Theory Of Superconductivity Research Articles

Comment on “Inconsistency of the conventional theory of superconductivity” by Hirsch J. E.

J. E. Hirsch [EPL 130 (2020) 17006] claimed an inconsistency between thermodynamics and the theory of superconductivity. We argue that he overlooked a crucial term which determines the supercurrent dynamics and ensures energy conservation by providing an internal energy source for the Joule heating. Thermodynamic consistency is restored by restoring energy conservation. The correct dynamics is given by Maxwell's equations in the superconductor.

Superconductor fault current limiter effect on the performance of doubly-fed induction generators

<span>Between different wind turbine-generator configurations, one of the most accepted and highly regarded structures in the industry is the wind turbine with doubly-fed induction generator. The DFIG wind turbines are very sensitive to grid disturbances especially to voltage drop during grid faults due to relatively low power of the power converters. Fault in a power system causes voltage drop, current increase in stator and rotor coils, and over voltage in the DC shin. Several control methods have been proposed so far. A model based on power electronic instruments and superconductor theory, superconductor fault current limiter (SCFCL), has been proposed in this paper to improve domain and the attenuation time of the parameters under control such as voltage, current, and speed and voltage of the DC link against various types of faults (single-phase, two-phase, and three-phase). In addition to this, in order to compare the results with convectional models (crowbar) and study the innovation of the proposed model, a simulation of the system under two-phase fault and use of crowbar method to control the fault has been conducted using MATLAB-SIMULINK and also, the performance of the proposed method has been assessed. </span>

Topological superconductivity facilitated by exchange interaction on the surface of FeTe0.5Se0.5

FeTe1−xSex is a family of iron-based superconductors with a well-known critical temperature (Tc) of 14.5 K for x = 0.45. Also well-established is the presence of topological surface states of FeTe0.55Se0.45 in which topological superconductivity sets in. By using density functional calculations and the Bardeen–Cooper–Schrieffer (BCS) theory for traditional superconductors we calculated the Tc of the surface layers of FeTe0.5Se0.5 with the exchange interaction as the source of attractive force to form the Cooper pairs. The estimated Tc is in reasonable agreement with the experimental value and suggests that the exchange interaction is behind the topological superconductivity on the surface of FeTe0.55Se0.45.

Exact theory for superconductivity in a doped Mott insulator

Because the cuprate superconductors are doped Mott insulators, it would be advantageous to solve even a toy model that exhibits both Mottness and superconductivity. We consider the Hatsugai–Kohmoto model1,2, an exactly solvable system that is a prototypical Mott insulator. Upon either doping or reducing the interaction strength, our exact calculations show that the system becomes a non-Fermi liquid metal with a superconducting instability. In the presence of a weak pairing interaction, the instability produces a thermal transition to a superconducting phase, which is distinct from the traditional state described by Bardeen–Cooper–Schrieffer (BCS) theory, as evidenced by a gap-to-transition temperature ratio exceeding the universal BCS limit. The elementary excitations of this superconductor are not Bogoliubov quasiparticles but rather superpositions of doublons and holons, composite excitations that show that the superconducting ground state of the doped Mott insulator inherits the non-Fermi liquid character of the normal state. An unexpected feature of this model is that it exhibits a superconductivity-induced transfer of spectral weight from high to low energies, as seen in the cuprates3, as well as a suppression of the superfluid density relative to that in BCS theory.

Combining Eliashberg Theory with Density Functional Theory for the Accurate Prediction of Superconducting Transition Temperatures and Gap Functions.

We propose a practical alternative to Eliashberg equations for the abinitio calculation of superconducting transition temperatures and gap functions. Within the recent density functional theory for superconductors, we develop an exchange-correlation functional that retains the accuracy of Migdal's approximation to the many-body electron-phonon self-energy, while having a simple analytic form. Our functional is based on a parametrization of the Eliashberg self-energy for a superconductor with a single Einstein frequency, and enables density functional calculations of experimental excitation gaps. By merging electronic structure methods and Eliashberg theory, the present approach sets a new standard in quality and computational feasibility for the prediction of superconducting properties.

Magnetic-field and temperature dependence of the superconducting gap through current-density functional theory for superconductors

Quantitative prediction of the gap behavior via first-principles calculations has thus far been restricted to temperature dependence. Here, we present a gap equation developed based on the current-density functional theory for superconductors. This equation is applicable to superconductors immersed in a magnetic field and enables us to quantitatively describe the magnetic-field and temperature dependence of the superconducting gap. We also develop a practical scheme in which the gap equation is solved simultaneously with a proposed relation between the energy gain of the superconducting state at zero magnetic field and that at a finite magnetic field. The presented scheme is applied to aluminum immersed in a magnetic field, and successfully reveals the temperature and magnetic-field dependences of the superconducting gap. The critical magnetic field thus obtained shows good agreement with experimental results.

Superconductivity in Quantum Complex Matter: the Superstripes Landscape

While in XX century the theory of superconductivity has focused on a homogeneous metal with a rigid lattice which can be reduced to a single effective conduction band in the dirty limit. Today in the XXI century, the physics of superconductivity is focusing on complexity of quantum matter where novel quantum functionalities with lattice inhomogeneity at nanoscale (between 1 nm and 100 nm) and at mesoscopic scale (in the range 100-10000 nm), where the electronic structure need to be described by multiple Fermi surfaces and multiple gaps in the superconducting phase in the clean limit. The present issue of Journal of superconductivity and Novel magnetism collects papers presented at the International Conference Superstripes 2019 which was held on June 23-29, 2019, in Ischia Island, Italy. The series of Stripes conference started on Dec 8 1996 and it has contributed to scientific advances in the new physics of superconductivity in quantum complex systems in these last 23 years where polarons, strain, multigap superconductivity, exchange interaction between condensates, granular superconductivity and percolation play a key role. The articles collected in this issue cover hot topics of the new quantum physics of complex matter including the mechanism of high temperature superconductivity, complex magnetic orders and orbital physics in strongly correlated materials which have been growing rapidly in these last two years opening new perspectives also in mesoscopic quantum engineering.

Nonlocal-In-Time kinetic energy description of superconductivity

A new nonlocal phenomenological theory of superconductivity is discussed based on extension of the quantum momentum operator which is one of the main consequences of nonlocal-in-time kinetic energy. The nonlocal Ginzburg-Landau equations are derived from the extended nonlocal pair-superconductor total free energy and a number of properties are discussed. A microscopic nonlocal quantum formulation of BCS superconductivity is set up and several features are revealed. A connection between the nonlocal-in-time parameter and the superconducting energy gap for excitations is obtained which permits to fix its numerical range and to interpret this parameter as a quantum time associated to superconductor's critical parameters. The theory predicts disordered superconductors, low-dimensional (atomic scales) superconductors and suggests the presence of a Type III superconductor which is intermediate between Types I and II. Additional features were obtained and discussed accordingly.

Full-bandwidth Eliashberg theory of superconductivity beyond Migdal's approximation

We solve the anisotropic, full-bandwidth and non-adiabatic Eliashberg equations for phonon-mediated superconductivity by fully including the first vertex correction in the electronic self-energy. The non-adiabatic equations are solved numerically here without further approximations, for a one-band model system. We compare the results to those that we obtain by adiabatic full-bandwidth, as well as Fermi-surface restricted Eliashberg-theory calculations. We find that non-adiabatic contributions to the superconducting gap can be positive, negative or negligible, depending on the dimensionality of the considered system, the degree of non-adiabaticity, and the coupling strength. We further examine non-adiabatic effects on the transition temperature and the electron-phonon coupling constant. Our treatment emphasizes the importance of overcoming previously employed approximations in estimating the impact of vertex corrections on superconductivity and opens a pathway to systematically study vertex correction effects in systems such as high-$T_c$, flat band and low-carrier density superconductors.

Superconductivity in Electronic Systems with Strong Correlations

We report a consistent microscopic theory of superconductivity for strongly correlated electronic systems. The electronic spectrum and superconductivity are studied using the Bogoliubov–Tyablikov Green functions for the projected (Hubbard) electronic operators. The extended Hubbard model is considered where the intersite Coulomb repulsion and the electron-phonon interaction are taken into account. The $$d$$ ‑wave pairing with high- $${{T}_{c}}$$ is found induced by the strong kinematical interaction of electrons with spin fluctuations that proves the spin-fluctuation mechanism of high-temperature superconductivity.

Pre-formed Cooper pairs in copper oxides and LaAlO3—SrTiO3 heterostructures

The Bardeen–Cooper–Schrieffer theory of superconductivity and the Landau–Fermi liquid theory form the basis of our current understanding of conventional superconductors and their parent non-superconducting phases. However, some exotic superconductors do not conform to this physical picture but instead feature an unusual ‘normal’ state that is not a Fermi liquid. One explanation of this unusual behaviour is that pre-formed pairs of electrons are established above the superconducting temperature Tc. Here, we highlight recent experiments that show the likely existence of these pre-formed pairs in two rather different materials—a high-temperature cuprate superconductor and strontium titanate. Moreover, in both materials the normal state from which superconductivity emerges has other shared properties, including a pseudogap and electronic nematicity—rotational symmetry breaking in the electron fluid that is not expected in Fermi liquid theory nor more generally from the crystal lattice symmetry. These experimental findings should provoke more interaction between the communities working on these materials and new insights into the underlying mechanism of the creation of pre-formed pairs. Pairs of electrons can form above the superconducting critical temperature. The authors review the similarities and differences in this phenomenology in copper-based superconductors and oxide heterostructures.

Modeling Superconductor SFN-Structures Using the Finite Element Method

We consider the problem of mathematical modeling of the current distribution in Josephson structures based on semiclassical equations of the microscopic theory of superconductivity (the Usadel equations). These equations are a system of quasilinear elliptic equations for Green’s functions $$\Phi _\omega (r)$$ and $$G_\omega (r) $$ and the pairing potential $$\Delta (r) $$ , which is determined from the equation of self-consistency by summation of the functions $$\Phi _\omega (r)$$ over the frequencies $$\omega $$ . To solve the quasilinear equations, we propose a special mixed finite element method, and to solve the self-consistency equations, we apply the successive approximation method and Anderson’s convergence acceleration algorithm. Results of calculations are provided for a structure with a wedge-shaped ferromagnetic layer.

In search for near-room-temperature superconducting critical temperature of metal superhydrides under high pressure: A review

An overview and the latest status of the superconductivity of metal superhydrides under high pressure are discussed in this review article. The searching for near-room-temperature superconductors have been one of the most enthusiastic fields in physics. This is because of several key factors in both theoretical and experimental sides. By advanced experiment innovation, pressure exceeded that of the earth’s core can be generated in laboratories. This allows scientists to explore new physics of materials under high pressure. In the synergy form, the theoretical calculation gives accountable predictions on the structural and electronic properties which can be served as a practical map for experimentalists. In this review, I also give a brief overview on the existing theory of superconductivity which leads to the calculation of the superconducting critical temperature, Tc. The key element for calculating Tc is stemmed from the so-called spectral function, which can now be evaluated from the density functional theory. In order to obtain insight information and gain deeper understanding, I model the spectral function with a simple constant function. This analysis gives a powerful suggestion on the way to search for a higher value of Tc.

Negative charge-transfer gap and even parity superconductivity in Sr2RuO4

A comprehensive theory of superconductivity in Sr$_2$RuO$_4$ must explain experiments that suggest even parity superconducting order and others that suggest broken time reversal symmetry. Completeness further requires that the theory applies to Ca$_2$RuO$_4$, a Mott-Hubbard semiconductor that exhibits an unprecedented insulator-to-metal transition driven by very small electric field, and also by doping with very small concentration of electrons, leading to a metallic state proximate to ferromagnetism. A valence transition model, previously proposed for superconducting cuprates [Phys. Rev. B {\bf 98}, 205153] is extended to Sr$_2$RuO$_4$ and Ca$_2$RuO$_4$. The insulator to metal transition is distinct from that expected from the simple melting of the Mott-Hubbard semiconductor. Rather, the Ru ions occur as low spin Ru$^{4+}$ in the semiconductor, and as high spin Ru$^{3+}$ in the metal, the driving force behind the valence transition being the strong spin-charge coupling and consequent large ionizaton energy in the low charge state. Metallic and superconducting ruthenates are two-component systems in which the half-filled high spin Ru$^{3+}$ ions determine the magnetic behavior but not transport, while the charge carriers are entirely on on the layer oxygen ions, which have an average charge -1.5. Spin singlet superconductivity evolves from the correlated lattice frustrated 3/4 filled band of layer oxygen ions alone, in agreement with quantum many body calculations that have demonstrated enhancement by electron-electron interactions of superconducting pair-pair correlations tions uniquely at or very close to this filling [Phys. Rev. B {\bf 93}, 165110 and {\bf 93}, 205111]. Several model specific experimental predictions are made, including that spin susceptibility due to Ru ions will remain unchanged as Sr$_2$RuO$_4$ is taken through superconducting Tc.

Effective theory of superconductivity in strongly coupled amorphous materials

A theory of phonon-mediated superconductivity in strong-coupling amorphous materials is developed based on an effective description of structural disorder and its effect on the vibrational spectrum. The theory accounts for the diffusive-like transport of vibrational excitations due to disorder-induced scattering within the Eliashberg theory of strong-coupling superconductivity. The theory provides a good analytical description of the Eliashberg function $\alpha^{2}F(\omega)$ in comparison with experiments, and allows one to disentangle the effects of transverse and longitudinal excitations on the Eliashberg function. In particular, it shows that the transverse excitations play a crucial role in driving an increase or excess in the Eliashberg function at low energy, which is related to the boson peak phenomenon in vibrational spectra of glasses. This low-energy excess, on one hand drives an enhancement of the electron-phonon coupling but at the same time reduces the characteristic energy scale $\omega_{log}$ in the Allen-Dynes formula. As a consequence, the non-monotonicity of $T_{c}$ as a function of alloying (disorder) in $\text{Pb}$-based systems can be rationalized. The case of $\text{Al}$-based systems, where disorder increases $T_{c}$ from the start, is also analyzed. General material-design principles for enhancing $T_{c}$ in amorphous superconductors are presented.

Reentrant Superconductivity in UTe2

The reentrant superconductivity is the peculiar phenomenon observed in paramagnetic metal UTe2 in magnetic field parallel to the hard magnetisation axis. It is difficult to explain it in terms of field dependent intensity of magnetic fluctuations like it is done for explanation of the formally similar phenomena in the ferromagnetic uranium superconductors URhGe, UCoGe. Extremely large initial slope of the upper critical field temperature dependence suggests that the phenomenon has quasi-two-dimensional nature. Indeed, according to the recent band structure calculations by Y. Xu et al. (Phys. Rev. Lett. 123, 217002 (2019)) the Fermi surface of UTe2 consists of two types slightly corrugated cylinders. The theory of reentrant superconductivity in UTe2 based on its quasi-two-dimensional structure is presented here.

Joule heating in the normal-superconductor phase transition in a magnetic field

Joule heating is a non-equilibrium dissipative process that occurs in a normal metal when an electric current flows, in an amount proportional to the metal’s resistance. When it is induced by eddy currents resulting from a change in magnetic flux, it is also proportional to the rate at which the magnetic flux changes. Here we show that in the phase transformation between normal and superconducting states of a metal in a magnetic field, the total amount of Joule heating is determined by the thermodynamic properties of the system and is independent of the resistivity of the normal metal. Under the reasonable assumption that the magnetic field at the phase boundary is given by the thermodynamic critical field, we show that Joule heating occurs only in the normal region of the material, hence no Joule heating occurs in the superconducting region next to the phase boundary where normal current is expected to flow according to the conventional theory of superconductivity. We discuss the significance of this result.

How Alfven’s theorem explains the Meissner effect

Alfven’s theorem states that in a perfectly conducting fluid magnetic field lines move with the fluid without dissipation. When a metal becomes superconducting in the presence of a magnetic field, magnetic field lines move from the interior to the surface (Meissner effect) in a reversible way. This indicates that a perfectly conducting fluid is flowing outward. I point this out and show that this fluid carries neither charge nor mass, but carries effective mass. This implies that the effective mass of carriers is lowered when a system goes from the normal to the superconducting state, which agrees with the prediction of the unconventional theory of hole superconductivity and with optical experiments in some superconducting materials. The 60-year old conventional understanding of the Meissner effect ignores Alfven’s theorem and for that reason I argue that it does not provide a valid understanding of real superconductors.

Thermodynamic inconsistency of the conventional theory of superconductivity

A type I superconductor expels a magnetic field from its interior to a surface layer of thickness [Formula: see text], the London penetration depth. [Formula: see text] is a function of temperature, becoming smaller as the temperature decreases. Here we analyze the process of cooling (or heating) a type I superconductor in a magnetic field, with the system remaining always in the superconducting state. The conventional theory predicts that Joule heat is generated in this process, the amount of which depends on the rate at which the temperature changes. Assuming the final state of the superconductor is independent of history, as the conventional theory assumes, we show that this process violates the first and second laws of thermodynamics. We conclude that the conventional theory of superconductivity is internally inconsistent. Instead, we suggest that the alternative theory of hole superconductivity may be able to resolve this problem.

Chern-Simons Current of Left and Right Chiral Superspace in Graphene Wormhole

Starting from the basic definitions of Chern-Simons current, it is possible to calculate its values with a quantum machine learning approach, the so-called supersymmetric support Dirac machine. The related supercurrent is generated from the coupling between three states of the quantum flux of a modified Wilson loop of Cooper pairs. We adopt the Holo-Hilbert spectrum, in frequency modulation, to visualize the network as the coupling of convolutional neuron network in a superstatistic theory where the theory of superconductors is applied. According to this approach, it is possible to calculate the number of carbon atoms in the spinor network of a graphene wormhole. A supercurrent of Cooper pairs is produced as graviphoton states by using the Holo-Hilbert spectral analysis.