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We theoretically study the superconductivity in hole-doped cuprate superconductors by employing a model composed of surface and bulk CuO 2 layers; small polarons are assumed to be formed from the doped holes in the bulk layer, but not in the surface layer due to the lack of a charge reservoir layer that covers the surface CuO 2 layer and stabilizes the small polarons. In this model, spin-vortices are created in the bulk with the small polarons at their centers and spin-twisting itinerant motion of electrons occurs; it gives rise to a gauge field from the singularities of the many-body wave function existing at the centers of the spin-twisting motion. We assume that the d-wave pairing is realized in the surface CuO 2 layer through the appearance of the number changing operators generated by the emergent gauge field. To deal with this situation, we employ the particle number conserving Bogoliubov-de Gennes equations developed by one of the present authors. The obtained single-particle excitations explain the experimentally observed Fermi arc in the ARPES and V-shaped differential conductance in the STS. [ABSTRACT FROM AUTHOR]

A fundamentally revised version of superconductivity theory has been put forward since the standard theory of superconductivity based on the BCS theory cannot explain superconductivity in cuprates discovered in 1986, and reexaminations on several experimental results on the conventional superconductors indicate the necessity for a fundamental revision. The revision is made on the origin of the superconducting phase variable, which is attributed to a Berry connection arising from many-body wave functions. With this revision, the theory can be cast into a particle number conserving formalism. We have developed a method to calculate superconducting states with the Berry connection using the particle number conserving version of the Bogoliubov-de Gennes equations. [ABSTRACT FROM AUTHOR]

Although the standard theory of superconductivity based on the BCS theory is a successful one, several experimental results indicate the necessity for a fundamental revision. We argue that the revision is on the origin of the phase variable for superconductivity; this phase appears as a consequence of the electron-pairing in the standard theory, but its origin is a Berry connection arising from many-body wave functions. When this Berry connection is non-trivial, it gives rise to a collective mode that generates supercurrent; this collective mode creates number-changing operators for particles participating in this mode, and these number-changing operators stabilize the superconducting state by exploiting the Cooper instability. In the new theory, the role of the electron-pairing is to stabilize the nontrivial Berry connection; it is not the cause of superconductivity. In BCS superconductors, however, the simultaneous appearance of the nontrivial Berry connection and the electron-pairing occurs. Therefore, the electron-pairing amplitude can be used as an order parameter for the superconducting state. We revisit the Andreev−Saint-James reflection and the Josephson effect. They are explained as consequences of the presence of the Berry connection. Bogoliubov quasiparticles are replaced by the particle-number conserving Bogoliubov excitations that describe the transfer of electrons between the collective and single-particle modes. There are two distinct cases for the Josephson effect; one of them contains the common Bogoliubov excitations for the two superconductors in the junction, and the other does different Bogoliubov excitations for different superconductors. The latter case is the one considered in the standard theory; in this case, the Cooper pairs tunnel through without Bogoliubov excitations, creating an impression that the supercurrent is a flow of Cooper pairs; however, it does not explain the observed ac Josephson effect under the experimental boundary condition. On the other hand, the former case explains the ac Josephson effect under the experimental boundary condition. In this case, it is clearly shown that the supercurrent is a flow of electrons brought about by the non-trivial Berry connection which provides an additional U(1) gauge field besides the electromagnetic one. [ABSTRACT FROM AUTHOR]

Although the standard theory of superconductivity based on the BCS theory is a successful one, there are several experimental results that indicate the necessity for fundamental revisions. One of them is the mass in the London moment. Experiments indicate the mass in the London moment is the free electron mass although the BCS theory and its extension predict it to be an effective mass. We show that this discrepancy is lifted if we install the London's superpotential in the theory, and identify it as the Berry phase arising from the many-body wave functions. Then, the induced current by the applied magnetic field becomes a stable current calculated using the free energy in contrast to the linear response current assumed in the standard theory which yields the Nambu-Goldstone mode. The Nambu-Goldstone mode arising from the breakdown of the global U(1) gauge invariance in the standard theory is replaced by the collective mode arising from the Berry connection. Then, the free electron mass appears in the London moment. [ABSTRACT FROM AUTHOR]

We show that two phenomena of superfluidity, superfluidity of weakly interacting bosons and superconductivity of the BCS model, are unified using the collective mode arising from the Berry connection for many-body wave functions. The superfluidity is attributed to the presence of this mode, which is stabilized by the interaction between particles that causes fluctuations of the number of particles participating in it. It is suggested that the existence of this collective mode and its stabilization is more fundamental to the occurrence of superconductivity than the electron-pair formation. [ABSTRACT FROM AUTHOR]

Superconductivity is a phenomenon where an external feeding current flows through the system without voltage drop. This is explained if an energy minimum exists under the current feeding boundary condition. We have found such minima in the system exhibiting spin-twisting itinerant motion of electrons with the Rashba spin–orbit interaction due to constraints of the charge conservation and single-valued requirement of the wave function. The supercurrent is shown to have the London equation form that exhibits the flux quantum h/2e. [ABSTRACT FROM AUTHOR]

We examine some consequences of the duality that a U(1) phase factor added on a wave function describes a whole system motion and also plays the role of a U(1) gauge potential. First, we show that the duality solves a long-standing puzzling problem that the 'flux rule' (the Faraday's induction formula) and the Lorentz force calculation for an emf emerging in an electron system moving in a magnetic field give the same result (Feynman et al. 1963). Next, we examine a U(1) phase factor induced on the wave function for an electron system due to the single-valuedness requirement of the wave function with respect to the electron coordinates, and its consequential appearance of a U(1) instanton. This instanton explains the Meissner effect, supercurrent generation, flux quantization in the units of ${{h} \over {2e}}$ , and the voltage quantization in the units of ${{hf} \over {2e}}$ across the Josephson junction in the presence of a radiation field with frequency f. In the experiment, a radiation field must be present to have a finite voltage across the Josephson junction; but a clear explanation for it has been lacking. The present work provides an explanation for it, and also explains the high precision of the quantized voltage as due to a topological effect. [ABSTRACT FROM AUTHOR]

A theoretical calculation for the superconducting transition temperature of the hole-doped cuprate is performed based on supercurrent generation by the spin-twisting itinerant motion of electrons. The superconducting transition temperature, T, is determined by a numerical simulation as the stabilization temperature of the coherence-length-sized loop currents, 'spin-vortex-induced loop currents (SVILCs),' generated by the spin-twisting itinerant motion of electrons. The simulation indicates that the stabilization of the SVILCs occurs in two steps; when temperature is decreased from room temperature, first, the phase where the sum of the winding numbers of the SVILCs is zero appears; with further decrease of the temperature, the phase where the winding numbers of the SVILCs are fixed appears. We identify the latter to the superconducting phase, and the former to the temperature below which the Kerr rotation is observed. The calculated T value is close to the experimental value around the optimal doping. It scales as ${{t^{2}} \over U}$ in a similar manner to the antiferromagnetic spin-fluctuation, where t is the nearest neighbor transfer integral and U is the on-site Coulomb repulsion parameter. The calculated T disagrees in the underdoped and overdoped regions. These disagreements are explained as due to the reduction of T by the quantum criticality arising from the two quantum critical points at the lowest and highest ends of the hole density x of the superconducting phase, where the former corresponds to the percolation threshold of the spin-vortices, and the latter to the spin-vortex formation-destruction critical point. [ABSTRACT FROM AUTHOR]

In a uniform magnetic field, the BCS type pairing is taken over by the pairing of spin-twisting itinerant motion states due to the Rashba spin-orbit interaction. It gives rise to stable eddy currents forced to flow by the single-valued requirement of the wave function. They are stabilized by the energy gap of the electron pairing and protected by topological winding numbers of the wave function for the spin-twisting itinerant motion. The supercurrent is generated by a collection of such eddy currents. [ABSTRACT FROM AUTHOR]

Based on a new supercurrent generation mechanism proposed for the cuprate superconductivity (as reported by Koizumi (J. Supercond. Nov. Magn. 24:1997, ); Hidekata and Koizumi (J. Supercond. Nov. Magn. 24:2253, ); Koizumi et al. (J. Supercond. Nov. Magn. 27:121, ); Koizumi et al. (J. Supercond. Nov. Magn. ), we re-derive the ac Josephson effect including the current flow through the leads connected to the Josephson junction and the impressed electromotive force. It is noted that the actual experimental boundary condition where the Josephson frequency 2 e V/ h ( h is Planck's constant, e is the absolute value of electron charge, and V is the dc voltage across the Josephson junction) is measured differently from the one assumed by Josephson, and 2 e V/ h is obtained by the electron tunneling instead of the Cooper pair tunneling. It is also indicated that the standard textbook description for the Josephson relation, 'if a dc voltage V is applied, the time-variation of ϕ occurs' (as reported by Feynman et al. (); Ashcroft and Mermin (); Kittel (); Tinkham () ( ϕ is related to the tunneling current as J = J sin ϕ) should be rephrased, 'if the time-variation of ϕ is introduced, a voltage difference V appears.' We show that by adding the Rashba spin-orbit interaction to the Bardeen, Cooper, and Schrieffer (BCS) Hamiltonian, the spin-twisting itinerant motion of electrons is stabilized in the BCS superconductors; thus, it is suggested that the present, new supercurrent generation mechanism is also relevant to the BCS superconductors, i.e., the true origin of the supercurrent generation in the BCS superconductors may also be the spin-twisting itinerant motion of electrons. [ABSTRACT FROM AUTHOR]

We propose a novel supercurrent generation mechanism in the cuprate. The supercurrent is generated as a collection of the spin-vortex-induced loop currents created with the doped holes at their centers. A quartet of the spin-vortices with width 4 a ( a is the lattice constant of the CuO plane) is the stable unit of the spin-vortices, and an assembly of them creates a network channel for the supercurrent flow. A macroscopic supercurrent flows when they cover the whole CuO plane. The Ginzburg-Landau macroscopic wave function formalism is also derived from the present supercurrent generation mechanism. [ABSTRACT FROM AUTHOR]

The persistent current generation in the cuprate is theoretically investigated based on the spin-vortex superconductivity theory. We present a way to impose the single-valued condition on wave functions and clarify the appearance of a vector potential and the persistent current generation by it when the spin-vortices are created by the conduction electrons. We attribute the reason for the very high superconducting transition temperature in the cuprate to the enhanced stability of the spin-vortices by the strong hole-lattice interaction. [ABSTRACT FROM AUTHOR]

We explain several anomalous phenomena observed in the pseudogap phase of hole-doped cuprates based on the recently proposed spin-vortex superconductivity theory. In this theory, doped-holes become almost immobile small polarons, and spin-vortices are formed with those small polarons as their centers. A Hartree-Fock field for conduction electrons that is optimized for the interaction energy of local moments is derived; it contains a fictitious magnetic field arising from spin-vortices, and yields current carrying states. The obtained currents are loop currents around spin-vortices, i.e., the spin-vortex-induced loop currents (SVILCs), and a collection of them produces a macroscopic current. The SVILC explains (1) nonzero Kerr rotation in zero-magnetic field after exposed in a strong magnetic field; (2) the change of the sign of the Hall coefficient with temperature change; (3) the suppression of superconductivity in the x=1/8 static-stripe ordered sample; and (4) a large anomalous Nernst signal, including its sign-change with temperature change. We show that the hourglass-shaped magnetic excitation spectrum is the evidence for the existence of spin-vortices. We further argue that the 'Fermi-arc' in the ARPES is a support for the presence of localized moments in the bulk; a disconnected arc-shaped Fermi surface is obtained by assuming an antiferromagnetic interaction between the localized moments in the bulk and itinerant electrons in the surface region. [ABSTRACT FROM AUTHOR]

We present a theory of superconductivity based on the theoretical prediction that a macroscopic persistent current is generated by spin-vortices. It explains the origin of the phase variable θ that is canonical conjugate to the superfluid density as a Berry phase arising from the spin-vortex formation. This superconductivity does not require Cooper-pairs as charge carriers, thus, is not directly related to the standard theory based on the BCS one; however, it exhibits the flux quantization in the unit Φ= hc/2| e|, where h is Planck's constant, c the speed of light, and e the electron charge; and the AC Josephson frequency, f=2| e| V/ h, where V is the voltage of the battery connected to the superconductor-insulator-superconductor junction. In due course, it is found that the standard derivation of the AC Josephson frequency misses a term arising from the flow of particles through the leads connected to the junction. If this contribution is included, the observed f indicates that the phase θ is a variable conjugate to the number density of charge e carriers instead of the currently accepted charge 2 e carriers. We propose an experiment that discriminates whether it is e or 2 e. If the above claim is verified, it means that the BCS theory cannot predict whether a particular compound is a superconductor or not since it does not explain the origin of θ. A connection between the present mechanism and the BCS mechanism is discussed; the fact that the BCS theory gives an excellent estimate of T is attributed to the fact that it predicts the temperature at which spin-vortices become long-lived due to the energy gap formation; since the stabilization by the electron-pair formation is compatible with the present mechanism, asymmetries observed in the even and odd number of electron systems are preserved. The most notable difference is that the persistent current generation is formulated in a strictly particle-number-conserving manner. Thus, it does not violate the superselection rule for the total charge. [ABSTRACT FROM AUTHOR]