Theory Of Superconductivity Research Articles

Review of Single Crystal Synthesis of 11 Iron-Based Superconductors.

The 11 system in the iron-based superconducting family has become one of the most extensively studied materials in the research of high-temperature superconductivity, due to their simple structure and rich physical properties. Many exotic properties, such as multiband electronic structure, electronic nematicity, topology and antiferromagnetic order, provide strong support for the theory of high-temperature superconductivity, and have been at the forefront of condensed matter physics in the past decade. One noteworthy aspect is that a high upper critical magnetic field, large critical current density and lower toxicity give the 11 system good application prospects. However, the research on 11 iron-based superconductors faces numerous obstacles, mainly stemming from the challenges associated with producing high-quality single crystals. Since the discovery of FeSe superconductivity in 2008, researchers have made significant progress in crystal growth, overcoming the hurdles that initially impeded their studies. Consequently, they have successfully established the complete phase diagrams of 11 iron-based superconductors, including FeSe1-xTex, FeSe1-xSx and FeTe1-xSx. In this paper, we aim to provide a comprehensive summary of the preparation methods employed for 11 iron-based single crystals over the past decade. Specifically, we will focus on hydrothermal, chemical vapor transport (CVT), self-flux and annealing methods. Additionally, we will discuss the quality, size, and superconductivity properties exhibited by single crystals obtained through different preparation methods. By exploring these aspects, we can gain a better understanding of the advantages and limitations associated with each technique. High-quality single crystals serve as invaluable tools for advancing both the theoretical understanding and practical utilization of high-temperature superconductivity.

A testable theory for high-Tc superconductivity in cuprates

A number of theories for the superconductivity in cuprates, have been proposed in the more than 30 years that have elapsed since its discovery. A common feature of these theories is the small number, or even the absence, of quantitative predictions that could be compared to a vast number of experimental data, which are, conversely, available. Such theories are, consequently non-testable. We describe the foundations and a number of applications of a theory describing High-Tc Superconductivity in cuprates, which we proposed recently, that besides being testable, has proven to meet successfully the tests to which it has been submitted so far.

The validity of the BCS-like theory of Fermi-liquid superconductivity in overdoped cuprates

In this paper, we study the key and challenging issues arising in the physics of doped cuprate superconductors, which depending on the doping level (or the Fermi energy [Formula: see text]) and the characteristic energy [Formula: see text] of the attractive interaction between the charge carriers (holes or electrons) might be either in the limit of fermionic (weakly-bound) Cooper pairs just like in ordinary metals or in the limit of bosonic (tightly-bound) Cooper pairs. We argue that the underlying mechanism of superconductivity in doped cuprates depends on the fermionic or bosonic nature of Cooper pairs. We examine the validity criterion of the Bardeen–Cooper–Schrieffer (BCS)-like theory of Fermi-liquid superconductivity in these materials and determine the doping level at which this criterion is well satisfied. We find that the specific overdoped cuprates (with [Formula: see text] or [Formula: see text][Formula: see text]eV) can become the BCS-type superconductors. Using a pertinent BCS-like pairing theory, we calculate the superconducting order parameter (defined as a BCS-like gap [Formula: see text]) and the critical temperature [Formula: see text] of the superconducting transition and the doping dependences of [Formula: see text] and [Formula: see text] in various overdoped cuprates. Our results for [Formula: see text] and [Formula: see text] in specific overdoped cuprates are in fair agreement with the experimental findings reported for these systems.

Colloquium : Room temperature superconductivity: The roles of theory and materials design

For half a century after the discovery of superconductivity, materials exploration for better superconductors proceeded without knowledge of the underlying mechanism. The 1957 BCS theory cleared that up: the superconducting state occurs due to pairing of electrons over the Fermi surface. Over the following half century higher critical temperature T$_c$ was achieved only serendipitously as new materials were synthesized. Meanwhile the formal theory of phonon-coupled superconductivity at the material-dependent level became highly developed: given a known compound, its value of T$_c$, the superconducting gap function, and several other properties of the superconducting state became available independent of further experimental input. More recently, density functional theory based computational materials design has progressed to a predictive level -- new materials can be predicted on the basis of various numerical algorithms. Taken together, these capabilities enable theoretical prediction of new superconductors. Here the process that resulted in three new highest temperature superconductors, predicted numerically, confirmed experimentally -- SH$_3$, LaH$_{10}$, and YH$_9$ -- is recounted. These hydrides have T$_c$ in the 200-280K range at megabar pressures, and here the development will be chronicled. Current activities and challenges are discussed, together with Regularities in compressed hydrides that can guide further exploration.

Superconductivity, what the H? the emperor has no clothes

Considerations on the current status of the theory of superconductivity, the bibliometric H-index, and H. C. Andersen’s tale about the emperor’s new clothes. First appeared in the APS Forum on Physics and Society quarterly newsletter, January 2020.

Weinberg-Salam model as non-Abelian Landau-Ginzburg theory of superconductivity

We propose that the Weinberg-Salem model well known as the standard model of the electroweak unification could also describe the non-Abelian ferromagnetic superconductivity made of two-component (spin-up and spin-down) Cooper pair, which could be viewed as the SU(2)xU(1) extension of the Abelian Landau-Ginzburg theory. In this interpretation the two gauge couplings of SU(2) and U(1) (and thus the Weinberg's mixing angle) are completely fixed by the electromagnetic coupling e. And the massless photon in the standard model plays the role of the massless non-Abelian spinon which induces the long range magnetic order and the spin waves in non-Abelian ferromagnetic superconductors. Moreover, the massive Z boson plays the role of the massive photon which generates the well known Meissner effect in ordinary superconductors, and the W boson becomes the charged massive spinon whose mass determines the range of the non-Abelian spin flip interaction in the ferromagnetic superconductors. We discuss the physical implications of the non-Abelian Landau-Ginzburg theory.

Sparse Modeling Approach for Quasiclassical Theory of Superconductivity

We propose the sparse modeling approach for quasiclassical theory of superconductivity, which reduces the computational cost of solving the gap equations. The recently proposed sparse modeling approach is a consequence of the Green’s function having less information than its spectral function and hence is compressible without loss of relevant information. Using the intermediate representation of the Green’s function in the sparse modeling approach, the gap equation can be solved with only 10–100 sampled Matsubara Green’s functions, whereas the conventional quasiclassical theory requires 100–1000. The efficiency of the proposed method is demonstrated in bulk and vortex states, through self-consistently solve of the Eilenberger and gap equations. Consequently, the sparse modeling approach is concluded to be appropriate for all theoretical methods based on the Matsubara formalism in the quasiclassical theory of superconductivity.

SuperConga: An open-source framework for mesoscopic superconductivity

We present SuperConga, an open-source framework for simulating equilibrium properties of unconventional and ballistic singlet superconductors, confined to two-dimensional (2D) mesoscopic grains in a perpendicular external magnetic field, at arbitrary low temperatures. It aims at being both fast and easy to use, enabling research without access to a computer cluster, and visualization in real-time with OpenGL. The core is written in C++ and CUDA, exploiting the embarrassingly parallel nature of the quasiclassical theory of superconductivity by utilizing the parallel computational power of modern graphics processing units. The framework self-consistently computes both the superconducting order-parameter and the induced vector potential and finds the current density, free energy, induced flux density, local density of states (LDOS), and the magnetic moment. A user-friendly Python frontend is provided, enabling simulation parameters to be defined via intuitive configuration files, or via the command-line interface, without requiring a deep understanding of implementation details. For example, complicated geometries can be created with relative ease. The framework ships with simple tools for analyzing and visualizing the results, including an interactive plotter for spectroscopy. An overview of the theory is presented, as well as examples showcasing the framework's capabilities and ease of use. The framework is free to download from https://gitlab.com/superconga/superconga, which also links to the extensive user manual, containing even more examples, tutorials, and guides. To demonstrate and benchmark SuperConga, we study the magnetostatics, thermodynamics, and spectroscopy of various phenomena. In particular, we study flux quantization in solenoids, vortex physics, surface Andreev bound-states, and a “phase crystal.” We compare our numeric results with analytics and present experimental observables, e.g., the magnetic moment and LDOS, measurable with, for example, scanning probes, STM, and magnetometry.

Unconventional superconductivity with preformed pairs in twisted bilayer graphene

We present a theory of superconductivity in magic-angle twisted bilayer graphene and analyze the superconducting phase diagram in presence of the magnetic field. Namely, we consider a model of a granular array hosting localized states, which are hybridized via the delocalized fermions in the inter-grain regions. We study a strong coupling situation when the interactions lead to an incoherent state with preformed Cooper pairs inside the grains. The Andreev scattering among different grains manifests itself through the global phase-coherent superconducting state at lower temperatures. We demonstrate that a new phase transition between the preformed Cooper pairing state and the Larkin-Ovchinnikov-Fulde-Ferrell state might be induced by the spin pair-breaking effect of in-plane magnetic field. The upper critical magnetic field is shown to be enhanced in the strong coupling case.

Rigorous formalism for unconventional symmetry breaking in Fermi liquid theory and its application to nematicity in FeSe

Unconventional symmetry breaking due to nonlocal order parameters has attracted considerable attention in many strongly correlated metals. Famous examples are the nematic order in Fe-based superconductors and the star-of-David charge density order in kagome metals. Such exotic symmetry breaking in metals is a central issue of modern condensed matter physics, while its theoretical foundation is still unclear in comparison with the well-established theory of superconductivity. To overcome this difficulty, here we introduce the "form factor" that generalizes the nonlocal order parameter into the Luttinger-Ward (LW) Fermi liquid theory. We then construct a rigorous formalism of the "density-wave equation" that gives the thermodynamically stable form factor, similarly to the superconducting-gap equation. In addition, a rigorous expression of the Ginzburg-Landau free-energy for the unconventional order is presented to calculate various thermodynamic properties. In the next stage, we apply the derived formalism to a typical Fe-based superconductor FeSe, by using the one-loop LW function that represents the free-energy gain due to the interference among paramagnons. The following key experiments are naturally explained: (i) Lifshitz transition (=disappearance of an electron-pocket) due to the bond+orbital order below $T_c$. (ii) Curie-Weiss behavior of the nematic susceptibility at higher T, and the deviation from the Curie-Weiss behavior at lower T near the nematic quantum-critical-point. (iii) Scaling relation of the specific heat jump at $T_c$, $\Delta C/T_c \propto T_c^b$ with $b \sim 3$. (Note that b=0 in the BCS theory.) These results lead to a conclusion that the nematicity in FeSe is the bond+orbital order due to the "paramagnon interference mechanism". The present theory paves the way for solving various unconventional phase transition systems.

Extended analytical BCS theory of superconductivity in thin films

We present an analytically solvable theory of Bardeen-Cooper-Schrieffer-type superconductivity in good metals which are confined along one of the three spatial directions, such as thin films. Closed-form expressions for the dependence of the superconducting critical temperature Tc as a function of the confinement size L are obtained, in quantitative agreement with experimental data with no adjustable parameters. Upon increasing the confinement, a crossover from a spherical Fermi surface, which contains two growing hollow spheres corresponding to states forbidden by confinement, to a strongly deformed Fermi surface, is predicted. This crossover represents a new topological transition, driven by confinement, between two Fermi surfaces belonging to two different homotopy classes. This topological transition provides a mechanistic explanation of the commonly observed non-monotonic dependence of Tc upon film thickness with a maximum which, according to our theory, coincides with the topological transition.

A 3D-Schrödinger operator under magnetic steps with semiclassical applications

We define a Schrödinger operator on the half-space with a discontinuous magnetic field having a piecewise-constant strength and a uniform direction. Motivated by applications in the theory of superconductivity, we study the infimum of the spectrum of the operator. We give sufficient conditions on the strength and the direction of the magnetic field such that the aforementioned infimum is an eigenvalue of a reduced model operator on the half-plane. We use the Schrödinger operator on the half-space to study a new semiclassical problem in bounded domains of the space, considering a magnetic Neumann Laplacian with a piecewise-constant magnetic field. We then make precise the localization of the semiclassical ground state near specific points at the discontinuity jump of the magnetic field.

Implications of Seiberg–Witten map on Type-I superconductors

Guided by Pippard superconductivity, we incorporate the Seiberg–Witten map in the classical London theory of Type-I superconductors when an external magnetic field is applied. After defining the noncommutative Maxwell potentials, we derive the London equation for the supercurrent as a function of the noncommutative parameter, up to second order in gauge fields expansions. Keeping track of the effects of noncommutative gauge fields, we argue that noncommutative magnetic field effects can be cast in the London penetration length similar to nonlocal Pippard superconductivity. Also, we show that the flux quantization remains consistent relative to the commutative case. Our effective London penetration length reduces to the standard one in the commutative limit. These results allow us to argue that the framework of noncommutative electrodynamics can give some insights into the anisotropic and nonlocal structure of superconductivity and Condensed Matter Systems, perhaps out of the ultra-microscopic scale regime.

Ginzburg–Landau equations and their generalizations

The Ginzburg–Landau equations were proposed in the superconductivity theory to describe mathematically the intermediate state of superconductors in which the normal conductivity is mixed with the superconductivity. It turned out that these equations have interesting and non-trivial generalizations. First of all, they can be extended to arbitrary compact Riemann surfaces. Next, they can be generalized to dimension 3 as dynamical (or hyperbolic) Ginzburg–Landau equations. They also have a 4-dimensional extension provided by Seiberg–Witten equations. In this review we describe all these interesting topics together with some unsolved problems.

Effective quasiclassical models for odd-frequency superconductivity: Energy-inversion symmetry, preserved spectral weight, and Meissner response

The odd-frequency superconducting state appears generally in hybrid structures consisting of conventional superconductors and other materials, and features electrons that form temporally nonlocal Cooper pairs. The quasiclassical theory of superconductivity has been extensively used to model such systems, finding in many cases excellent agreement with experimental measurements. Therefore, it is of interest to study effective models of odd-frequency superconductivity to predict new phenomena associated with this form of unconventional pairing. We establish necessary criteria that the quasiclassical Green's functions in odd-frequency superconducting systems in the dirty limit must satisfy in order to be physically reasonable, including conservation of spectral weight. We show that it is possible to write down effective models, which satisfy all the above-mentioned criteria, but which still predict different behavior when it comes to the density of states and the magnetic response of the superconductor. For instance, an effective model for the odd-frequency anomalous Green's function that gives a conserved spectral weight can yield either a peaked or gapped density of states at the Fermi energy, and exhibit conventional, zero, or unconventional Meissner response. This finding demonstrates the importance of carefully considering the properties of effective models describing odd-frequency superconductivity in order to obtain physically reasonable results.

Superconductivity and bosonic fluid emerging from moiré flat bands

Although evidence of inter-valley attraction-mediated by phonon or topological fluctuations is accumulating, the origin of superconductivity in the flat-band quantum moir\'e materials remains an open question. Here, instead of attempting to pinpoint the origin of the superconductivity, we aim at identifying universal properties of moir\'e flat bands that shall emerge in the presence of inter-valley attractions. We show that by matching the interaction strength of inter-valley attraction with intra-valley repulsion, the flat-band limit becomes exactly solvable. Away from the flat-band limit, the system can be simulated via quantum Monte Carlo (QMC) methods without sign problem for any fillings. Combining analytic solutions with large-scale numerical simulations, we show that upon increasing temperature, the superconducting phase melts into a bosonic fluid of Cooper pairs with large/diverging compressibility. In contrast to flat-band attractive Hubbard models, where similar effects arise only for on-site interactions, our study indicates this physics is a universal property of moir\'e flat bands, regardless of microscopic details such as the range of interactions and/or spin-oribt couplings. At higher temperature, the boson fluid phase gives its way to a pseudo gap phase, where some Cooper pairs are torn apart by thermal fluctuations, resulting in fermion density of states inside the gap. Unlike the superconducting transition temperature, which is very sensitive to doping and twisting angles, the gap and the temperature scale of the boson fluid phase and the pseudo gap phase are found to be nearly independent of doping level and/or flat-band bandwidth. The relevance of these phases with experimental discoveries in the flat band quantum moir\'e materials is discussed.

Causes and Consequences of Ordering and Dynamic Phases of Confined Vortex Rows in Superconducting Nanostripes.

Understanding the behaviour of vortices under nanoscale confinement in superconducting circuits is important for the development of superconducting electronics and quantum technologies. Using numerical simulations based on the Ginzburg-Landau theory for non-homogeneous superconductivity in the presence of magnetic fields, we detail how lateral confinement organises vortices in a long superconducting nanostripe, presenting a phase diagram of vortex configurations as a function of the stripe width and magnetic field. We discuss why the average vortex density is reduced and reveal that confinement influences vortex dynamics in the dissipative regime under sourced electrical current, mapping out transitions between asynchronous and synchronous vortex rows crossing the nanostripe as the current is varied. Synchronous crossings are of particular interest, since they cause single-mode modulations in the voltage drop along the stripe in a high (typically GHz to THz) frequency range.

Fermi-Liquid Nonadiabatic Highly Compressed Cesium Iodide Superconductor

The experimental discovery that compressed sulfur hydride exhibits superconducting transition temperature of Tc=203 K by Drozdov et al. (Nature 2015, 525, 73–76) sparked studies of compressed hydrides. This discovery was not a straightforward experimental examination of a theoretically predicted phase, but instead it was a nearly five-decade-long experimental quest for superconductivity in highly compressed matters, varying from pure elements (hydrogen, oxygen, sulfur), hydrides (SiH4, AlH3) to semiconductors and ionic salts. One of these salts was cesium iodide, CsI, which exhibits the transition temperature of Tc≅1.5 K at P=206 GPa (Eremets et al., Science 1998, 281, 1333–1335). Detailed first principles calculations (Xu et al., Phys Rev B 2009, 79, 144110) showed that CsI should exhibit Tc~0.03 K (P=180 GPa). In an attempt to understand the nature of this discrepancy between the theory and the experiment, we analyzed the temperature-dependent resistance in compressed CsI and found that this compound is a perfect Fermi liquid metal which exhibits an extremely high ratio of Debye energy to Fermi energy, ℏωDkBTF≅17. This implies that direct use of the Migdal–Eliashberg theory of superconductivity to calculate the transition temperature in CsI is incorrect, because the theory is valid for ℏωDkBTF≪1. We also showed that CsI falls into the unconventional superconductors band in the Uemura plot.

First-order normal-to-superconductor phase transition of aluminum in magnetic field by current-density functional theory for superconductors

We demonstrate that the current-density functional theory for superconductors (sc-CDFT) can describe the magnetic-field-induced first-order phase transition of aluminum from a superconducting state to a normal state. This is accomplished by introducing a model for the magnetic-field dependence of the attractive interaction between superconducting electrons. This model states that the surface potential well produced by a penetrating magnetic field leads to the magnetic-field dependence of the attractive interaction. Specifically, the electron density near the surface increases with the magnetic field owing to the surface potential well, which causes a reduction in the attractive interaction because of the screening effect. We also develop a calculation scheme to solve the gap equation of the sc-CDFT by considering the magnetic-field dependence of the attractive interaction. The calculation results for the magnetic-field dependence of the superconducting gap are in good agreement with the experimental results of the first-order phase transition.

Prediction of quaternary hydrides based on densest ternary sphere packings

We exhaustively search quaternary metal hydrides based on the (13-2-1) and (13-3-1) structures that are two of the putative densest ternary sphere packings in cubic systems [R. Koshoji et al., Phys. Rev. E 104, 024101 (2021)]. The 73 304 candidate hydrides are generated by substituting the small spheres with hydrogen atoms, and the medium, large, and fourth spheres with metallic atoms. Specifically, the substitution of the small spheres with hydrogen atoms gives the unconventional hydrogen sublattices. We screen unstable hydrides in the candidates through geometrical optimizations, constant pressure molecular dynamics simulations, and phonon calculations under hydrostatic pressure of 10 GPa, and identify 23 hydrides with static and dynamic stability, including ${\mathrm{H}}_{12}{\mathrm{ScY}}_{2}\mathrm{La}$ and ${\mathrm{H}}_{12}\mathrm{Ti}{\mathrm{Ni}}_{3}\mathrm{Ba}$. The superconducting transition temperatures ${T}_{c}$, calculated by density functional theory for superconductors, are found to be 5.7 and 6.7 K for the selected two hydrides ${\mathrm{H}}_{12}{\mathrm{ScY}}_{2}\mathrm{Ca}$ and ${\mathrm{H}}_{12}{\mathrm{ScY}}_{2}\mathrm{Sr}$, respectively. We expect that the 23 candidates of hydrides screened by the exhaustive search for 73 304 hydrides provide a guideline to narrow down the search space for trials in the experimental synthesis of quaternary metal hydrides.