Dynamic Hubbard models describe the fact that the wavefunction of an electron in an atomic orbital expands when a second electron occupies the orbital. These models give rise to superconductivity driven by lowering of kinetic energy when the electronic energy band is almost full, with higher transition temperatures resulting when the ions are negatively charged. We show that the charge distribution in dynamic Hubbard models can be highly inhomogeneous in the presence of disorder, and that a finite system will expel {\it negative charge} from the interior to the surface, and that these tendencies are largest in the parameter regime where the models give rise to highest superconducting transition temperatures. High $T_c$ cuprate materials exhibit charge inhomogeneity and they exhibit tunneling asymmetry, a larger tendency to emit electrons rather than holes in NIS tunnel junctions. We propose that these properties, as well as their high $T_c$'s, are evidence that they are governed by the physics described by dynamic Hubbard models. Below the superconducting transition temperature the models considered here describe a negatively charged superfluid and positively charged quasiparticles, unlike the situation in conventional BCS superconductors where quasiparticles are charge neutral on average. We examine the temperature dependence of the superfluid and quasiparticle charges and conclude that spontaneous electric fields should be observable in the interior and in the vicinity of superconducting materials described by these models at sufficiently low temperatures. We furthermore suggest that the dynamics of the negatively charged superfluid and positively charged quasiparticles in dynamic Hubbard models can provide an explanation for the Meissner effect observed in superconducting materials.
Dynamic Hubbard models are extensions of the conventional Hubbard model that take into account the fact that atomic orbitals expand upon double occupancy. It is shown here that systems described by dynamic Hubbard models have a tendency to expel negative charge from their interior to the surface, and to develop charge inhomogeneity and even phase separation in the bulk. These effects are associated with lowering of electronic kinetic energy. We propose that these models may explain the charge inhomogeneity and negatively charged grain boundaries observed in cuprate oxides and other materials.
The Meissner effect and the Spin Meissner effect are the spontaneous generation of charge and spin current respectively near the surface of a metal making a transition to the superconducting state. The Meissner effect is well known but, I argue, not explained by the conventional theory, the Spin Meissner effect has yet to be detected. I propose that both effects take place in all superconductors, the first one in the presence of an applied magnetostatic field, the second one even in the absence of applied external fields. Both effects can be understood under the assumption that electrons expan…
Non-invasive magnetic field sensing using optically - detected magnetic resonance of nitrogen-vacancy (NV) centers in diamond was used to study spatial distribution of the magnetic induction upon penetration and expulsion of weak magnetic fields in several representative superconductors. Vector magnetic fields were measured on the surface of conventional, Pb and Nb, and unconventional, LuNi$_2$B$_2$C, Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$, Ba(Fe$_{0.93}$Co$_{0.07}$)$_2$As$_2$, and CaKFe$_4$As$_4$, superconductors, with diffraction - limited spatial resolution using variable - temperature confocal sy…
We review the literature on what classical physics has to say about the Meissner effect and the London equations. We first discuss the relevance of the Bohr-van Leeuwen theorem for the perfect diamagnetism of superconductors. The conclusion is that the theorem is based on assumptions that are not valid. We also point out results in the literature which prove that the magnetic flux expulsion from a sample cooled to superconductivity can be simply understood as an approach to the magnetostatic energy minimum. These results have been published several times but still many textbooks on magnetism c…
A recent study (arXiv:1109.1968v2, to be published in American Journal of Physics) claims to provide a classical explanation of the Meissner effect. However, the argument misuses de Gennes' derivation of flux expulsion in superconductors.
The magnetic response related to paramagnetic Meissner effect (PME) is studied in a high quality single crystal ZrB12 with non-monotonic vortex-vortex interactions. We observe the expulsion and penetration of magnetic flux in the form of vortex clusters with increasing temperature. A vortex phase diagram is constructed which shows that the PME can be explained by considering the interplay among the flux compression, the different temperature dependencies of the vortex-vortex and the vortex-pin interactions, and thermal fluctuations. Such a scenario is in good agreement with the results of the …
An electric current generates a magnetic field, and magnetic fields cannot exist in the interior of type I superconductors. As a consequence of these two facts, electric currents can only flow near the surface of a type I superconducting wire so that the self-field vanishes in the interior. Here we examine how an electric current flowing through the entire cross-section of a normal conducting wire becomes a surface current when it enters a superconducting portion of the wire. This geometry provides insight into the dynamics of magnetic flux expulsion that is not apparent in the Meissner effect…
It was recently pointed out that so-called "superhydrides", hydrogen-rich materials that appear to become superconducting at high temperatures and pressures, exhibit physical properties that are different from both conventional and unconventional standard type I and type II superconductors [1,2]. Here we consider magnetic field expulsion in the first material in this class discovered in 2015, sulfur hydride [3]. A nuclear resonant scattering experiment has been interpreted as demonstration that the Meissner effect takes place in this material [4,5]. Here we point out that the observed effect, …
The Meissner effect has been studied in Ba(Fe0.926Co0.074)2As2 and Ba0.6K0.4Fe2As2 single crystals and compared to well known, type-II superconductors LuNi2B2C and V3Si. Whereas flux penetration is mostly determined by the bulk pinning (and, perhaps, surface barrier) resulting in a large negative magnetization, the flux expulsion upon cooling in a magnetic field is very small, which could also be due to pinning and/or surface barrier effects. However, in stark contrast with the expected behavior, the amount of the expelled flux increases almost linearly with the applied magnetic field, at leas…
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 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 into the normal region. From a microscopic point of view it is shown that the perfect diamagnetism of superconductors requires that superconducting …
A theorem on the magnetic energy minimum in a perfect, or ideal, conductor is proved. Contrary to conventional wisdom the theorem provides a classical explanation of the expulsion of a magnetic field from the interior of a conductor that loses its resistivity. It is analogous to Thomson's theorem which states that static charge distributions in conductors are surface charge densities at constant potential since these have minimum energy. This theorem is proved here using a variational principle. Then an analogous result for the magnetic energy of current distributions is proved: magnetic energ…
In 1933, Meissner and Ochsenfeld reported the expulsion of magnetic flux, the diamagnetic Meissner effect, from the interior of superconducting lead. This discovery was crucial in formulating the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity. In exotic superconducting systems BCS theory does not strictly apply. A classical example is a superconductor-magnet hybrid system where magnetic ordering breaks time-reversal symmetry of the superconducting condensate and results in the stabilisation of an odd-frequency superconducting state. It has been predicted that under appropriate con…
It is proposed that superconductors possess a hidden `hole core' buried deep in the Fermi sea. The proposed hole core is a small region of the Brillouin zone (usually at the center of the zone) where the lowest energy states in the normal state reside. We propose that in the superconducting state these energy states become {\it singly occupied} with electrons of a definite spin helicity. In other words, that holes of a definite spin helicity condense from the top to the bottom of the band in the transition to superconductivity, and electrons of that spin helicity `float' on top of the hole cor…
We use a scanning nanometer-scale superconducting quantum interference device (SQUID) to image individual vortices in amorphous superconducting MoSi thin films. Spatially resolved measurements of the magnetic field generated by both vortices and Meissner screening satisfy the Pearl model for vortices in thin films and yield values for the Pearl length and bulk penetration depth at 4.2 K. Flux pinning is observed and quantified through measurements of vortex motion driven by both applied currents and thermal activation. The effects of pinning are also observed in metastable vortex configuration…
The Meissner effect, magnetic field expulsion, is a hallmark of superconductivity. Associated with it, superconductors exclude applied magnetic fields. Recently Minkov et al. presented experimental results reportedly showing "definitive evidence of the Meissner effect" in sulfur hydride and lanthanum hydride under high pressure [1], and more recently Eremets et al. argued that "the arguments against superconductivity (in hydrides) can be either refuted or explained" [2]. Instead, we show here that the evidence presented in those papers does not support the case for superconductivity in these m…
Theoretical explanation of the Meissner effect involves proportionality between current density and vector potential [1], which has many deep consequences. Amongst them, one can speculate that superconductors in a magnetic field "find an equilibrium state where the sum of kinetic and magnetic energies is minimum" and this state "corresponds to the expulsion of the magnetic field" [2]. This statement still leaves an open question: from which source is superconducting current acquiring its kinetic energy? A naïve answer, perhaps, is from the energy of the magnetic field. However, one can conside…
The theory of hole superconductivity proposes that superconductivity is driven by lowering of quantum kinetic energy and is associated with expansion of electronic orbits and expulsion of negative charge from the interior to the surface of superconductors and beyond. This physics provides a dynamical explanation of the Meissner effect. Here we propose that similar physics takes place in superfluid helium 4. Experimental manifestations of this physics in $^4He$ are the negative thermal expansion of $^4He$ below the $λ$ point and the "Onnes effect", the fact that superfluid helium will creep up …
From the outset of superconductivity research it was assumed that no electrostatic fields could exist inside superconductors, and this assumption was incorporated into conventional London electrodynamics. Yet the London brothers themselves initially (in 1935) had proposed an electrodynamic theory of superconductors that allowed for static electric fields in their interior, which they unfortunately discarded a year later. I argue that the Meissner effect in superconductors necessitates the existence of an electrostatic field in their interior, originating in the expulsion of negative charge fro…
Magnetic flux trapped during the cooldown of superconducting radio-frequency cavities through the transition temperature due to incomplete Meissner state is known to be a significant source of radio-frequency losses. The sensitivity of flux trapping depends on the distribution and the type of defects and impurities which pin vortices, as well as the cooldown dynamics when the cavity transitions from a normal to superconducting state. Here we present the results of measurements of the flux trapping sensitivity on 1.3 GHz elliptical cavities made from large-grain niobium with different purity fo…
In paper III of this series (arXiv:0901.3612) we proposed a scenario of superconductivity driven by hole "undressing" that involved a complete redistribution of the occupation of single particle energy levels: the holes near the top of the band were proposed to all condense to the bottom of the band. Here we consider a less drastic redistribution involving electrons with a definite spin chirality and show that it is in fact energetically favored by the Coulomb exchange matrix element $J$ over the scenario proposed earlier. It is shown that spin splitting with chiral states reduces the Coulomb …
We report an unusual enhancement of the magnetic induction in single crystals of the magnetic superconductor RbEuFe$_4$As$_4$ , highlighting the interplay between superconducting and magnetic subsystems in this material. Contrary to the conventional Meissner expulsion of magnetic flux below the superconducting transition temperature, we observe a substantial boost of the magnetic flux density upon approaching the magnetic transition temperature, Tm. Direct imaging of the flux evolution with a magneto-optical technique, shows that the magnetic subsystem serves as an internal magnetic flux pump,…
Microscopic variations in composition or structure can lead to nanoscale inhomogeneity in superconducting properties such as the magnetic penetration depth, but measurements of these properties are usually made on longer length scales. We solve a generalized London equation with a non-uniform penetration depth, lambda(r), obtaining an approximate solution for the disorder-averaged Meissner effect. We find that the effective penetration depth is different from the average penetration depth and is sensitive to the details of the disorder. These results indicate the need for caution when interpre…
Measuring with high precision the electrical resistance of highly ordered natural graphite samples from a Brazil mine, we have identified a transition at $\sim$350~K with $\sim$40~K transition width. The step-like change in temperature of the resistance, its magnetic irreversibility and time dependence after a field change, consistent with trapped flux and flux creep, and the partial magnetic flux expulsion obtained by magnetization measurements, suggest the existence of granular superconductivity below 350~K. The zero-field virgin state can only be reached again after zero field cooling the s…
Anisotropic interface-confined superconductivity in FeTe-based heterostructures
Ames National Laboratory（艾姆斯国家实验室）；Department of Physics and Astronomy, Iowa State University（爱荷华州立大学物理与天文系）；Department of Physics, The Pennsylvania State University（宾夕法尼亚州立大学物理系）
