Conventional Theory Of Superconductivity Research Articles

Rare-region onset of superconductivity in niobium nanoislands

We report measurements of the superconducting properties of isolated Nb nanoislands (600--2500 nm diameters) and explain their unusual behavior in terms of rare-region onset effects, predicted for random metal-superconductor granular systems [B. Spivak, P. Oreto, and S. A. Kivelson, Phys. Rev. B 77, 214523 (2008)]. We find that the island ${T}_{c}$ is strongly suppressed even at large island diameters, exceeding 1 \ensuremath{\mu}m. This behavior is unexpected given that conventional theories of superconductivity in small grains predict suppression of ${T}_{c}$ only at a length scale that is two orders of magnitude smaller. In addition, we observe large island-to-island variations in ${T}_{c}$ for nominally identical islands. These two experimental observations, coupled with direct measurement of grain distribution using transmission electron microscopy, conductive atomic force microscopy, and computer simulations, provide evidence for our picture in which the onset of superconductivity on an island coincides with the transition temperature of its largest constituent grain, and then spreads to other grains due to proximity coupling.

Defying Inertia: How Rotating Superconductors Generate Magnetic Fields

AbstractI discuss the process of magnetic field generation in rotating superconductors in simply connected and multiply connected geometries. In cooling a normal metal into the superconducting state while it is rotating, electrons slow down or speed up depending on the geometry and their location in the sample, apparently defying inertia. I argue that the conventional theory of superconductivity does not explain these processes. Instead, the theory of hole superconductivity does. Its predictions agree with experimental observations of Hendricks, King and Rohrschach for solid and hollow cylinders.

Alfven-like waves along normal-superconductor phase boundaries

Alfven waves are transverse magneto-hydrodynamic waves resulting from motion of a conducting fluid in direction perpendicular to an applied magnetic field, that propagate along the magnetic field direction. I propose that Alfven-like waves can propagate along normal-superconductor phase boundaries in the presence of a magnetic field. This requires charge flow and backflow across the normal-superconductor phase boundary when the boundary moves, which is predicted by the theory of hole superconductivity but not by the conventional theory of superconductivity. The magnetic field and the domain wall energy provide elasticity, and the normal charge carriers’ effective mass provides inertia. It is essential that the normal state charge carriers are holes. I propose an experimental search for Alfven-like waves in superconductors.

Erratum: “Entropy generation and momentum transfer in the superconductor–normal and normal–superconductor phase transformations and the consistency of the conventional theory of superconductivity”

Erratum: “Entropy generation and momentum transfer in the superconductor–normal and normal–superconductor phase transformations and the consistency of the conventional theory of superconductivity”

Entropy generation and momentum transfer in the superconductor–normal and normal–superconductor phase transformations and the consistency of the conventional theory of superconductivity

Since the discovery of the Meissner effect, the superconductor to normal (S–N) phase transition in the presence of a magnetic field is understood to be a first-order phase transformation that is reversible under ideal conditions and obeys the laws of thermodynamics. The reverse (N–S) transition is the Meissner effect. This implies in particular that the kinetic energy of the supercurrent is not dissipated as Joule heat in the process where the superconductor becomes normal and the supercurrent stops. In this paper, we analyze the entropy generation and the momentum transfer between the supercurrent and the body in the S–N transition and the N–S transition as described by the conventional theory of superconductivity. We find that it is not possible to explain the transition in a way that is consistent with the laws of thermodynamics unless the momentum transfer between the supercurrent and the body occurs with zero entropy generation, for which the conventional theory of superconductivity provides no mechanism. Instead, we point out that the alternative theory of hole superconductivity does not encounter such difficulties.

Conventional superconductivity in the type-II Dirac semimetal PdTe2

The transition metal dichalcogenide PdTe$_2$ was recently shown to be a unique system where a type II Dirac semimetallic phase and a superconducting phase co-exist. This observation has led to wide speculation on the possibility of the emergence of an unconventional topological superconducting phase in PdTe$_2$. Here, through direct measurement of the superconducting energy gap by scanning tunneling spectroscopy (STS), and temperature and magnetic field evolution of the same, we show that the superconducting phase in PdTe$_2$ is conventional in nature. The superconducting energy gap is measured to be 326 $\mu$eV at 0.38 K and it follows a temperature dependence that is well described within the framework of Bardeen-Cooper-Schriefer's (BCS) theory of conventional superconductivity. This is surprising because our quantum oscillation measurements confirm that at least one of the bands participating in transport has topologically non-trivial character.

Momentum of superconducting electrons and the explanation of the Meissner effect

Momentum and energy conservation are fundamental tenets of physics, that valid physical theories have to satisfy. In the reversible transformation between superconducting and normal phases in the presence of a magnetic field, the mechanical momentum of the supercurrent has to be transferred to the body as a whole and vice versa, the kinetic energy of the supercurrent stays in the electronic degrees of freedom, and no energy is dissipated nor entropy is generated in the process. We argue on general grounds that to explain these processes it is necessary that the electromagnetic field mediates the transfer of momentum between electrons and the body as a whole, and this requires that when the phase boundary between normal and superconducting phases is displaced, a flow and counterflow of charge occurs in direction perpendicular to the phase boundary. This flow and counterflow does not occur according to the conventional BCS-London theory of superconductivity, therefore we argue that within BCS-London theory the Meissner transition is a `forbidden transition'. Furthermore, to explain the phase transformation in a way that is consistent with the experimental observations requires that (i) the wavefunction $and$ charge distribution of superconducting electrons near the phase boundary extend into the normal phase, and (ii) that the charge carriers in the normal state have hole-like character. The conventional theory of superconductivity does not have these physical elements, the theory of hole superconductivity does.

Ubiquitous signatures of nematic quantum criticality in optimally doped Fe-based superconductors.

A key actor in the conventional theory of superconductivity is the induced interaction between electrons mediated by the exchange of virtual collective fluctuations (phonons in the case of conventional s-wave superconductors). Other collective modes that can play the same role, especially spin fluctuations, have been widely discussed in the context of high-temperature and heavy Fermion superconductors. The strength of such collective fluctuations is measured by the associated susceptibility. Here we use differential elastoresistance measurements from five optimally doped iron-based superconductors to show that divergent nematic susceptibility appears to be a generic feature in the optimal doping regime of these materials. This observation motivates consideration of the effects of nematic fluctuations on the superconducting pairing interaction in this family of compounds and possibly beyond.

On the dynamics of the Meissner effect

The question of how a metal becoming superconducting expels a magnetic field is addressed. It is argued that the conventional theory of superconductivity has not answered this question despite its obvious importance. We argue that the growth of the superconducting region into the normal region and associated expulsion of magnetic field from the superconducting region can only be understood if it is accompanied by motion of charge from the superconducting region into the normal region. From a microscopic point of view it is shown that the perfect diamagnetism of superconductors requires that superconducting electrons reside in orbits of spatial extent , with the London penetration depth. Associated with this physics, the spin–orbit interaction of the electron magnetic moment and the positively charged ionic background gives rise to a ‘Spin Meissner’ effect, the generation of a macroscopic spin current near the surface of superconductors. We point out that both the Meissner and the Spin Meissner effect can be understood dynamically under the assumption that the superfluid condensate wavefunction does not screen itself, just like the for an electron in a hydrogen atom. We argue that the conventional theory of superconductivity cannot explain the Meissner effect because it does not contain the physical elements discussed here.

High temperature superconductivity in sulfur hydride under ultrahigh pressure: A complex superconducting phase beyond conventional BCS

AbstractThe recent report of superconductivity under high pressure at the record transition temperature of Tc =203 K in pressurized H2S has been identified as conventional in view of the observation of an isotope effect upon deuteration. Here it is demonstrated that conventional theories of superconductivity in the sense of BCS or Eliashberg formalisms cannot account for the pressure dependence of the isotope coefficient. The only way out of the dilemma is a multi-band approach of superconductivity where already small interband coupling suffices to achieve the high values of Tc together with the anomalous pressure dependent isotope coefficient. In addition, it is shown that anharmonicity of the hydrogen bonds vanishes under pressure whereas anharmonic phonon modes related to sulfur are still active.

Conventional superconductivity at 203 kelvin at high pressures in the sulfur hydride system.

A superconductor is a material that can conduct electricity without resistance below a superconducting transition temperature, Tc. The highest Tc that has been achieved to date is in the copper oxide system: 133 kelvin at ambient pressure and 164 kelvin at high pressures. As the nature of superconductivity in these materials is still not fully understood (they are not conventional superconductors), the prospects for achieving still higher transition temperatures by this route are not clear. In contrast, the Bardeen-Cooper-Schrieffer theory of conventional superconductivity gives a guide for achieving high Tc with no theoretical upper bound--all that is needed is a favourable combination of high-frequency phonons, strong electron-phonon coupling, and a high density of states. These conditions can in principle be fulfilled for metallic hydrogen and covalent compounds dominated by hydrogen, as hydrogen atoms provide the necessary high-frequency phonon modes as well as the strong electron-phonon coupling. Numerous calculations support this idea and have predicted transition temperatures in the range 50-235 kelvin for many hydrides, but only a moderate Tc of 17 kelvin has been observed experimentally. Here we investigate sulfur hydride, where a Tc of 80 kelvin has been predicted. We find that this system transforms to a metal at a pressure of approximately 90 gigapascals. On cooling, we see signatures of superconductivity: a sharp drop of the resistivity to zero and a decrease of the transition temperature with magnetic field, with magnetic susceptibility measurements confirming a Tc of 203 kelvin. Moreover, a pronounced isotope shift of Tc in sulfur deuteride is suggestive of an electron-phonon mechanism of superconductivity that is consistent with the Bardeen-Cooper-Schrieffer scenario. We argue that the phase responsible for high-Tc superconductivity in this system is likely to be H3S, formed from H2S by decomposition under pressure. These findings raise hope for the prospects for achieving room-temperature superconductivity in other hydrogen-based materials.

Dynamics of the normal–superconductor phase transition and the puzzle of the Meissner effect

The analysis of Pippard (1950) for the growth of the normal phase into the superconducting phase in the presence of a magnetic field H>Hc is applied in reverse to the case H<Hc (Hc= critical magnetic field). We carry out the analysis both for a planar and a cylindrical geometry. As the superconducting phase grows into the normal phase, a supercurrent is generated at the superconductor–normal phase boundary that flows in direction opposite to the Faraday electric field resulting from the moving phase boundary. This supercurrent motion is in direction opposite to what is dictated by the Lorentz force on the current carriers, and in addition requires that mechanical momentum of opposite sign be transferred to the system as a whole to ensure momentum conservation. In the cylindrical geometry case, a macroscopic torque of unknown origin acts on the body as a whole as the magnetic field is expelled. We argue that the conventional BCS-London theory of superconductivity cannot explain these facts, and that as a consequence the Meissner effect remains unexplained within the conventional theory of superconductivity. We propose that the Meissner effect can only be understood by assuming that there is motion of charge in direction perpendicular to the normal–superconductor phase boundary and point out that the unconventional theory of hole superconductivity describes this physics.

Fabrication of nanometer-spaced superconducting Pb electrodes

We report the fabrication of superconducting Pb electrodes with nanometer-sized separation by using the electromigration technique. Below the superconducting transition temperature, the electrodes show current-voltage characteristics consistent with the tunneling between two superconducting electrodes, which can be well understood within conventional theory of superconductivity. The electrodes can be reversibly switched between the normal and superconducting states by the application of an external magnetic field. These electrodes are suited for electron-transport studies of chemically synthesized nanostructures and the utility is demonstrated by making single-molecule transistors incorporating individual Co-porphyrin molecules.

Charge Expulsion, Spin Meissner Effect, and Charge Inhomogeneity in Superconductors

Superconductivity occurs in systems that have a lot of negative charge: the highly negatively charged (CuO2)= planes in the cuprates, negatively charged (FeAs)− planes in the iron arsenides, and negatively charged B − planes in magnesium diboride. And, in the nearly filled (with negative electrons) bands of almost all superconductors, as evidenced by their positive Hall coefficient in the normal state. No explanation for this charge asymmetry is provided by the conventional theory of superconductivity, within which the sign of electric charge plays no role. Instead, the sign of the charge carriers plays a key role in the theory of hole superconductivity, according to which metals become superconducting because they are driven to expel negative charge (electrons) from their interior. This is why NIS tunneling spectra are asymmetric, with larger current for negatively biased samples. The theory also offers a compelling explanation of the Meissner effect: as electrons are expelled towards the surface in the presence of a magnetic field, the Lorentz force imparts them with azimuthal velocity, thus generating the surface Meissner current that screens the interior magnetic field. In type II superconductors, the Lorentz force acting on expelled electrons that do not reach the surface gives rise to the azimuthal velocity of the vortex currents. In the absence of applied magnetic field, expelled electrons still acquire azimuthal velocity, due to the spin–orbit interaction, in opposite direction for spin-up and spin-down electrons: the “Spin Meissner effect.” This results in a macroscopic spin current flowing near the surface of superconductors in the absence of applied fields, of magnitude equal to the critical charge current (in appropriate units). Charge expulsion also gives rise to an interior outward-pointing electric field and to excess negative charge near the surface. In strongly type II superconductors this physics should give rise to charge inhomogeneity and spin currents throughout the interior of the superconductor, to large sensitivity to (non-magnetic) disorder and to a strong tendency to phase separation.

Electromagnetic response of unconventional superconductors

We derive the current response to the linearly polarized electromagnetic field with finite frequency and wave vector incident normally on the specular surface of a clean nonconventional superconductor with orbital spontaneous magnetization parallel to the crystal axis and perpendicular to the crystal surface. The result includes the usual part known from the theory of conventional superconductivity and as well the magneto-optical term typical for the superconductors with spontaneous time reversal breaking. As an application of the basic current-field relation we consider the Kerr effect for the rotation of polarization of infrared light reflected from the superconductor surface.

Do superconductors violate Lenz's law? Body rotation under field cooling and theoretical implications

When a magnetic field is turned on, a superconducting body acquires an angular momentum in direction opposite to the applied field. This gyromagnetic effect has been established experimentally and is understood theoretically. However, the corresponding situation when a superconductor is cooled in a pre-existent field has not been examined. We argue that the conventional theory of superconductivity does not provide a prediction for the outcome of that experiment that does not violate fundamental laws of physics, either Lenz's law or conservation of angular momentum. The theory of hole superconductivity predicts an outcome of this experiment consistent with the laws of physics.

Explanation of the Tao Effect: Theory for the Spherical Aggregation of Superconducting Microparticles in an Electric Field

In a series of experiments Tao and co-workers found that superconducting microparticles in the presence of a strong electrostatic field aggregate into balls of macroscopic dimensions. No explanation of this phenomenon exists within the conventional theory of superconductivity. We show that this effect can be understood within an alternative electrodynamic description of superconductors recently proposed that follows from an unconventional theory of superconductivity. Experiments to test the theory are discussed.

The Lorentz force and superconductivity

To change the velocity of an electron requires that a Lorentz force acts on it, through an electric or a magnetic field. We point out that within the conventional understanding of superconductivity electrons appear to change their velocity in the absence of Lorentz forces. This indicates a fundamental problem with the conventional theory of superconductivity. A hypothesis is proposed to resolve this difficulty. This hypothesis is consistent with the theory of hole superconductivity.

Theory of high-T c superconductivity based on the fermion-condensation quantum phase transition

A theory of high-temperature superconductivity based on the combination of the fermion-condensation quantum phase transition and the conventional theory of superconductivity is presented. This theory describes maximum values of the superconducting gap, which can be as big as Δ1∼0.1ε F , with ε F being the Fermi level. We show that the critical temperature 2T c ≃Δ1. If the pseudogap exists above T c , then 2T*≃Δ1 and T* is the temperature at which the pseudogap vanishes. A discontinuity in the specific heat at T c is calculated. The transition from conventional superconductors to high-T c ones as a function of the doping level is investigated. The single-particle excitations and their lineshape are also considered

Relativistic fluctuations and anomalous Darwin terms in superconductors

The anomalous Darwin term, one of the recently derived relativistic corrections to the conventional theory of superconductivity, is analyzed in detail. This analysis leads to the prediction of unusual types of fluctuations, of relativistic origin, in superconductors. An alternative derivation of the anomalous Darwin term, much simpler than that given originally, is presented and used to clarify some puzzling features of the original derivation. The question of observability of the anomalous Darwin term and the relativistic fluctuations is discussed and the relation to the conventional Darwin term and to earlier proposed superconducting Darwin terms is clarified.