which the first and the BKT orders gradually weaken into the second-order tricritical point.

Comprehensive studies on the universality of BKT transitions—machine-learning study, Monte Carlo simulation, and level-spectroscopy method

Comprehensive studies are made on the six-state clock universality of two models using several approaches. We apply the machine-learning technique of phase classification to the antiferromagnetic (AF) three-state Potts model on the square lattice with ferromagnetic next-nearest-neighbor (NNN) coupling and the triangular AF Ising model with anisotropic NNN coupling to study two Berezinskii–Kosterlitz–Thouless transitions. We also use the Monte Carlo simulation paying attention to the ratio of correlation functions of different distances for these two models. The obtained results are compared with those of the previous studies using the level-spectroscopy method. We directly show the six-state clock universality for totally different systems with the machine-learning study.

Machine-learning detection of the Berezinskii-Kosterlitz-Thouless transition and the second-order phase transition in XXZ models

We propose two machine-learning methods based on neural networks, which we respectively call the phase-classification method and the temperature-identification method, for detecting different types of phase transitions in the XXZ models without prior knowledge of their critical temperatures. The XXZ models have exchange couplings which are anisotropic in the spin space where the strength is represented by a parameter $\Delta(>0)$. The models exhibit the second-order phase transition when $\Delta>1$, whereas the Berezinskii-Kosterlitz-Thouless (BKT) phase transition when $\Delta<1$. In the phase-classification method, the neural network is trained using spin or vortex configurations of well-known classical spin models other than the XXZ models, e.g., the Ising models and the XY models, to classify those of the XXZ models to corresponding phases. We demonstrate that the trained neural network successfully detects the phase transitions for both $\Delta>1$ and $\Delta<1$, and the evaluated critical temperatures coincide well with those evaluated by conventional numerical calculations. In the temperature-identification method, on the other hand, the neural network is trained so as to identify temperatures at which the input spin or vortex configurations are generated by the Monte Carlo thermalization. The critical temperatures are evaluated by analyzing the optimized weight matrix, which coincide with the result of numerical calculation for the second-order phase transition in the Ising-like XXZ model with $\Delta=1.05$ but cannot be determined uniquely for the BKT transition in the XY-like XXZ model with $\Delta=0.95$.

Unconventional Berezinskii-Kosterlitz-Thouless Transition in the Multicomponent Polariton System.

We study a four-component polariton system in the optical parametric oscillator regime consisting of exciton, photon, signal, and idler modes across the Berezinskii-Kosterlitz-Thouless (BKT) transition. We show that all four components share the same BKT critical point, and algebraic decay of spatial coherence with the same critical exponent. However, while the collective excitations in different components are strongly locked, both close to and far from criticality, the spontaneous creation of topological defects in the vicinity of the phase transition is found to be largely independent of the intercomponent mode locking, and instead strongly dependent on the density within a given mode. This peculiar characteristic allows us to reveal a novel state of matter, characterized by configurations of topological defects proliferating on top of a superfluid with algebraic decay of coherence, observation of which is demonstrated to be within reach of current experiments.

Emergent Halperin–Saslow mode, gauge glass and quenched disorders in quantum Ising magnet TmMgGaO4

Quenched disorders could bring novel quantum excitations and models to certain quantum magnets. Motivated by recent experiments on the quantum Ising magnet TmMgGaO4, we explore the effects of the quenched disorder and the interlayer coupling in this triangular lattice Ising antiferromagnet. It is pointed out that the weak quenched (nonmagnetic) disorder would convert the emergent 2D Berezinskii–Kosterlitz–Thouless (BKT) phase and the critical region into a U(1) gauge glass. There will be an emergent Halperin–Saslow mode associated with this gauge glass. Using the Imry-Ma’s renormalization group result, we explain the fate of the finite-field [Formula: see text] symmetry breaking transition at the low temperatures. The ferromagnetic interlayer coupling would suppress the BKT phase and generate a tiny ferromagnetism. With quenched disorders, this interlayer coupling changes the 2D gauge glass into a 3D gauge glass, and the Halperin–Saslow mode persists. This work merely focuses on addressing a phase regime in terms of emergent U(1) gauge glass behaviors and hope to inspire future works and thoughts in weakly disordered frustrated magnets in general.

Field-Tunable Berezinskii-Kosterlitz-Thouless Correlations in a Heisenberg Magnet.

We report the manifestation of field-induced Berezinskii-Kosterlitz-Thouless (BKT) correlations in the weakly coupled spin-1/2 Heisenberg layers of the molecular-based bulk material [Cu(pz)_{2}(2-HOpy)_{2}](PF_{6})_{2}. At zero field, a transition to long-range order occurs at 1.38K, caused by a weak intrinsic easy-plane anisotropy and an interlayer exchange of J^{'}/k_{B}≈1 mK. Because of the moderate intralayer exchange coupling of J/k_{B}=6.8 K, the application of laboratory magnetic fields induces a substantial XY anisotropy of the spin correlations. Crucially, this provides a significant BKT regime, as the tiny interlayer exchange J^{'} only induces 3D correlations upon close approach to the BKT transition with its exponential growth in the spin-correlation length. We employ nuclear magnetic resonance measurements to probe the spin correlations that determine the critical temperatures of the BKT transition as well as that of the onset of long-range order. Further, we perform stochastic series expansion quantum MonteCarlo simulations based on the experimentally determined model parameters. Finite-size scaling of the in-plane spin stiffness yields excellent agreement of critical temperatures between theory and experiment, providing clear evidence that the nonmonotonic magnetic phase diagram of [Cu(pz)_{2}(2-HOpy)_{2}](PF_{6})_{2} is determined by the field-tuned XY anisotropy and the concomitant BKT physics.

Bosonic topological insulators at the superconductor-to-superinsulator transition

We review the topological gauge theory of the superconductor-to-superinsulator transition. The possible intermediate Bose metal phase intervening between these two states is a bosonic topological insulator. We point out that the correct treatment of a bosonic topological insulator requires a normally neglected, additional dimensionless parameter, which arises because of the non-commutativity between the infinite gap limit and phase space reduction. We show that the bosonic topological insulator is a functional first Landau level. The additional parameter drives two Berezinskii–Kosterlitz–Thouless (BKT) quantum transitions to superconducting and superinsulating phases, respectively. The two BKT correlation scales account for the emergent granularity observed around the transition. Finally, we derive the ground state wave function for a system of charges and vortices in the Bose metal phase.

Fractonic Berezinskii-Kosterlitz-Thouless transition from a renormalization group perspective

Proliferation of defects is a mechanism that allows for topological phase transitions. Such a phase transition is found in two dimensions for the XY model, which lies in the Berezinskii-Kosterlitz-Thouless (BKT) universality class. The transition point can be found using renormalization group analysis. We apply renormalization group arguments to determine the nature of BKT transitions for the three-dimensional plaquette-dimer model, which is a model that exhibits fractonic mobility constraints. We show that an important part of this analysis demands a modified dimensional analysis that changes the interpretation of scaling dimensions upon coarse-graining. Using this modified dimensional analysis, we compute the beta functions of the model and predict a finite critical value above which the fractonic phase melts, proliferating dipoles. Importantly, the transition point is found through a renormalization group analysis that accounts for the phenomenon of UV/IR mixing, characteristic of fractonic models.

Two-dimensional superconducting nature of Bi2Sr2CaCu2O8+δ thin films revealed by BKT transition.

High-quality Bi2Sr2CaCu2O8+δ superconducting thin films are successfully grown on a SrTiO3 substrate by the Pulsed Laser Deposition technique. Superconducting critical transition temperatures Tc,zero have reached up to 85 K by using optimized growth parameters. In addition, we demonstrated the two-dimensional nature of the superconductivity of thin films by virtue of exhibiting Berezinskii-Kosterlitz-Thouless (BKT) physics and anisotropic magnetic response. Furthermore, three distinct regimes are identified based on the analysis of direct current resistance. The non-Fermi liquid phase and BKT phase fluctuation zone almost perfectly merge together, which implies that the system undergoes a unique topological state that is determined by the BKT phase fluctuation preceding the onset of the superconducting state. The emergence of such a topological state radically differentiates from the three-dimensional superconducting transition, which spontaneously breaks the gauge symmetry. The current studies on the Bi2Sr2CaCu2O8+δ superconducting thin films provide some new insights for understanding the rich quantum states of matter that emerge in the vicinity of the superconducting phase transition and highlight the significant role of BKT fluctuation on two-dimensional superconducting transition.

Phase transitions driven by topological excitations and their tensor network approach

The fundamental concepts of phases of matter and thermal phase transitions constitute the cornerstone of our understanding of the physical universe. The historical development of the phase transition theory from Landau's spontaneous symmetry breaking paradigm to modern topological phase transition theories represents a major milestone in the evolution of numerous scientific disciplines. From the perspective of emergent philosophy, the interplay of topological excitations leads to enriched physical phenomena. One prominent prototype is the Berezinskii-Kosterlitz-Thouless (BKT) phase transition, where unbinding of integer vortices occurs in the absence of spontaneous breaking of continuous &lt;i&gt;U&lt;/i&gt;(1) symmetry. Using the state-of-the-art tensor network methods, we express the partition function of the two-dimensional &lt;i&gt;XY&lt;/i&gt;-related system in terms of a product of one-dimensional transfer operators. From the singularities of the entanglement entropy of the one-dimensional transfer operator, we accurately determine the complete phase diagram of the partition function. This method provides new insights into the emergent phenomenon driven by topological excitations, and sheds new light on future studies of 2D systems with continuous symmetries.

On self-energy contributions near Berezinskii–Kosterlitz–Thouless transition in interacting homogeneous 2D Bose system

ABSTRACT We explore the consequences of including quantum corrections in an interacting 2D Bose system near Berezinskii–Kosterlitz–Thouless (BKT) transition. To go beyond mean-field theory and treat correlations, we use Matsubara Green's function method, and, following a previous novel approach, study features of the interacting Green's function just above the transition. We numerically obtain self-consistent solutions of boson self-energy to second order as well as higher order (re-summation of ladder and bubble diagrams) in the interaction strength, for the entire range of momentum, k, and compare our findings with analytic results in the limits of low- and high-k. Thereby, in the weak interaction limit, we retrieve the universal transition condition and calculate the universal scaling parameter (independent of interaction strength). The renormalised single-particle Green's function is found to decay algebraically at large distance r.

Topological magnetic phase transition in Eu-based A -type antiferromagnets

Recently, a colossal magnetoresistance (CMR) was observed in $\mathrm{Eu}{\mathrm{Cd}}_{2}{\mathrm{P}}_{2}$, a compound that does not fit the conventional mixed-valence paradigm. Instead, experimental evidence points to a resistance driven by strong magnetic fluctuations within the two-dimensional ferromagnetic planes of the layered antiferromagnetic structure. While the experimental results have not yet been fully understood, a recent theory relates the CMR to a topological vortex-antivortex unbinding, i.e., Berezinskii-Kosterlitz-Thouless (BKT), phase transition. Motivated by these observations, in this work we explore the magnetic phases hosted by a microscopic classical magnetic model for $\mathrm{Eu}{\mathrm{Cd}}_{2}{\mathrm{P}}_{2}$, which easily generalizes to other Eu A-type antiferromagnetic compounds. Using Monte Carlo techniques to probe the specific heat and the helicity modulus, we show that our model can exhibit a vortex-antivortex unbinding phase transition. We find that this phase transition displays the same sensitivity to in-plane magnetization, interlayer coupling, and easy-plane anisotropy that is observed experimentally in the CMR signal, providing qualitative numerical evidence that the effect is related to a magnetic BKT transition.

Review of recent developments of the functional renormalization group for systems out of equilibrium

We recapitulate recent developments of the functional renormalization group (FRG) approach to the steady state of systems out of thermal equilibrium. In particular, we discuss second-order truncation schemes which account for the frequency-dependence of the two particle vertex and which incorporate inelastic processes. Our focus is on two different types of one-dimensional fermion chains: (i) infinite, open systems which feature a translation symmetry, and (ii) finite systems coupled to left and right reservoirs. In addition to giving a detailed and unified review of the technical derivation of the FRG schemes, we briefly summarize some of the key physical results. In particular, we compute the non-equilibrium phase diagram and analyze the fate of the Berezinskii–Kosterlitz–Thouless transition in the infinite, open system.Graphic abstract

Complex Phase-Fluctuation Effects Correlated with Granularity in Superconducting NbN Nanofilms

Superconducting nanofilms are tunable systems that can host a 3D-2D dimensional crossover leading to the Berezinskii-Kosterlitz-Thouless (BKT) superconducting transition approaching the 2D regime. Reducing the dimensionality further, from 2D to quasi-1D superconducting nanostructures with disorder, can generate quantum and thermal phase slips (PS) of the order parameter. Both BKT and PS are complex phase-fluctuation phenomena of difficult experiments. We characterized superconducting NbN nanofilms thinner than 15 nm, on different substrates, by temperature-dependent resistivity and current-voltage (I-V) characteristics. Our measurements evidence clear features related to the emergence of BKT transition and PS events. The contemporary observation in the same system of BKT transition and PS events, and their tunable evolution in temperature and thickness was explained as due to the nano-conducting paths forming in a granular NbN system. In one of the investigated samples, we were able to trace and characterize the continuous evolution in temperature from quantum to thermal PS. Our analysis established that the detected complex phase phenomena are strongly related to the interplay between the typical size of the nano-conductive paths and the superconducting coherence length.

Insulating phase in two-dimensional Josephson junction arrays investigated by nonlinear transport

We present experimental investigations of transport properties in the insulating phase of two-dimensional Josephson-junction arrays (JJAs) by systematically changing the ratio of Josephson energy $E_\mathrm{J}$ and charging energy $E_\mathrm{C}$. The observed temperature dependence of resistance indicates that the JJAs do not show a sharp phase transition but exhibit a gradual crossover to the insulating phase. At low temperatures, the current-voltage ($I$-$V$) characteristics become nonlinear as described by $I=cV+bV^a$ ($a$, $b$, and $c$ are temperature dependent coefficients). This nonlinear behavior is understood in terms of the Berezinskii-Kosterlitz-Thouless (BKT) mechanism by taking into account the influence of a finite-range cutoff of the logarithmic interaction between Cooper pairs. From the analysis of the nonlinearity, we deduce the crossover temperature to the insulating phase and determine the phase diagram in the insulating side as a function of $E_\mathrm{J} /E_\mathrm{C}$. We also show that, at very low temperatures, the $I$-$V$ characteristics continuously develop into the negative differential conductance caused by coherent single-Cooper-pair tunneling.

An Elementary Proof of Phase Transition in the Planar XY Model

Using elementary methods we obtain a power-law lower bound on the two-point function of the planar XY spin model at low temperatures. This was famously first rigorously obtained by Fröhlich and Spencer (Commun Math Phys 81(4):527–602, 1981) and establishes a Berezinskii–Kosterlitz–Thouless phase transition in the model. Our argument relies on a new loop representation of spin correlations, a recent result of Lammers (Probab Relat Fields, 2021) on delocalisation of general integer-valued height functions, and classical correlation inequalities.

Berezinskii-Kosterlitz-Thouless phases in ultrathin PbTiO3/SrTiO3 superlattices

We study the emergence of Berezinskii-Kosterlitz-Thouless (BKT) phases in ${({\mathrm{PbTiO}}_{3})}_{3}/{({\mathrm{SrTiO}}_{3})}_{3}$ superlattices by means of second-principles simulations. Between a tensile epitaxial strain of $\ensuremath{\epsilon}=0.25--1\phantom{\rule{0.16em}{0ex}}%$, the local dipole moments within the superlattices are confined to the film-plane, and thus the polarization can be effectively considered as two-dimensional. The analysis of the decay of the dipole-dipole correlation with the distance, together with the study of the density of defects and its distribution as a function of temperature, supports the existence of a BKT phase in a range of temperature mediating the ordered ferroelectric (stable at low $T$), and the disordered paraelectric phase that appears beyond a critical temperature ${T}_{\mathrm{BKT}}$. This BKT phase is characterized by quasi-long-range order (whose signature is a power-law decay of the correlations with the distance), and the emergence of tightly bound vortex-antivortex pairs whose density is determined by a thermal activation process. The proposed ${\mathrm{PbTiO}}_{3}/{\mathrm{SrTiO}}_{3}$ superlattice model and the imposed mechanical boundary conditions are both experimentally feasible, making it susceptible for an experimental observation of these new topological phases in ferroelectric materials.

Theoretical analysis of the Berezinskii–Kosterlitz–Thouless transition critical dynamics near the zero temperature

Theoretical analysis of the Berezinskii–Kosterlitz–Thouless transition critical dynamics near the zero temperature

Low-temperature magnetic order rearrangement in the layered van der Waals compound MnPS3

To stabilize the long-range magnetic ordering in two-dimensional (2D) materials is a challenge from both fundamental and application points of view. It is difficult to be realized due to the delicate competition between thermal energy, magnetic exchange energy, and spin frustration. Here we study the temperature and field effects on the spin structure of two-dimensional van der Waals system ${\mathrm{MnPS}}_{3}$ using dc magnetic susceptibility and electron spin resonance (ESR) techniques. Clear development of three-step transitions was observed in the in-plane susceptibility. A low-temperature plateau from 78 to 38 K can be related to the Heisenberg antiferromagnetic (HAFM) ordering with spins pointing to the $z$ direction. Following, a sharp rising after the plateau suggests a transition into the $XY$ system. The rising slope slows down at 30 K indicating a transition into another phase, possibly a vortex-antivortex state. By fitting the temperature-dependent ESR parameters with the Berezinskii-Kosterlitz-Thouless (BKT) model in the range 100--300 K, we propose a spin 2D system with the vortex-antivortex structure below the HAFM transition. Susceptibility and ESR data show that the application of a high field along the $z$ direction destroys both the $XY$ phase and the BKT transition, reconciling to the scenario of a topological phase transition at zero field.