Berezinskii-Kosterlitz-Thouless Research Articles

The interplay of topology and antiferromagnetic order in two-dimensional van der Waals crystals of (Ni x Fe1−x )2P2S6

The Mermin–Wagner theorem forbids spontaneous symmetry breaking of spins in one/two-dimensional (2D) systems at a finite temperature and rules out the stabilization of this ordered state. However, it does not apply to all types of phase transitions in low dimensions, such as the topologically ordered phase rigorously shown by Berezinskii–Kosterlitz–Thouless (BKT) and experimentally realized in very limited systems such as superfluids and superconducting thin films. Quasi-2D van der Waals magnets provide an ideal platform to investigate the fundamentals of low-dimensional magnetism. We explored the quasi-2D honeycomb antiferromagnetic single crystals of (Ni x Fe1−x )2P2S6 (x = 1, 0.7, 0.5, 0.3, and 0) using in-depth temperature-dependent Raman measurements supported by first-principles calculations of the phonon frequencies. Quite surprisingly, we observed renormalization of the phonon modes much below the long-range magnetic ordered temperature attributed to the topological ordered state, namely the BKT phase, which is also found to change as a function of doping. The extracted critical exponent of the order-parameter (spin–spin correlation length, ξ(T) ) evinces the signature of a topologically active state driven by vortex–antivortex excitations. As a function of doping, a tunable transition from paramagnetic to antiferromagnetic ordering is shown via phonons reflected in the strong renormalization of the self-energy parameters of the Raman active phonon modes. The extracted exchange parameter (J) is found to vary by ∼100% by increasing the value of doping, ranging from ∼6 meV (for x = 0.3) to 13 meV (for x = 1).

Electronic inhomogeneity and phase fluctuation in one-unit-cell FeSe films

One-unit-cell FeSe films on SrTiO3 substrates are of great interest owing to significantly enlarged pairing gaps characterized by two coherence peaks at ±10 meV and ±20 meV. In-situ transport measurement is desired to reveal novel properties. Here, we performed in-situ microscale electrical transport and combined scanning tunneling microscopy measurements on continuous one-unit-cell FeSe films with twin boundaries. We observed two spatially coexisting superconducting phases in domains and on boundaries, characterized by distinct superconducting gaps (Δ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\Delta }_{1}$$\\end{document}~15 meV vs. Δ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\Delta }_{2}$$\\end{document}~10 meV) and pairing temperatures (Tp1~52.0 K vs. Tp2~37.3 K), and correspondingly two-step nonlinear V~Iα\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V \\sim {I}^{\\alpha }$$\\end{document} behavior but a concurrent Berezinskii–Kosterlitz–Thouless (BKT)-like transition occurring at TBKT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${T}_{{{{{{\\rm{BKT}}}}}}}$$\\end{document}~28.7 K. Moreover, the onset transition temperature Tconset\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${T}_{{{{{{\\rm{c}}}}}}}^{{{{{{\\rm{onset}}}}}}}$$\\end{document}~54 K and zero-resistivity temperature Tczero\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${T}_{{{{{{\\rm{c}}}}}}}^{{{{{{\\rm{zero}}}}}}}$$\\end{document}~31 K are consistent with Tp1 and TBKT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${T}_{{{{{{\\rm{BKT}}}}}}}$$\\end{document}, respectively. Our results indicate the broadened superconducting transition in FeSe/SrTiO3 is related to intrinsic electronic inhomogeneity due to distinct two-gap features and phase fluctuations of two-dimensional superconductivity.

Giant amplification of Berezinskii-Kosterlitz-Thouless transition temperature in superconducting systems characterized by cooperative interplay of small-gapped valence and conduction bands

Two-dimensional superconductors and electron-hole superfluids in van der Waals heterostructures having tunable valence and conduction bands in the electronic spectrum are emerging as rich platforms to investigate novel quantum phases and topological phase transitions. In this work, by adopting a mean-field approach considering multiple-channel pairings and the Kosterlitz-Nelson criterion, we demonstrate giant amplifications of the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature and a shrinking of the pseudogap for small energy separations between the conduction and valence bands and small density of carriers in the conduction band. The presence of the holes in the valence band, generated by intra-band and pair-exchange couplings, contributes constructively to the phase stiffness of the total system, adding up to the phase stiffness of the conduction band electrons that is boosted as well, due to the presence of the valence band electrons. This strong cooperative effect avoids the suppression of the BKT transition temperature for low density of carriers, that occurs in single-band superconductors where only the conduction band is present. Thus, we predict that in this regime, multi-band superconducting and superfluid systems with valence and conduction bands can exhibit much larger BKT critical temperatures with respect to single-band and single-condensate systems.

Field-controlled multicritical behavior and emergent universality in fully frustrated quantum magnets

Phase transitions in condensed matter are a source of exotic emergent properties. We study the fully frustrated bilayer Heisenberg antiferromagnet to demonstrate that an applied magnetic field creates a previously unknown emergent criticality. The quantum phase diagram contains four states with distinctly different symmetries, all but one pair separated by first-order transitions. We show by quantum Monte Carlo simulations that the thermal phase diagram is dominated by a wall of discontinuities extending between the dimer-triplet phases and the singlet-containing phases. This wall is terminated at finite temperatures by a critical line, which becomes multicritical where the Berezinskii-Kosterlitz-Thouless (BKT) transition of the dimer-triplet antiferromagnet and the thermal Ising transition of the singlet-triplet crystal phase also terminate. The combination of merging symmetries leads to a 4-state Potts universality not contained in the microscopic Hamiltonian, which we interpret within the Ashkin-Teller model. Our results represent a systematic step in understanding emergent phenomena in quantum magnetic materials, including the “Shastry-Sutherland compound” SrCu2(BO3)2.

In-Plane Anisotropy of Electrical Transport in Y0.85Tb0.15Ba2Cu3O7-x Films.

We fabricated high-quality c-axis-oriented epitaxial YBa2Cu3O7-x films with 15% of the yttrium atoms replaced by terbium (YTBCO) and studied their electrical properties. The Tb substitution reduced the charge carrier density, resulting in increased resistivity and decreased critical current density compared to pure YBa2Cu3O7-x films. The electrical properties of the YTBCO films showed an in-plane anisotropy in both the superconducting and normal states that, together with the XRD data, provided evidence for, at least, a partially twin-free film. Unexpectedly, the resistive transition of the bridges also demonstrated the in-plane anisotropy that could be explained within the framework of Tinkham's model of resistive transition and the Berezinskii-Kosterlitz-Thouless (BKT) model, depending on the sample parameters. Measurements of the differential resistance in the temperature range of the resistive transition confirmed the occurrence of the BKT transition in the YTBCO bridges. Therefore, we consider the YTBCO films to be a promising platform for both the fabrication of devices with high kinetic inductance and fundamental research on the BKT transition in cuprate superconductors.

Nonequilibrium phase transitions in a Brownian p-state clock model.

We introduce a Brownian p-state clock model in two dimensions and investigate the nature of phase transitions numerically. As a nonequilibrium extension of the equilibrium lattice model, the Brownian p-state clock model allows spins to diffuse randomly in the two-dimensional space of area L^{2} under periodic boundary conditions. We find three distinct phases for p>4: a disordered paramagnetic phase, a quasi-long-range-ordered critical phase, and an ordered ferromagnetic phase. In the intermediate critical phase, the magnetization order parameter follows a power-law scaling m∼L^{-β[over ̃]}, where the finite-size scaling exponent β[over ̃] varies continuously. These critical behaviors are reminiscent of the double Berezinskii-Kosterlitz-Thouless (BKT) transition picture of the equilibrium system. At the transition to the disordered phase, the exponent takes the universal value β[over ̃]=1/8, which coincides with that of the equilibrium system. This result indicates that the BKT transition driven by the unbinding of topological excitations is robust against the particle diffusion. On the contrary, the exponent at the symmetry-breaking transition to the ordered phase deviates from the universal value β[over ̃]=2/p^{2} of the equilibrium system. The deviation is attributed to a nonequilibrium effect from the particle diffusion.

Two-dimensional Rashba superconductivity in Ni/Bi bilayers evidenced by nonreciprocal transport

When two different materials are brought together, a plethora of quantum phenomena and functionalities can emerge. A prominent example is the superconductivity in Ni/Bi bilayers, which arises from the artificial layered structure composed of the non-superconducting ferromagnetic and heavy metals. Although this system has been shown to exhibit unconventional superconducting properties, the underlying mechanism of the superconductivity remains elusive. Here, we provide experimental evidence of the microscopic coexistence of two-dimensional (2D) superconductivity and broken space-inversion symmetry in the Ni/Bi bilayer. The evidence is obtained from nonreciprocal transport around the superconducting transition temperature, where the resistance depends on the direction of an applied current and an external magnetic field. We find that the nonreciprocal superconducting transport is most pronounced around the Berezinskii–Kosterlitz–Thouless transition temperature. These observations support the 2D Rashba superconductivity in the Ni/Bi bilayer, which will serve as a basis for advancing the understanding of unconventional superconductivity.

An exactly solvable model of randomly pinned charge density waves in two dimensions

The nature of the interplay between fluctuations and quenched random disorder is a long-standing open problem, particularly in systems with a continuous order parameter. This lack of a full theoretical treatment has been underscored by recent advances in experiments on charge density wave materials. To address this problem, we formulate an exactly solvable model of a two-dimensional randomly pinned incommensurate charge density wave, and use the large-N technique to map out the phase diagram and order parameter correlations. Our approach captures the physics of the Berezinskii–Kosterlitz–Thouless phase transition in the clean limit at large N. We pay particular attention to the roles of thermal fluctuations and quenched random field disorder in destroying long-range order, finding a novel crossover between weakly- and strongly-disordered regimes.

Detection of Berezinskii–Kosterlitz–Thouless transitions for the two-dimensional q-state clock models with neural networks

Detection of Berezinskii–Kosterlitz–Thouless transitions for the two-dimensional q-state clock models with neural networks

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..

Role of Inter-site Hubbard Interactions in MnS Monolayer: DFT+U+V Investigation

The stable MnS monolayer was recently predicted using first-principles density functional theory (DFT) including Hubbard U (DFT+U) correction and Monte Carlo (MC) simulations. It is shown to exhibit an indirect band gap of 0.68 eV semiconductor with a high Neel temperature (T_N) of 720 K and an in-plane easy axis magnetic anisotropy energy (MAE). The considered on-site Hubbard U correction takes into account only the Mn (3d) localized nature. To correct the inter-site errors due to strong hybridization between bonded Mn (3d) and S (2p) states, the Hubbard +V inter-site parameter should be added to the calculations. In this study, the band gap of MnS is found to be increased to 1.24 eV (twice that for DFT+U) after considering the inter-site V correction (DFT+U+V). Since the MnS monolayer prefers an in-plane easy axis for the MAE, the estimated Berezinskii Kosterlitz Thouless transition (BKT) transition temperature is as high as 1667.8 K. The carrier mobility is calculated based on the deformation potential and effective mass and it is found that holes (2.12 〖cm〗^2 v^(-1) S^(-1)) are twice the size of these electrons (1.21 〖cm〗^2 v^(-1) S^(-1)). The results are expected to improve the potential of the MnS monolayers in multiple AFM spintronic device applications.

Searching for Unconventional Superfluid in Excitons of Monolayer Semiconductors.

It is well known that two-dimensional (2D) bosons in homogeneous space cannot undergo real Bose-Einstein condensation, and the superfluid to normal phase transition is Berezinskii-Kosterlitz-Thouless (BKT) type, associated with vortex-antivortex pair unbinding. Here we point out a 2D bosonic system whose low energy physics goes beyond conventional paradigm of 2D homogeneous bosons, i.e., intralayer excitons in monolayer transition metal dichalcogenides. With intrinsic valley-orbit coupling and valley Zeeman energy, exciton dispersion becomes linear at small momentum, giving rise to a series of novel features. The critical temperature of Bose-Einstein condensation of these excitons is nonzero, suggesting true long-range order in 2D homogeneous system. The dispersion of Goldstone mode at long wavelength has the form ϵ(q)∼sqrt[q], in contrast to conventional linear phonon spectrum. The vortex energy deviates from the usual logarithmic form with respect to system size, but instead has an additional linear term. Superfluid to normal phase transition is no longer BKT type for system size beyond a characteristic scale, without discontinuous jump in superfluid density. With the recent experimental progress on exciton fluid at thermal equilibrium in monolayer semiconductors, our work points out an experimentally accessible system to search for unconventional 2D superfluids beyond BKT paradigm.

The interplay between anomalous metallic and superconducting states tuned by disorder in thin flakes of Kagome metal KV3Sb5

Recently, V-based Kagome metals have attracted intense attention due to the coexistence of their topological nontrivial electronic structure, charge density wave, and superconductivity. Here, we report the fabrication and physical investigations of single-crystalline thin flakes of the Kagome metal KV3Sb5. For samples with a thickness of , Berezinskii–Kosterlitz–Thouless type behavior is revealed by the temperature dependent resistance and voltage–current data, which indicates the presence of two-dimensional superconductivity. Meanwhile, a temperature-independent resistance behavior is observed in a wide field region, supplying the hallmark of the anomalous metallic (AM) state. Importantly, by comparing the interplay between the superconducting and AM states of two samples with different levels of disorder, a striking competitive evolution with the external field between these two states is uncovered.

Disordering complexion transition of grain boundaries in bcc metals: Insights from atomistic simulations

Complexion transitions (CTs) of grain boundaries (GBs) have been a subject of extensive discussions in the last years, but many aspects of this phenomenon are still unclear. Here we studied temperature-induced disordering transitions of GBs in several body-centered cubic metals by means of classical atomistic simulations. Our study shows that gradual heating from room temperature to the melting temperature (Tm) leads to continuous disordering of the GB structure due to spontaneous formation of point defects in all studied metals. This disordering is accompanied by two CTs and exhibits analogies to transitions described by the Berezinskii–Kosterlitz–Thouless–Halperin–Nelson–Young theory. The first CT occurs at temperatures of about 0.7Tm and is characterized by significant changes of mechanical and kinetic properties. The second CT at about 0.9Tm is a premelting transition when the GB order parameter becomes zero.

Kardar–Parisi–Zhang roughening associated with nucleation-limited steady crystal growth

The roughness of crystal surfaces and the shape of crystals play important roles in multiscale phenomena. For example, the roughness of the crystal surface affects the frictional and optical properties of materials such as ice or silica. Theoretical studies on crystal surfaces based on the symmetry principle proposed that the growing surfaces of crystal growth could be classified in the universal class of Kardar–Parisi–Zhang (KPZ), but experiments rarely observe KPZ properties. To fill this the gap, extensive numerical calculations of the crystal growth rates and the surface roughness (surface width) have been performed for a nanoscale lattice model using the Monte Carlo method. The results indicate that a (001) surface is smooth within the single nucleation growth region. In contrast, the same surface is atomically smooth but thermodynamically rough in the poly-nucleation growth region in conjunction with a KPZ roughness exponent. Inclined surfaces are known to become Berezinskii–Kosterlitz–Thouless (BKT) rough surfaces both at and near equilibrium. The two types of steps associated with the (001) and (111) terraces were found to induce KPZ surface roughness, while the interplay between steps and multilayered islands promoted BKT roughness.

Oscillating paramagnetic Meissner effect and Berezinskii-Kosterlitz-Thouless transition in underdoped Bi2Sr2CaCu2O8+δ.

Superconducting phase transitions in two dimensions lie beyond the description of the Ginzburg-Landau symmetry-breaking paradigm for three-dimensional superconductors. They are Berezinskii-Kosterlitz-Thouless (BKT) transitions of paired-electron condensate driven by the unbinding of topological excitations, i.e. vortices. The recently discovered monolayers of layered high-transition-temperature ([Formula: see text]) cuprate superconductor Bi2Sr2CaCu2O8+δ (Bi2212) meant that this 2D superconductor promised to be ideal for the study of unconventional superconductivity. But inhomogeneity posed challenges for distinguishing BKT physics from charge correlations in this material. Here, we utilize the phase sensitivity of scanning superconducting quantum interference device microscopy susceptometry to image the local magnetic response of underdoped Bi2212 from the monolayer to the bulk throughout its phase transition. The monolayer segregates into domains with independent phases at elevated temperatures below [Formula: see text]. Within a single domain, we find that the susceptibility oscillates with flux between diamagnetism and paramagnetism in a Fraunhofer-like pattern up to [Formula: see text]. The finite modulation period, as well as the broadening of the peaks when approaching [Formula: see text] from below, suggests well-defined vortices that are increasingly screened by the dissociation of vortex-antivortex plasma through a BKT transition. In the multilayers, the susceptibility oscillation differs in a small temperature regime below [Formula: see text], consistent with a dimensional crossover led by interlayer coupling. Serving as strong evidence for BKT transition in the bulk, we observe a sharp jump in phase stiffness and paramagnetism at small fields just below [Formula: see text]. These results unify the superconducting phase transitions from the monolayer to the bulk underdoped Bi2212, and can be collectively referred to as the BKT transition with interlayer coupling.

Berezinskii-Kosterlitz-Thouless transition from neural network flows.

We adopt the neural network (NN) flow method to study the Berezinskii-Kosterlitz-Thouless (BKT) phase transitions of the two-dimensional q-state clock model with q≥4. The NN flow consists of a sequence of the same units that proceed with the flow. This unit is a variational autoencoder trained by the data of Monte Carlo configurations in unsupervised learning. To gauge the difference among the ensembles of Monte Carlo configurations at different temperatures and the uniqueness of the ensemble of NN-flow states, we adopt the Jensen-Shannon divergence (JSD) as the information-distance measure "thermometer." This JSD thermometer compares the probability distribution functions of the mean spin value of two ensembles of states. Our results show that the NN flow will flow an arbitrary spin state to some state in a fixed-point ensemble of states. The corresponding JSD of the fixed-point ensemble takes a unique profile with peculiar features, which can help to identify the critical temperatures of BKT phase transitions of the underlying Monte Carlo configurations.

Berezinskii—Kosterlitz—Thouless correlations in copper-based quasi-2D spin systems (Review Article)

We present an overview of selected copper-based quasi-2D square-lattice spin-1/2 materials with an easy-plane anisotropy, providing the possibility to study emergent Berezinskii-Kosterlitz-Thouless (BKT) correlations. In particular, in those materials with a comparatively small exchange coupling, the effective XY anisotropy of the low-temperature spin correlations can be controlled by an applied magnetic field, yielding a systematic evolution of the BKT correlations. In cases where the residual interlayer correlations are small enough, dynamical BKT correlations in the critical regime may be observed experimentally, whereas the completion of the genuine BKT transition is preempted by the onset of long-range order.

Observation of a magnetic phase transition in monolayer NiPS3

Monolayer magnet of $\mathit{XY}$ type composes a pivotal part of the two-dimensional magnetism. As an important suspected $\mathit{XY}$-type antiferromagnet, whether $1L \mathrm{NiP}{\mathrm{S}}_{3}$ exhibits magnetic order remains elusive. Herein by helicity-resolved Raman and ultrafast spectroscopy of $\mathrm{NiP}{\mathrm{S}}_{3}$ from bulk to monolayer, we find that $1L \mathrm{NiP}{\mathrm{S}}_{3}$ is magnetically ordered with a Berezinskii-Kosterlitz-Thouless (BKT) transition at ${T}_{\mathrm{BKT}}\ensuremath{\approx}140$ K. We have also performed large-scale density-matrix renormalization-group calculations to verify the ground state zigzag antiferromagnetic order and Monte Carlo simulation to confirm the BKT-transition temperature in $1L \mathrm{NiP}{\mathrm{S}}_{3}$. Our investigations establish $1L \mathrm{NiP}{\mathrm{S}}_{3}$ to be an $\mathit{XY}$ antiferromagnet with a relatively high-temperature BKT transition, providing an important platform for investigating complex couplings and topological excitations.

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.