Chapter 18 - Superconductivity

The utilization of the current-interference phenomenon in superconductors for producing electrical measuring instruments serves greatly to expand the boundary of electromagnetic measurements towards very small values. Moreover, it was found that the voltage, current, and magnetic flux are related to the fundamental physical constant, the magnetic flux quantum h/2e. This fact makes it possible to expect a transfer in the field of electromagnetic measurements to a natural electromagnetic reference standard.

Conventional superconductivity in bulk objects is characterized by three phenomenological features: zero resistivity, perfect diamagnetism (Meissner effect) and energy gap in the excitation spectrum. In this paper we demonstrate that these attributes of superconductivity do not apply to ultra-small objects governed by the essentially nanoscale phenomenon which is quantum fluctuations. The observation results in fundamental limitations of utilization of superconducting elements in nanoelectronic circuits. However, together with this rather pessimistic conclusion, the indicated size phenomena lead to a new class of nanoscale devices and applications.

In 1950 Vitaly Ginzburg and Lev Landau introduced in their seminal work1 (which will be referred to as GL hereafter) the equations which have been known ever since as GinzburgLandau (GL) equations and which became among the most universal equations of modern physics. Ginzburg-Landau equations either in their original or modified form describe a wealth of phenomena and systems including superconductivity and superfluidity, nonlinear waves in active media, pat-tern formation and liquid crystals and supersymmetric conformal field theories2. Ginzburg-Landau equations were one of the first nonlinear theories to demonstrate solutions in the form of topological singularities. Historically, GL theory was an extension of the Landau theory of second-order phase transitions3 onto the quantum phenomenon of superconductivity. It was based on the idea that the normal metal-superconducting state transition is, in the absence of a magnetic field, a thermodynamic second-order transition. An order parameter Ψ of the GL theory is an averaged wave function of superconducting electrons. Because of its (comparative) simplicity and physical transparency, GL theory has become one of the most universal and powerful tools in studies of superconductivity. In what follows, we briefly review the history and the content of GL theory and discuss its most standard applications.

Based on the non-adiabatic ab initio theory of complex electronic ground states, treating electronic structure as explicitly dependent on nuclear dynamics, i.e. on instantaneous nuclear coordinates Q and momenta P, it has been shown that electron-phonon coupling in superconductors induces temperature-dependent electronic structure instability related to analytic critical point (ACP) fluctuation of bands across the Fermi level (FL). As ACP approaches FL, the adiabatic chemical potential μ ad is substantially reduced to μ antad (μ ad ≫ μ antad < ℏω) and the adiabatic Born-Oppenheimer approximation is violated. Due to the effect of nuclear dynamics, the system is stabilized as an antiadiabatic state of broken symmetry with a gap in its one-particle spectrum. Distorted nuclear structure, which is related to nuclei in the phonon mode r inducing transition to an anti-adiabatic state, has fluxional character. Geometric degeneracy of the antiadiabatic ground state enables formation of mobile bipolarons that can move over lattice in external electric potential as super-carriers without dissipation. Thermodynamic properties in the anti-adiabatic state correspond to thermodynamics of superconductors. It has been shown that Cooper-pair formation is not the primary reason for transition into superconducting state, but it is a consequence of anti-adiabatic state formation and represents correction to electron correlation energy. As illustrative examples, results of application of anti-adiabatic theory in study of superconductors MgB2, YB6, YBa2Cu3O7, Nb3Ge and corresponding (non superconducting) analogues are presented.

The specific heat of Mn3−xFexSi was measured over a wide temperature range. Aside from the lattice and electronic specific heat components, another component had a significant contribution to the specific heat at low temperatures in the case of x = 0.2; however, its contribution decreased when x = 1.0. It is observed that the net component was retained at temperatures significantly higher than TN for both x. The XAFS spectra of the Mn K-edge for x = 0 not only indicated a smooth structure near the edge, but also an unusually small amplitude in the extended high energy region; however, these features disappeared with Fe doping. The specific heat and XAFS data were discussed in terms of the charge degree of freedom or electronic inhomogeneity.

A boltzon (low density) gas at reduced temperature must ultimately be described by quantum mechanics. The statistical mechanical treatment of such ensembles requires retention of summation forms to admit noncontinuum behavior. Anomalous specific heat is demonstrated with the prospect of multiple peaks for anisotropic energy surfaces. Moreover, a new equation of state arises which reflects the presence of a zero-point translational energy, requiring departure from the ideal gas law asT→0. It is also shown that passage from wave mechanical to kinetic theory of gases follows both simply and naturally via de Broglie’s relation.

Superconductivity: BCS theory

If the Coulomb field between charged particles in an insulator is equivalent to a cloud of virtual photons which may dissociate to virtual electron - positron pairs, a chain reaction of electron - positron annihilations through the insulator is equivalent to a direct current not hindered by ohmic resistance. Zusammungfassung. Wenn das Coulombfeld zwischen geladenen Partikeln in einem Isolator einer Wolke virtuelle Photonen gleichwertig ist, und wenn sich virtuelle Photonen zu virtuellen Elektron - Positron Paaren vervandeln können, dann ist eine Kettenreaktion von Elektron - Positron - Annihilationen durch den Isolator möglich, welches zu einem Strom gleichwertig ist, der vom Ohmischen widerstand nicht behindert wird. An insulator with infinite ohmic resistance does not allow a direct current due to conduction electrons to pass. Nevertheless, a direct current through an insulator can be expected if the Coulomb interactions between the nuclei and electrons of the insulator are equivalent to a cloud of virtual photons, and if a virtual photon may dissociate to a virtual electron - positron pair. If the number of virtual photons per is of the order , where Z is the number of protons per in the insulator and is the fine structure constant, and if a virtual photon has a probability to dissociate to a virtual electron - positron pair, then for protons per , the insulator would contain of the order virtual electron - positron pairs per , i.e. the volume seems to be filled with a gas of virtual electron - positron pairs. If such an insulator is in between a positive anode and a negative cathode, the virtual electrons are attracted to the positive anode and the virtual positrons to the negative cathode. (Inside a good conductor with no electric field, no such polarization can be obtained.) Therefore, a conduction electron which is halted at the cathode side of the insulator can be annihilated by a virtual positron. Its associated virtual electron partner nearer to the anode is then free to be annihilated by a virtual positron, and so on through the insulator, and finally a free electron appears at the anode side of the insulator. Hence, electric charge may be transported through the insulator not by conduction electrons but by a chain reaction of successive electron - positron annihilations not hindered by ohmic resistance. Transport of electric charge without transport of conduction electrons not hindered by ohmic resistance is superconduction. A chain reaction of annihilations which finally give a free electron at the anode conserves energy in the total process. An external magnetic or electric field may disturb the orientation of the virtual electron - positron pairs and the chain reaction, and thus destroy the superconductivity. Since the effect described above is possible only in extremely good insulators and not in conductors, it may remind one of the high- superconduction in ceramics first seen by Bednorz and Müller [1]. For a vacuum, which is a good insulator, the only source of virtual electron - positron pairs is vacuum fluctuations allowed by Heisenberg's uncertainty relation. Leakage or discharge through a vacuum due to such electron - positron pairs is not inconceivable. Vice versa, observation of leakage or discharge through a vacuum is consistent with the concept of virtual electron - positron pairs in a vacuum.

Magnetization and calorimetric investigations carried out on various representative austenitic stainless steel alloys reveal complicated temperature-dependent magnetic structures. A low-temperature calorimetric anomaly characteristic of superparamagnetism is exhibited by 310S stainless steel [1]. Nitronic 33 possesses not only an anomalous low-temperature specific heat, but also a distinct antiferromagnetic transition at about 180 K. The calorimetric behavior of Inconel X750 is comparable to that of 310S stainless steel [1]; the former, however, contains γ′ precipitates whose contribution to the observed magnetic properties is unclear. This investigation focuses attention on the magnetic and calorimetric properties of Inconel X750 whose weakly magnetic behavior and anomalous low-temperature heat capacity lead to a description in terms of superparamagnetism.

Singly quantized magnetic fluxes in superconducting lead films have been directly observed in the form of magnetic-flux-line distributions by using an electron-holography technique. Combining this with the digital-phase-analysis method, we were able to determine the flux quantum h/2e for individual fluxes with a precision of \ensuremath{\sim}h/100e, and analyze the distributions of field-vector components around the fluxon centers. The internal-field distributions obtained were compared with those calculated from the Ginzburg-Landau equations with use of some models, and an overall agreement was found between them. We also observed the changes of the magnetic-flux structures of lead thin films as a function of their thickness. Fluxon pairs were observed in 0.2-\ensuremath{\mu}m-thick films, which may correspond to those suggested by Kosterlitz-Thouless theory.

Anomalous lattice specific heat and rattling phonon modes in quadruple perovskites

Anomalous shock compressibility and specific heat of diamond

Four different mixtures such as complex mixture A, [Co(H2O)4(HPO4)](C3H4N2)(H2O)2 ∙ 0.2 (C3H4N2), complex mixture B, [Co(H2O)6](H2PO4)(OH)(H2O) ∙(C3H4N2)2, mixture C, 0.34 Co(PO3)2∙0.15(C3H3N2Na), and complex mixture D, 0.03Co(PO3)2∙0.25(C3H3N2Na) ∙0.1 [Co(H2O)6]SO4.H2O∙0.6(C3H4N2), were synthesized using ortho-phosphoric acid and meta-phosphoric acid with cobalt sulfate heptahydrate and imidazole in ambient conditions. These mixtures have been well characterized by different thermo-analytical techniques. Differential Scanning Calorimetry (DSC) has been carried out at different heating rates such as 5, 10, 20, and 30 K min−1 at atmospheric conditions. The specific heat capacity was measured at low temperatures up to 173 K for mixture C at a rate of 10 K min−1. From the thermal analysis, it can be observed that the complex mixtures A and B prepared using phosphoric acid and mixture C prepared using meta-phosphoric acid behave as heat repellent material owing to their exothermic behavior at high temperature. The anomalous negative specific heat capacity exhibited by the mixtures is explained using partial molar quantities. Among all the four complex mixtures, the complex mixture A has been found to be the best heat repellent material. The complex mixture B can be used as heat storage material up to temperature ~550 K due to its endothermic behavior. These phosphate materials can be used for longer period of time due to their stability and insolubility in aqueous media. The heat can be extracted from any system that is coated with these phosphate mixtures using high conductivity copper rod.

Three-body problem involving two valence holes and a single conduction electron, which appears in the study of the final state of the resonant photoemission in insulators and semiconductors, is formulated to be solved exactly in a two-band Hubbard model by use of Faddeev's scattering theory. The wave functions and energy eigenvalues are calculated numerically in a one-dimensional model. By use of this exact solution of the three-body problem, resonance photoemission spectra are studied from a weak correlation resion to a strong one. It is shown that the approximation used in the past analysis, in which two valence holes are assumed to be localized, deviates from the present results even in the strong correlation region U v v ∼2 W v with U v v and W v denoting the Coulomb integral and the band width of valence holes, respectively.

Dense cerium and uranium compounds, which can be considered as lattice extensions of the diluted ‘one-impurity Kondo system’, present new interesting physical effects, mainly due to the interaction between f electrons and the conductions electrons. If the f electron energy er is very close to the Fermi energy i;F there are valence fluctuations.