Model Of Superconductivity Research Articles

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.

Nonminimal coupling holographic superconductors

We explore a holographic superconductor model in which a real scalar field is nonminimally coupled to a gauge field. We consider several types of the nonminimal coupling function h(ψ) including exponential, hyperbolic (cosh), power-law, and fractional forms. We investigate the influences of the nonminimal coupling parameter α on condensation, critical temperature, and conductivity. We can categorize our results in two groups. In the first group, conductor/superconductor phase transition is easier to occur for larger values of α, while in the second group stronger effects of the nonminimal coupling makes the formation of scalar hair harder. Although the real and imaginary parts of conductivity are impressed by different forms of h(ψ), they follow some universal behaviors such as connecting with each other through Kramers–Kronig relation in ω → 0 limit or the appearance of gap frequency at low temperatures around ωg ∼ 8 Tc, which shifts to larger values by increasing the strength of α. Among all forms of h(ψ) we observe that h(ψ) = 1 + αψ2 gives us better information in wide range of nonminimal coupling constant and temperature. Choosing the best form of h(ψ), we construct a family of solutions for holographic conductor/superconductor phase transitions to discover the effect of the hyperscaling violation when the gauge and scalar fields are nonminimally coupled. we find that the critical temperature increases for higher effects of hyperscaling violation θ and nonminimal coupling constant α. By increasing these two parameters, we obtain lower values of condensation which means that conductor/superconductor phase transition will acquire easier. Furthermore, we understand that the hyperscaling violation affects the conductivity σ of the holographic superconductors and changes the expected relation in the gap frequency. Some universal behaviors like infinite DC conductivity are observed. In addition, we consider a five-dimensional Gauss–Bonnet (GB) black hole with a flat horizon. We find out that the critical temperature decreases for larger values of GB coupling constant, λ, or smaller values of nonminimal coupling constant, α, which means that the condensation is harder to form. Moreover, we study the electrical conductivity in the holographic setup. We observe that the gap frequency shifts to larger values for stronger λ, and becomes flat by increasing α.

Electromagnetic-thermal modeling of high-temperature superconducting coils with homogenized method and different formulations: a benchmark

Abstract High-temperature superconducting coils are used in various large-scale
applications, like rotating machines and high-field magnets. However, modeling
these coils is a complicated and time-consuming process, especially due to the non-
linearity of the current-voltage characteristics of the superconductors and the complex
multiphysics involved. In this work, we used a fast homogenized method to model
the coupled electromagnetic and electrothermal properties of racetrack and pancake
coils for different applications. For this purpose, various formulations wielding
homogenization methods are used and benchmarked with each other, as well as with
models considering the detailed structure of the HTS tapes. We observe a very good
agreement between different models (homogenized and detailed), and we discuss the
pros and cons of the inclusion of insulating layers between the turns in homogenization.
This work was performed under the collaboration of the COST action modeling teams
and can be used as a review of the state-of-the-art superconductor modeling techniques,
and a source for the development and benchmark of future numerical methods.

One-dimensional Z4 topological superconductor

We describe the mean-field model of a one-dimensional topological superconductor with two orbitals per unit cell. Time-reversal symmetry is absent, but a nonsymmorphic symmetry, involving a translation by a fraction of the unit cell, mimics the role of time-reversal symmetry. As a result, the topological superconductor has Z4 topological phases, two that support Majorana bound states and two that do not, in agreement with a prediction based on K-theory classification [K. Shiozaki, M. Sato, and K. Gomi, ]. As with the Kitaev chain, the presence of Majorana bound states gives rise to the 4π-periodic Josephson effect. A random matrix with nonsymmorphic time-reversal symmetry may be block diagonalized, and every individual block has time-reversal symmetry described by one of the Gaussian orthogonal, unitary, or symplectic ensembles. We show how this is manifested in the energy level statistics of a random system in the Z4 class as the spatial period of the nonsymmorphic symmetry is varied from much less than to of the order of the system size. Published by the American Physical Society 2024

Coupled axial and transverse currents method for finite element modelling of periodic superconductors

In this paper, we propose the Coupled Axial and Transverse currents (I) (CATI) method, as an efficient and accurate finite element approach for modelling the electric and magnetic behavior of periodic composite superconducting conductors. The method consists of a pair of two-dimensional models coupled via circuit equations to account for the conductor geometrical periodicity. This allows to capture three-dimensional effects with two-dimensional models and leads to a significant reduction in computational time compared to conventional three-dimensional models. After presenting the method in detail, we verify it by comparison with reference finite element models, focussing on its application to twisted multifilamentary superconducting strands. In particular, we show that the CATI method captures the transition from uncoupled to coupled filaments, with accurate calculation of the interfilament coupling time constant. We then illustrate the capabilities of the method by generating detailed loss maps and magnetization curves of given strand types for a range of external transverse magnetic field excitations, with and without transport current.

A study of layered holographic superconductor

We have investigated a holographic model of a multi-layered superconductor in (2+1)-dimensions using the AdS/CFT correspondence. This correspondence allows us to study strongly interacting condensed matter systems through a weakly interacting gravitational theory. Our study focused on the effects of a finite system size on the superconductor’s properties. We observed significant variations in the critical temperature and critical magnetic field depending on the number of layers and the spacing between them. Notably, our results capture the transition from a two-dimensional (2D) to a three-dimensional (3D) behavior in the limit of a large number of closely spaced layers. This transition signifies a change in how the superconductivity operates within real material.

A comprehensive machine learning-based investigation for the index-value prediction of 2G HTS coated conductor tapes

Index-value, or so-called n-value prediction is of paramount importance for understanding the superconductors’ behaviour specially when modeling of superconductors is needed. This parameter is dependent on several physical quantities including temperature, the magnetic field’s density and orientation, and affects the behaviour of high-temperature superconducting devices made out of coated conductors in terms of losses and quench propagation. In this paper, a comprehensive analysis of many machine learning (ML) methods for estimating the n-value has been carried out. The results demonstrated that cascade forward neural network (CFNN) excels in this scope. Despite needing considerably higher training time when compared to the other attempted models, it performs at the highest accuracy, with 0.48 root mean squared error (RMSE) and 99.72% Pearson coefficient for goodness of fit (R-squared). In contrast, the rigid regression method had the worst predictions with 4.92 RMSE and 37.29% R-squared. Also, random forest, boosting methods, and simple feed forward neural network can be considered as a middle accuracy model with faster training time than CFNN. The findings of this study not only advance modeling of superconductors but also pave the way for applications and further research on ML plug-and-play codes for superconducting studies including modeling of superconducting devices.

Crossover from clean to dirty superconducting limit in YBCO films with modulated disorder

Magnetotransport measurements have been carried out for pristine and irradiated Y Ba2Cu3O7−x films. The measurements reveal a crossover from the clean superconducting limit to the dirty one with an increase in the impurity scattering rate Γ produced by a certain dose of irradiation. For the clean limit, the critical temperature Tc0 decreases with Γ, while the initial slope K=|dHc2/dT|Tc0 increases. We find a nice agreement between these experimental data and a model of d-wave superconductors with anisotropic impurity scattering. Such dose-dependencies of Tc0 and K reveal the superconducting coherence length ξ0 to be quasi-invariant in the clean limit. For the dirty limit, ξ0 increases with Γ due to a decrease in both the quantities Tc0 and K. Though, this decrease appears slower than predicted by the textbook picture of d-wave superconductors. Such discrepancy can be produced by an irradiation-induced modulated disorder responsible for the formation of (d+s)-wave pairing.

Non-homogeneous pairing in disordered two-orbital s-wave superconductors

We investigate the effects of non-magnetic disorder in a hybridized two-dimensional two-orbital s-wave superconductor (SC) model. The situation in which electronic orbitals overlap such that the hybridization among them is antisymmetric, under inversion symmetry, was taken into account. The on-site disorder is given by a random impurity potential W. We find that while the random disorder acts to the detriment of superconductivity, hybridization proceeds to favor it. Accordingly, hybridization plays an important role in two-orbital models of superconductivity, in order to hold the long-range order against the increase of disorder. This makes the present model eligible to describe real materials, since the hybridization may be induced by pressure or doping. In addition, the regime from moderate to strong disorder reveals that the system is broken into SC islands with correlated local order parameters. These correlations persist to distances of several order lattice spacing which corresponds to the size of the SC-Islands.

Investigation of anisotropic upper critical magnetic field in two-band model for the copper-based superconductors $$\mathbf {YBa_{2}Cu_{4}O_{8}}$$ and $$\mathbf {Bi_{2}Sr_{2}CaCu_{2}O_{8}}$$

Investigation of anisotropic upper critical magnetic field in two-band model for the copper-based superconductors $$\mathbf {YBa_{2}Cu_{4}O_{8}}$$ and $$\mathbf {Bi_{2}Sr_{2}CaCu_{2}O_{8}}$$

Experimental demonstration of position-controllable topological interface states in high-frequency Kitaev topological integrated circuits

Topological integrated circuits are integrated-circuit realizations of topological systems. Here we show an experimental demonstration by taking the case of the Kitaev topological superconductor model. An integrated-circuit implementation enables us to realize high resonant frequency as high as 13GHz. We explicitly observe the spatial profile of a topological edge state. In particular, the topological interface state between a topological segment and a trivial segment is the Majorana-like state. We construct a switchable structure in the integrated circuit, which enables us to control the position of a Majorana-like interface state arbitrarily along a chain. Our results contribute to the development of topological electronics with high frequency integrated circuits.

Holographic entanglement entropy with Power-Maxwell electrodynamics in higher dimensional AdS black hole spacetime* *Supported by the National Natural Science Foundation of China (11665015), the Guizhou Provincial Science and Technology Planning Project of China (qiankehejichu-ZK[2021]yiban026), and the Guizhou Province ordinary institutions of higher learning top science and technology talents Support plan of China (qianjiaoheKY[2019]062).

We investigate the behaviors of the scalar operator and holographic entanglement entropy in the metal/superconductor phase transition with Power-Maxwell electrodynamics in a higher dimensional background away from the probe limit. We observe that the larger parameters b and q make the condensation of the scalar operator more difficult, and the critical temperature decreases more slowly as the factors increase. In the belt geometry, the value of the entanglement entropy in the metal and superconductor phases is not only related to the the strength of the Power-Maxwell field but also to the width of the strip geometry. At the phase transition point, the discontinuous slope of entanglement entropy is universal for different model factors. It turns out that holographic entanglement entropy is a powerful tool to probe the properties of the phase transition in this holographic superconductor model.

$H$-$\phi$ Formulation in Sparselizard Combined With Domain Decomposition Methods for Modeling Superconducting Tapes, Stacks, and Twisted Wires

The growing interest in the modeling of superconductors has led to the development of effective numerical methods and software. One of the most utilized approaches for magnetoquasistatic simulations in applied superconductivity is the $H$ formulation. However, due to the large number of degrees of freedom (DOFs) present when modeling large and complex systems (e.g. large coils for fusion applications, electrical machines, and medical applications) using the standard $H$ formulation on a desktop machine becomes infeasible. The $H$ formulation solves the Faraday's law formulated in terms of the magnetic field intensity $\mathbf{H}$ using edge elements in the whole modeling domain. For this reason, a very high resistivity is assumed for the non-conducting domains, leading to an ill-conditioned system matrix and therefore long computation times. In contrast, the $H$-$\phi$ formulation uses the $H$ formulation in the conducting region, and the $\phi$ formulation (magnetic scalar potential) in the surrounding non-conducting domains, drastically reducing DOFs and computation time. In this work, we use the $H$-$\phi$ formulation in 2D for the magnetothermal (AC losses and quench) analysis of stacks of REBCO tapes. The same approach is extended to a 3D case for the AC loss analysis of a twisted superconducting wire. All the results obtained by simulations in Sparselizard are compared with results obtained with COMSOL. Our custom tool allows us to distribute the simulations over hundreds of CPUs using domain decomposition methods, considerably reducing the simulation times without compromising accuracy.

Preliminary Tc Calculations for Iron-Based Superconductivity in NaFeAs, LiFeAs, FeSe and Nanostructured FeSe/SrTiO3 Superconductors.

Many theoretical models of iron-based superconductors (IBSC) have been proposed, but the superconducting transition temperature (Tc) calculations based on these models are usually missing. We have chosen two models of iron-based superconductors from the literature and computed the Tc values accordingly; recently two models have been announced which suggest that the superconducting electron concentration involved in the pairing mechanism of iron-based superconductors may have been underestimated and that the antiferromagnetism and the induced xy potential may even have a dramatic amplification effect on electron-phonon coupling. We use bulk FeSe, LiFeAs and NaFeAs data to calculate the Tc based on these models and test if the combined model can predict the superconducting transition temperature (Tc) of the nanostructured FeSe monolayer well. To substantiate the recently announced xy potential in the literature, we create a two-channel model to separately superimpose the dynamics of the electron in the upper and lower tetrahedral plane. The results of our two-channel model support the literature data. While scientists are still searching for a universal DFT functional that can describe the pairing mechanism of all iron-based superconductors, we base our model on the ARPES data to propose an empirical combination of a DFT functional for revising the electron-phonon scattering matrix in the superconducting state, which ensures that all electrons involved in iron-based superconductivity are included in the computation. Our computational model takes into account this amplifying effect of antiferromagnetism and the correction of the electron-phonon scattering matrix, together with the abnormal soft out-of-plane lattice vibration of the layered structure. This allows us to calculate theoretical Tc values of LiFeAs, NaFeAs and FeSe as a function of pressure that correspond reasonably well to the experimental values. More importantly, by taking into account the interfacial effect between an FeSe monolayer and its SrTiO3 substrate as an additional gain factor, our calculated Tc value is up to 91 K and provides evidence that the strong Tc enhancement recently observed in such monolayers with Tc reaching 100 K may be contributed from the electrons within the ARPES range.

Deep Generative Model for Inverse Design of High-Temperature Superconductor Compositions with Predicted Tc > 77 K.

Identifying new superconductors with high transition temperatures (Tc > 77 K) is a major goal in modern condensed matter physics. The inverse design of high Tc superconductors relies heavily on an effective representation of the superconductor hyperspace due to the underlying complexity involving many-body physics, doping chemistry and materials, and defect structures. In this study, we propose a deep generative model that combines two widely used machine learning algorithms, namely, the variational auto-encoder (VAE) and the generative adversarial network (GAN), to systematically generate unknown superconductors under the given high Tc condition. After training, we successfully identified the distribution of the representative hyperspace of superconductors with different Tc, in which many superconductor constituent elements were found adjacent to each other with their neighbors in the periodic table. Equipped with the conditional distribution of Tc, our deep generative model predicted hundreds of superconductors with Tc > 77 K, as predicted by the published Tc prediction models in the literature. For the copper-based superconductors, our results reproduced the variation in Tc as a function of the Cu concentration and predicted an optimal Tc = 129.4 K, when the Cu concentration reached 2.41 in Hg0.37Ba1.73Ca1.18Cu2.41O6.93Tl0.69. We expect that such an inverse design model and comprehensive list of potential high Tc superconductors would greatly facilitate future research activities in superconductors.

Finite-temperature dynamical quantum phase transition in a non-Hermitian system

We investigate the interplay between the non-Hermiticity and finite temperature in the context of mixed state dynamical quantum phase transition (MSDQPT). We consider a $p$-wave superconductor model, encompassing complex hopping and non-Hermiticity that can lead to gapless phases in addition to gapped phases, to examine the MSDQPT and winding number via the intra-phase quench. We find that the MSDQPT is always present irrespective of the gap structure of the underlying phase, however, the profile of Fisher zeros changes between the above phases. Such occurrences of MSDQPT are in contrast to the zero-temperature case where DQPT does not take place for the gapped phase. Surprisingly, the half-integer jumps in winding number at zero-temperature are washed away for finite temperature in the gapless phase. We study the evolution of the minimum time required by the system to experience MSDQPT with the inverse temperature such that gapped and gapless phases can be differentiated. Our study indicates that the minimum time shows monotonic (non-monotonic) behavior for the gapped (gapless) phase.

Classical Majorana-like zero modes in an acoustic Kitaev chain

The one-dimensional Kitaev chain, being one of the most significant superconductor models that support Majorana fermions, has been considered as a highly probable method to host nonlocal qubits for topological quantum computation. Here we theoretically introduce the concept into the classical-wave systems and report the first experimental prototype of the acoustic Kitaev chain. We rigorously demonstrate the acoustic correspondence of the Kitaev chain and experimentally observe the classical unpaired Majorana-like zero mode in a well-designed acoustic spinless $p$-wave superconductor. In particular, clear physical evidence also demonstrates such exotic acoustic modes can be manipulated to a certain extend like a quasiparticle, which is directly identified by employing a Kitaev ``keyboard.'' These results are expected to open new avenues for novel applications of topological acoustics.

Electron-Hole Asymmetry of Quantum Collective Excitations in High-Tc Copper Oxides

We carry out a systematic study of collective spin- and charge excitations for the canonical single-band Hubbard, $t$-$J$-$U$, and $t$-$J$ models of high-temperature copper-oxide superconductors, both on electron- and hole-doped side of the phase diagram. Recently developed variational wave function approach, combined with the expansion in inverse number of fermionic flavors, is employed. All three models exhibit a substantial electron-hole asymmetry of magnetic excitations, with a robust paramagnon emerging for hole-doping, in agreement with available resonant inelastic $x$-ray scattering data for the cuprates. The $t$-$J$ model yields additional high-energy peak in the magnetic spectrum that is not unambiguously identified in spectroscopy. For all considered Hamiltonians, the dynamical charge susceptibility contains a coherent mode for both hole- and electron doping, with overall bandwidth renormalization controlled by the on-site Coulomb repulsion. Away from the strong-coupling limit, the antiferromagnetic ordering tendency is more pronounced on electron-doped side of the phase diagram.

Topological characterization and stability of Floquet Majorana modes in Rashba nanowires

We theoretically investigate a practically realizable Floquet topological superconductor model based on a one-dimensional Rashba nanowire and proximity-induced $s$-wave superconductivity in the presence of a Zeeman field. The driven system hosts regular 0-Majorana end modes and anomalous $\ensuremath{\pi}$-Majorana end modes (MEMs). By tuning the chemical potential and the frequency of the drive, we illustrate the generation of multiple MEMs in our theoretical setup. We utilize the chiral symmetry operator to topologically characterize these MEMs via a dynamical winding number constructed out of the periodized evolution operator. Interestingly, the robustness of the 0- and $\ensuremath{\pi}$-MEMs is established in the presence of on-site time-independent random disorder potential. We employ the twisted boundary condition to define the dynamical topological invariant for this translational-symmetry broken system. The interplay between the Floquet driving and the weak disorder can stabilize the MEMs, giving rise to a quantized value of the dynamical winding number for a finite range of drive parameters. This observation might be experimentally helpful in scrutinizing the topological nature of the Floquet MEMs. We showcase another driving protocol, namely, a periodic kick in the chemical potential, to study the generation of Floquet MEMs in our setup. Our work paves a realistic way to engineer multiple MEMs in a driven system.

Inner skin effects on non-Hermitian topological fractals

Non-Hermitian (NH) crystals, quasicrystals, and amorphous network display an accumulation of a macroscopic number of states near one of its specific interfaces with vacuum, such as edge, surface, hinge, or corner. This phenomenon is known as the NH skin effect, which can only be observed with open boundary condition. In this regard self-similar fractals, manifesting inner boundaries in the interior of the system, harbor a novel phenomenon, the inner skin effect (ISE). Then the NH skin effect appears at the inner boundaries of the fractal lattice with periodic boundary condition. We showcase this observation by implementing prominent models for NH insulators and superconductors on representative planar Sierpinski carpet fractal lattices. They accommodate both first-order and second-order ISEs at inner edges and corners, respectively, for charged as well as neutral Majorana fermions. Furthermore, over extended parameter regimes ISEs are tied with nontrivial bulk topological invariants, yielding intrinsic ISEs. With the recent success in engineering NH topological phases on highly tunable metamaterial platforms, such as photonic and phononic lattices, as well as topolectric circuits, the proposed ISEs can be observed experimentally at least on fractal metamaterials with periodic boundary condition.