Kosterlitz-Thouless Research Articles

Superconductivity in the pressurized nickelate La3Ni2O7 in the vicinity of a BEC–BCS crossover

Ever since the discovery of high-temperature superconductivity in cuprates, gaining microscopic insights into the nature of pairing in strongly correlated systems has remained one of the greatest challenges in modern condensed matter physics. Following recent experiments reporting superconductivity in the bilayer nickelate La3Ni2O7 (LNO) with remarkably high critical temperatures of Tc = 80 K, it has been argued that the low-energy physics of LNO can be described by the strongly correlated, mixed-dimensional bilayer t–J model. Here we investigate this bilayer system and utilize density matrix renormalization group techniques to establish a thorough understanding of the model and the magnetically induced pairing through comparison to the perturbative limit of dominating inter-layer spin couplings. In particular, this allows us to explain appearing finite-size effects, firmly establishing the existence of long-range superconducting order in the thermodynamic limit. By analyzing binding energies, we predict a BEC–BCS crossover as a function of the Hamiltonian parameters. We find large binding energies of the order of the inter-layer coupling that suggest strikingly high critical temperatures of the Berezinskii–Kosterlitz–Thouless transition, raising the question of whether (mixD) bilayer superconductors possibly facilitate critical temperatures above room temperature.

Novel B6P6X (X=As, Sb) monolayers for antiferromagnetic spintronics and hydrogen storage

Embedding foreign atoms into porous two-dimensional (2D) materials has emerged as a promising strategy to tailor their electronic, magnetic, and adsorption properties, enabling promising applications in energy storage and spintronics devices. In this work, spin-polarized density functional theory (DFT) calculations were employed to investigate the ground state properties and hydrogen (H2) storage of interstitially X = As and Sb atom doped B6P6 (B6P6X) graphenylene monolayers. The resulting B6P6X (X = As, Sb) monolayers exhibit very good mechanical, dynamical, and thermal stabilities with antiferromagnetic (AFM) ground states. Electronic structure calculations reveal AFM semiconducting behavior for both monolayers, with indirect/direct band gaps of 0.71/0.60 eV (PBE) and 2.19/2.14 eV (HSE06) for B6P6As/B6P6Sb, respectively. All B6P6X monolayers exhibit an in-plane easy magnetization axis. The obtained Berezinskii-Kosterlitz–Thouless transition (BKT) temperature value of B6P6Sb monolayer is 268.74 K. Furthermore, the H2 storage capabilities of these B6P6X monolayers were examined. We find that B6P6As and B6P6Sb monolayers can each adsorb up to 48H2 molecules with an average adsorption energy (Ea) of -0.14 eV/H2. The corresponding H2 storage gravimetric capacities are 6.91 wt% for B6P6As@48H2 and 6.10 wt% for B6P6As@48H2, surpassing the U.S. Department of Energy’s 2025 target of 5.50 wt%. These findings highlighting the potential of B6P6X (X = As, Sb) monolayers for AFM spintronics and H2 storage applications.

Bounds on the superconducting transition temperature

I summarize recent progress on obtaining rigorous upper bounds on superconducting transition temperature [Formula: see text] in two dimensions independent of pairing mechanism or interaction strength. These results are derived by finding a general upper bound for the superfluid stiffness for a multi-band system with arbitrary interactions, with the only assumption that the external vector potential couples to the kinetic energy and not to the interactions. This bound is then combined with the universal relation between the superfluid stiffness and the Berezinskii–Kosterlitz–Thouless [Formula: see text] in 2D. For parabolic dispersion, one obtains the simple result that [Formula: see text], which has been tested in recent experiments. More generally, the bounds are expressed in terms of the optical spectral weight and lead to stringent constraints for the [Formula: see text] of low-density, strongly correlated superconductors. Results for [Formula: see text] bounds for models of flat-band superconductors, where the kinetic energy vanishes and the vector potential must couple to interactions, are briefly summarized. Upper bounds on [Formula: see text] in 3D remains an open problem, and I describe how questions of universality underlie the challenges in 3D.

Generalized XY Models with Arbitrary Number of Phase Transitions

We propose spin models that can display an arbitrary number of phase transitions. The models are based on the standard XY model, which is generalized by including higher-order nematic terms with exponentially increasing order and linearly increasing interaction strength. By employing Monte Carlo simulation we demonstrate that under certain conditions the number of phase transitions in such models is equal to the number of terms in the generalized Hamiltonian and, thus, it can be predetermined by construction. The proposed models produce the desirable number of phase transitions by solely varying the temperature. With decreasing temperature the system passes through a sequence of different phases with gradually decreasing symmetries. The corresponding phase transitions start with a presumably BKT transition that breaks the U(1) symmetry of the paramagnetic phase, and they proceed through a sequence of discrete Z2 symmetry-breaking transitions between different nematic phases down to the lowest-temperature ferromagnetic phase.

Measurements of fluctuation-induced in-plane magneto-conductivity of granular aluminum film

The phenomenon of Berezinskii–Kosterlitz–Thouless (BKT) phase fluctuations and the superconducting fluctuations is investigated in a 40 nm thick granular aluminum film using magneto-transport measurements. The transport measurements suggest the possibility of strong electron–phonon (el–ph) interactions in contrast to a Bardeen–Cooper–Schrieffer superconductor. It shows a BKT transition of 2.304 K and a superconducting mean-field transition at 2.32 K. The presence of the resistive tail even before the BKT transition reflects the abundance of thermally activated free vortices. By analyzing the excess conductivity, Gaussian–Ginzburg–Landau superconducting fluctuations are observed above the superconducting transition, which causes rounding of the transition region even before the superconducting transition. The temperature dependence of the fluctuation conductivity in zero magnetic field exhibits distinct signatures of the two-dimensional direct Aslamazov–Larkin theory, with a significant contribution from the Maki–Thompson (MT) model. Furthermore, the anomalous behavior of the fluctuation conductivity at higher temperatures and perpendicular magnetic fields (up to 700 mT) is explained in terms of the total-energy cutoff (=0.72) in the low-wavelength region of the superconducting fluctuations and a pair-breaking parameter (∼0.031). Further studies on the pair-breaking parameter indicate the presence of the el–ph scattering, which diminishes the MT contribution. Our study carries important bearings on how the BKT phase fluctuations and superconducting amplitude fluctuations control the conductivity of granular superconductor near and above the transition region as non-equilibrium properties of weakly disordered granular superconductors. This research is of significance, offering insights into the fundamental properties of granular superconductivity and aiding in the comprehension of nano-structured thin film devices.

Berezinskii–Kosterlitz–Thouless Transition of the Two-Dimensional XY Model on the Honeycomb Lattice

Abstract The Berezinskii–Kosterlitz–Thouless (BKT) transition of the two-dimensional $XY$ model on the honeycomb lattice is investigated using both the techniques of Neural network (NN) and Monte Carlo simulations. It is demonstrated in the literature that, with certain plausible assumptions, the associated critical temperature $T_{\text{BKT,H}}$ is found to be ${1}/{\sqrt{2}}$ exactly. Surprisingly, the value of $T_{\text{BKT,H}}$ obtained from our NN calculations is 0.572(3), which deviates significantly from ${1}/{\sqrt{2}}$. In addition, based on the helicity modulus, the $T_{\text{BKT,H}}$ determined is 0.576(4), agreeing well with that resulting from the NN estimation. It will be interesting to carry out a more detailed analytic calculation to obtain a theoretical value consistent with the numerical result reached here.

Stability, electronic and magnetic properties of boronphosphide (BP) graphenylene induced by interstitial atomic doping

In the context of low-dimensional materials, incorporating foreign atoms through doping processes has the potential to modulate the properties of host materials, which is favorable for diverse functional applications. In this study, we introduce a series of six distinct B6P6X ternary graphenylene monolayers. The B6P6X is designed through interstitial X = Cl, Br, I, O, S, and Te atomic doping of pure BP graphenylene. Through spin-polarized density functional theory (DFT), we comprehensively investigate the stability, electronic, and magnetic properties of B6P6X monolayers. We demonstrate that B6P6X monolayers are mechanically, dynamically and thermally stable with ferromagnetic ground state properties. We show that the metallic features of B6P6X (X = Cl, Br, I, O, S) and half-metallic property of B6P6Te monolayers at the PBE level can be further modulated when subjected to the HSE06 level. It is revealed that the B6P6X (X = O, S) monolayers exhibit a sizeable magnetic moment and a large magnetic anisotropy energy (MAE) value with an easy out-of-plane magnetization axis. We also found an out-of-plane MAE magnetization axis for B6P6X (X = Br, I) monolayers and an in-plane easy magnetization axis for B6P6X (X = Cl, Te) monolayers. Further investigation show that the B6P6S monolayer exhibit above room-temperature TC up to 565 K. The estimated Berezinskii–Kosterlitz–Thouless transition (BKT) temperature value of B6P6Te monolayer is 254 K. Our findings show that the B6P6X monolayers, particularly doped with chalcogens are potential candidates for nanoscale electronics and spintronics applications.

Coulomb universality.

Motivated by a number of realizations of long-range interacting systems, including ultracold atomic and molecular gases, we study a neutral plasma with power-law interactions longer ranged than Coulombic. We find that beyond a crossover length, such interactions are universally screened down to a standard Coulomb form in all spatial dimensions. This implies, counterintuitively, that in two dimensions and below, such a "super-Coulombic" gas is asymptotically Coulombically confining at low temperatures. At higher temperatures, the plasma undergoes a deconfining transition that in two dimensions is the same Kosterlitz-Thouless transition that occurs in a conventional Coulomb gas, but at an elevated temperature that we calculate. We also predict that, in contrast, above two dimensions, even when naively the bare potential is confining, there is no confined phase of the plasma at any nonzero temperature. In addition, the super-Coulomb to Coulomb crossover is followed at longer length scales by an unconventional "Debye-Huckel" screening, which leads to faster-than-Coulombic, power-law decay of the screened potential, in contrast to the usual exponentially decaying Yukawa potential. Furthermore, we show that power-law potentials that fall off more rapidly than Coulomb are screened down to a shorter-ranged power law rather than an exponential Debye-Huckel Yukawa form. We expect these prediction to be testable in simulations and hope they will inspire experimental studies in various platforms.

Study of the Berezinskii–Kosterlitz–Thouless transition: an unsupervised machine learning approach

The Berezinskii–Kosterlitz–Thouless (BKT) transition in magnetic systems is an intriguing phenomenon, and estimating the BKT transition temperature is a long-standing problem. In this work, we explore anisotropic classical Heisenberg XY and XXZ models with ferromagnetic exchange on a square lattice and antiferromagnetic exchange on a triangular lattice using an unsupervised machine learning approach called principal component analysis (PCA). The earlier PCA studies of the BKT transition temperature ( TBKT ) using the vorticities as input fail to give any conclusive results, whereas, in this work, we show that the proper analysis of the first principal component-temperature curve can estimate TBKT which is consistent with the existing literature. This analysis works well for the anisotropic classical Heisenberg with a ferromagnetic exchange on a square lattice and for frustrated antiferromagnetic exchange on a triangular lattice. The classical anisotropic Heisenberg antiferromagnetic model on the triangular lattice has two close transitions: the TBKT and Ising-like phase transition for chirality at Tc , and it is difficult to separate these transition points. It is also noted that using the PCA method and manipulation of their first principal component not only makes the separation of transition points possible but also determines transition temperature.

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).

Binder Parameter in a Generalized Two-dimensional XY Model

We performed Monte Carlo simulation for a two-dimensional generalized XY model and calculated the magnetic and nematic Binder parameters. The phase diagram is re-examined based on these Binder parameters, demonstrating their power in studying generalized XY models. The Binder parameter has distinctive behaviors, resulting in different types of phase transition. More importantly, the magnetic Binder parameter gives more insights into the tricritical region where the Kosterlitz-Thouless, Ising, and 1/2 Kosterlitz-Thouless (KT) transition lines meet. It shows signatures for the intermediate region starting from the tricritical point, where the transition line is neither the same physics as the Ising transition below nor the KT transition far above the tricritical point.

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.

Symmetry breaking at a topological phase transition

Spontaneous symmetry breaking is a foundational concept in physics. In condensed matter, it characterizes conventional continuous phase transitions but is absent at topological phase transitions such as the Berezinskii–Kosterlitz–Thouless (BKT) transition—as in the BKT case the expected norm (i.e., the magnitude) of the U(1) order parameter vanishes in the thermodynamic limit at all nonzero temperatures. Phenomena consistent with low-temperature broken symmetry have been observed, however, in many different BKT experiments. Examples include recent experiments on superconducting films and the seminal work on two-dimensional arrays of Josephson junctions. While the inaccessibility of the above thermodynamic limit partially explains this paradox in finite systems, the full dynamical framework of symmetry breaking at the BKT transition remains unresolved. Here we provide this by introducing the broader concept of . This encompasses both spontaneous symmetry breaking and the BKT case by allowing the expected norm of the order parameter to go to zero in the thermodynamic limit, provided its directional phase fluctuations are asymptotically smaller. We demonstrate this asymptotically slow directional mixing in the low-temperature BKT phase. This explicitly shows that the order parameter arbitrarily chooses some well-defined direction in the thermodynamic limit, predicting negligible phase fluctuations compared to the expected norm in arbitrarily large experimental BKT systems. Our results provide a model for directional mixing timescales across the diverse array of experimental BKT systems. We suggest various experiments. Published by the American Physical Society 2024

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.

Ground-state phase diagram and universality of sequential topological valence-bond-solid quantum transitions in a mixed tetramer chain

The ground-state ordering of a quantum mixed-spin Heisenberg tetramer chain composed of an alternate sequence of s = 1 and S=3/2 dimers is studied in detail as a function of two considered exchange interactions ascribed to similar and dissimilar spin pairs. At zero magnetic field, the ferrimagnetic mixed spin-(1, 1, 3/2, 3/2) Heisenberg tetramer chain displays, depending on a mutual interplay between two considered exchange interactions, three distinct gapped valence-bond-solid phases separated by gap-closing quantum critical points. Using density-matrix renormalization group calculations we construct the full ground-state phase diagram as a function of the interaction ratio and magnetic field, which exhibits besides three gapped valence-bond-solid phases special Kosterlitz–Thouless and topological quantum critical points. A tangential finite-size scaling analysis is employed to obtain precise estimates of the zero-field valence-bond-solid transitions and unveil their common logarithmic correction to a power-law scaling of the correlation length.

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.

MXene Fe2C as a promising candidate for the 2D XY ferromagnet

Monolayer Fe2C is expected to possess strong electronic correlations, which can significantly contribute to electronic and magnetic properties. In this study we consider electronic and magnetic properties of MXene Fe2C within the DFT+DMFT approach. We establish the existence of local magnetic moments in this compound, characterized by sufficiently long lifetime of fs. We also calculate exchange interaction parameters accounting for electronic correlations using the recently developed approach for paramagnetic phase. At low temperatures, we obtain the strongest exchange interaction 11 meV between next nearest neighboring Fe atoms, located above (or below) the carbon plane, and the subleading interaction 6 meV between the next to next nearest neighboring atoms, located across the carbon plane. The resulting dependence of the Berzinskii–Kosterlitz–Thouless (BKT) and Curie temperatures on magnetic anisotropy is obtained. The BKT temperature for the pristine Fe2C is K, which makes this compound a good candidate for the two-dimensional ferromagnet with XY anisotropy.

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.

Critical line of the triangular Ising antiferromagnet in a field from a C_{3}-symmetric corner transfer matrix algorithm.

The corner transfer matrix renormalization group (CTMRG) algorithm has been extensively used to investigate both classical and quantum two-dimensional (2D) lattice models. The convergence of the algorithm can strongly vary from model to model depending on the underlying geometry and symmetries, and the presence of algebraic correlations. An important factor in the convergence of the algorithm is the lattice symmetry, which can be broken due to the necessity of mapping the problem onto the square lattice. We propose a variant of the CTMRG algorithm, designed for models with C_{3}-symmetry, which we apply to the conceptually simple yet numerically challenging problem of the triangular lattice Ising antiferromagnet in a field, at zero and low temperatures. We study how the finite-temperature three-state Potts critical line in this model approaches the ground-state Kosterlitz-Thouless transition driven by a reduced field (h/T). In this particular instance, we show that the C_{3}-symmetric CTMRG leads to much more precise results than both existing results from exact diagonalization of transfer matrices and Monte Carlo.