Gauge invariance, massless modes and topology of gauge fields in multi-band superconductors

Multi-phase physics is a new physics of multi-gap superconductors. Multi-band superconductors exhibit many interesting and novel properties. We investigate the dynamics of the phase-difference mode and show that this mode yields a new excitation mode. The phase-difference mode is represented as an abelian vector field. There are massless modes when the number of gaps is greater than three and the Josephson term is frustrated. The fluctuation of phase-difference modes with non-trivial topology leads to the existence of a fractional-quantum flux vortex in a magnetic field. A superconductor with a fractional-quantum flux vortex is regarded as a topological superconductor with the integer Chern number.Comment: Proceedings of the 12th Asia and Pacific Physics Conference (2013

Reply to "Comment on 'Isotope effect in multi-band and multi-channel attractive systems and inverse isotope effect in iron-based superconductors'"

The Comment insists on the following: in our model it is assumed that the effective interactions have specific energy ranges within the single band with a cutoff at \omega_1 for the phononic part and a range from \omega_1 to \omega_2 in the AF channel. Our reply is that we assume that V_i(k,k')\neq 0 if |\xi_k|<\omega_i and |\xi_{k'}|<\omega_i, and otherwise V_i(k,k')= 0 (i=1,2), as stated in our paper. This is the model of BCS type with two attractive interactions, and this assumption is the characteristic of the BCS approximation. The claim "the integration limits have been modified such that the AF channel mediated pairing sets in where the ph-channel pairing terminates and is limited at an energy given by \omega_j=\omega_{AF}" in the Comment is wrong. We describe the model and the method to solve the gap equation in more detail

Field resilient superconductivity in atomic layer crystalline materials

The recent study [S. Yoshizawa et al., Nature Communications 12, 1 (2021)] reported the field resilient superconductivity, that is, the enhancement of an in-plane critical magnetic field $H^{||}_{\rm c2}$ exceeding the paramagnetic limiting field in an atomic layer crystalline ($\sqrt{7}\times\sqrt{3}$)-In on a Si(111) substrate. The present article elucidates the origin of the observed field resilient noncentrosymmetric superconductivity in the highly crystalline two dimensional material. We developed the quasiclassical theory by incorporating the Fermi surface anisotropy together with an anisotropic spin splitting specific to atomic layer crystalline systems. The enhancement of the rescaled $H^{||}_{\rm c2}$ by the critical temperature at zero field occurs not only due to the disorder effect but also to an anisotropic non-ideal Rashba spin texture depending on the field direction. We also study the parity mixing effect to show the enhancement of $H^{||}_{\rm c2}$ is limited in the moderately clean regime because of the fragile $s$-wave pairing against nonmagnetic scattering in the case of the dominant odd parity component of a pair wavefunction. Furthermore, from the analysis of the transition line, we identify the field resilience factor taking account of the scattering and suppression of paramagnetic effects and discuss the origin of the field resilient superconductivity. Through the fitting of the $H^{||}_{\rm c2}$ data, the normal state electron scattering is discussed, mainly focusing on the role of atomic steps on a Si(111) surface.Comment: 13 pages, 6 figures, 1 tabl

Madelung Energy of the Valence Skipping Compound BaBiO3_3

Several elements show valence skip fluctuation, for instance, Tl forms the compounds in valence states +1 and +3, and Bi forms in +3 and +5 states. This kind of fluctuation gives rise to a negative effective attractive interaction and the Kondo effect. In the compounds of valence skipping elements, the carrier doping will induce superconductivity with high critical temperature. For example, Ba$_{1-x}$K$_x$BiO$_3$ shows high $T_c$ which is unlikely from the conventional electron-phonon mechanism. The reason for the missing of some valence states in such valence skip compounds remains a mystery. We have performed the evaluation of the Madelung potential for BaBiO$_3$, and have shown for the first time that charge-ordered state is stabilized if we take into account the polarization of the oxygen charge. We argue that the effective Coulomb interaction energy $U$ may be negative evaluating the local excitation energy

Sheet Dependence on Superconducting Gap in Oxygen-Deficient Iron-based Oxypnictide Superconductors NdFeAs0.85

Photoemission spectroscopy with low-energy tunable photons on oxygen-deficient iron-based oxypnictide superconductors NdFeAsO0.85 (Tc=52K) reveals a distinct photon-energy dependence of the electronic structure near the Fermi level (EF). A clear shift of the leading-edge can be observed in the superconducting states with 9.5 eV photons, while a clear Fermi cutoff with little leading-edge shift can be observed with 6.0 eV photons. The results are indicative of the superconducting gap opening not on the hole-like ones around Gamma (0,0) point but on the electron-like sheets around M(pi,pi) point.Comment: 8 pages, 3 figure

High-Energy Anomaly in the Band Dispersion of the Ruthenate Superconductor

We reveal a “high-energy anomaly" (HEA) in the band dispersion of the unconventional ruthenate superconductor Sr2RuO4, by means of high-resolution angle-resolved photoemission spectroscopy (ARPES) with tunable energy and polarization of incident photons. This observation provides another class of correlated materials exhibiting this anomaly beyond high-Tc cuprates. We demonstrate that two distinct types of band renormalization associated with and without the HEA occur as a natural consequence of the energetics in the bandwidth and the energy scale of the HEA. Our results are well reproduced by a simple analytical form of the self-energy based on the Fermi-liquid theory, indicating that the HEA exists at a characteristic energy scale of the multielectron excitations. We propose that the HEA universally emerges if the systems have such a characteristic energy scale inside of the bandwidth