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A recent study [S. Yoshizawa {\it et al}., Nature Communications {\bf 12}, 1462 (2021)] reported the occurrence of field-resilient superconductivity, that is, enhancement of the in-plane critical magnetic field $H^{||}_{\rm c2}$ beyond the paramagnetic limiting field, in 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 this highly crystalline two-dimensional material. We develop the quasiclassical theory of superconductivity by incorporating the Fermi surface anisotropy together with an anisotropic spin splitting and texture specific to atomic-layer crystalline systems. In Si(111)-($\sqrt{7}\times\sqrt{3}$)-In, a typical material with a large antisymmetric spin-orbit coupling (ASOC), we show an example where the combination of the ASOC and disorder effect suppresses the paramagnetic depairing and can lead to an enhancement of $H^{||}_{\rm c2}$ compared to an isotropic system only when a magnetic field is applied in a particular direction due to an anisotropic spin texture. We also study the parity-mixing effect to demonstrate that the enhancement of $H^{||}_{\rm c2}$ is limited in the moderately clean regime because of the fragile $s$+$p$-wave pairing against nonmagnetic scattering in the case of the dominant odd-parity component of a pair wavefunction. Furthermore, from 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 fitting of the $H^{||}_{\rm c2}$ data, the normal-state electron scattering is discussed with a prime focus on the role of atomic steps on a Si(111) surface., Comment: 17 pages, 9 figures, 1 table

Superconductors comprising 5d transition metals of Ir and Pt have been widely explored because they have the potential of unique superconductivity caused by the strong spin-orbit interaction (SOI). We successfully synthesized BaIr2, the last Laves phase remaining unsynthesized in the MgCu2-type AM2 (A = Ca, Sr, Ba; M = Rh, Pd, Ir, Pt). BaIr2 was crystallized at 925 C under a pressure of 3.3 GPa via a solid-state reaction between Ba and Ir powders; it was found to have the longest a-lattice constant of 8.038(1) A among AM2. BaIr2 exhibited bulk superconductivity at a transition temperature (Tc) of 2.7 K. BaIr2 was found to have a type-II superconductor with an upper critical field of 67.7 kOe, which was above the Pauli paramagnetic limit (50 kOe). The electron-phonon coupling constant and normalized specific heat jump were measured to be 0.63 and 1.2, respectively, indicating that BaIr2 is a weak-coupling superconductor. The electronic-structure calculations for BaIr2 revealed that the Ir-5d states are dominant at the Fermi energy (EF) and the density of states at the EF is strongly affected by SOI as in the case of CaIr2 and SrIr2., Comment: 9 pages, 8 figures

Antiperovskites are a promising candidate structure for the exploration of new materials. We discovered an antiperovskite phosphide, LaPd$_{3}$P, following our recent synthesis of $A$Pd$_{3}$P ($A$ = Ca, Sr, Ba). While $A$Pd$_{3}$P and (Ca,Sr)Pd$_{3}$P were found to be tetragonal or orthorhombic systems, LaPd$_{3}$P is a new prototype cubic system ($a$ = 9.0317(1) A) with a noncentrosymmetric space group ($I-43m$). LaPd$_{3}$P exhibited superconductivity with a transition temperature ($T_\mathrm{c}$) of 0.28 K. The upper critical field, Debye temperature, and Sommerfeld constant ($\gamma$) were determined as 0.305(8) kOe, 267(1) K, 6.06(4) mJ mol-1 K-2 f.u.-1, respectively. We performed first-principles electronic band structure calculations for LaPd$_{3}$P and compared the theoretical and experimental results. The calculated Sommerfeld constant (2.24 mJ mol-1 K-2 f.u.-1) was much smaller than the experimental value of $\gamma$ because the Fermi energy ($E_\mathrm{F}$) was located slightly below the density of states (DOS) pseudogap. This difference was explained by the increase in the DOS at $E_\mathrm{F}$ due to the approximately 5 at.% La deficiency (hole doping) in the sample. The observed Tc value was much lower than that estimated using the Bardeen-Cooper-Schrieffer equation. To explain the discrepancy, we examined the possibility of an unconventional superconductivity in LaPd$_{3}$P arising from the lack of space inversion symmetry., Comment: 13 pages, 5 figures, 4 tables

In the recently discovered antiperovskite phosphide (Ca,Sr)Pd$_3$P, centrosymmetric (CS) and non-centrosymmetric (NCS) superconducting phases appear depending on the Sr concentration, and their transition temperatures ($T_\mathrm{c}$) differ by as much as one order of magnitude. In this study, we investigated the superconducting properties and electronic band structures of CS orthorhombic (CSo) (Ca$_{0.6}$Sr$_{0.4}$)Pd$_3$P ($T_\mathrm{c}$ = 3.5 K) and NCS tetragonal (NCSt) (Ca$_{0.25}$Sr$_{0.75}$)Pd$_3$P ($T_\mathrm{c}$ = 0.32 K) samples with a focus on explaining their large $T_\mathrm{c}$ difference. Specific heat measurements indicated that CSo (Ca$_{0.6}$Sr$_{0.4}$)Pd$_3$P was an s-wave superconductor in a moderate-coupling regime with a 2$\Delta$$_0$/k$_B$$T_\mathrm{c}$ value of 4.0. Low-lying phonons leading to the strong coupling in the structurally analogous SrPt$_3$P were unlikely to be present in CSo (Ca$_{0.6}$Sr$_{0.4}$)Pd$_3$P. Given that CSo (Ca$_{0.6}$Sr$_{0.4}$)Pd$_3$P and NCSt (Ca$_{0.25}$Sr$_{0.75}$)Pd$_3$P exhibited similar Debye temperatures ($\Theta$$_D$) of approximately 200 K, the large $T_\mathrm{c}$ difference could not be attributed to $\Theta$$_D$.$T_\mathrm{c}$ of each phase was accurately reproduced based on the Bardeen-Cooper-Schrieffer (BCS) theory using experimental data and the density of states of the Fermi level $N$(0) calculated from their band structures. We concluded that the considerable suppression of $T_\mathrm{c}$ in NCSt (Ca$_{0.25}$Sr$_{0.75}$)Pd$_3$P can be primarily attributed to the decrease in $N$(0) associated with the structural phase transition without considering the lack of inversion symmetry., Comment: 14 pages, 8 figures

It is generally difficult to quantify the amounts of light elements in materials because of their low X-ray-scattering power, as this means that they cannot be easily estimated via X-ray analyses. Meanwhile, the recently reported layered superconductor, Sc$_{20}$C$_{8-x}$B$_x$C$_{20}$, requires a small amount of boron, which is a light element, for its structural stability. In this context, here, we quantitatively evaluate the optimal $x$ value using both the experimental and computational approaches. Using the high-pressure synthesis approach that can maintain the starting composition even after sintering, we obtain the Sc$_{20}$(C,B)$_{8}$C$_{20}$ phase by the reaction of the previously reported Sc$_{15}$C$_{19}$ and B (Sc$_{15}$B$_y$C$_{19}$). Our experiments demonstrate that an increase in $y$ values promotes the phase formation of the Sc$_{20}$(C,B)$_{8}$C$_{20}$ structure; however, there appears to be an upper limit to the nominal $y$ value to form this phase. The maximum $T_\mathrm{c}$ $(=7.6\text{ K})$ is found to correspond with the actual $x$ value of $x \sim 5$ under the assumption that the sample with the same $T_\mathrm{c}$ as the reported value $(=7.7\text{ K})$ possesses the optimal $x$ amount. Moreover, we construct the energy convex hull diagram by calculating the formation enthalpy based on first principles. Our computational results indicate that the composition of Sc$_{20}$C$_4$B$_4$C$_{20}$ $(x=4)$ is the most thermodynamically stable, which is reasonably consistent with the experimentally obtained value., Comment: 10 pages, 1 table, 7 figures

The discovery of nearly room-temperature superconductivity in superhydrides has motivated further materials research for conventional superconductors. To realize the moderately high critical temperature $(T_\mathrm{c})$ in materials containing light elements, we explored new superconducting phases in a scandium borocarbide system. Here, we report the observation of superconductivity in a new ternary Sc-B-C compound. The crystal structure, which was determined through a Rietveld analysis, belongs to tetragonal space group $P4/ncc$. By complementarily using the density functional theory calculations, a chemical formula of the compound was found to be expressed as Sc$_{20}$C$_{8-x}$B$_x$C$_{20}$($x=1\:\mathrm{or}\:2$). Interestingly, a small amount of B is essential to stabilize the present structure. Our experiments revealed the typical type-II superconductivity at $T_\mathrm{c}=7.7\:\mathrm{K}$. Additionally, we calculated the density of states within a first-principles approach and found that the contribution of the Sc-3d orbital was mainly responsible for the superconductivity., Comment: 13 pages, 3 tables, 8 figures

The search for non-centrosymmetric superconductors that may exhibit unusual physical properties and unconventional superconductivity has yielded the synthesis of a non-centrosymmetric phosphide Mg$_2$Rh$_3$P with an Al$_2$Mo$_3$C-type structure. Although stoichiometric Mg$_2$Rh$_3$P does not exhibit superconductivity at temperatures above 2 K, we found that an Mg deficiency of approximately 5 at.% in the Mg$_2$Rh$_3$P induced superconductivity at 3.9 K. Physical properties such as the lattice parameter a = 0.70881 nm, Sommerfeld constant $\gamma_n$ = 5.36 mJ mol$^{-1}$ K$^{-2}$, specific heat jump $\Delta$C$_{el}$/$\gamma_n$Tc = 0.72, electron-phonon coupling constant $\lambda$$_{e-p}$ = 0.58, upper critical field H$_{c2}$(0) = 24.3 kOe, and pressure effect dTc/dP = -0.34 K/GPa were measured for the superconducting Mg$_{2-\delta}$Rh$_3$P ($\delta$ $\sim$ 0.1). Band-structure calculations indicate that exotic fermions, which are not present in high-energy physics, exist in Mg$_2$Rh$_3$P. Since Mg, Rh, and P are the first elements used at each crystal site of Al$_2$Mo$_3$C-type compounds, the discovery of Mg$_2$Rh$_3$P may guide the search for new related materials., Comment: 12 pages, 9 figures. arXiv admin note: text overlap with arXiv:1603.03093 by other authors

We investigate quasi-particle excitation modes and the topological number of a fractional-flux quantum vortex in a layered (multi-component) superconductor. The Bogoliubov equation for a half-flux quantum vortex is solved to show that there is no low-lying Andreev bound state near zero energy in the core of a quantum vortex, which is surprisingly in contrast to the result for an inter-flux vortex. Related to this result, there are singular excitation modes that have opposite angular momenta, moving in the opposite direction around the core of the vortex. The topological index (skyrmion number) for a fractional-flux quantum vortex becomes fractional since the topological index is divided into two parts where one from the vortex (bulk) and the other from the kink (domain wall, boundary). The topological numbers for both the vortex and the kink (domain wall) are fractional, and their sum becomes an integer. This shows an interesting analogy between this result and the index theorem for manifolds with boundary. We argue that fractional-flux quantum vortices are not commutative each other and follow non-abelian statistics. This non-abelian statistics of vortices is different from that in p-wave superconductors., Comment: 6 pages, 10 figures

We report synthesis, crystal structure and superconductivity in ThCr2Si2-type LaFe2As2 (La122). La122 was synthesized at 960{\deg}C for 1.5 h under a pressure of 3.4 GPa. An as-synthesized La122 (non-superconductor) had a collapsed tetragonal structure with a short c-axis length of 11.0144(4) {\AA} as observed in CaFe2As2 under pressure. The collapsed tetragonal transformed into an uncollapsed tetragonal by annealing the as-synthesized La122 at 500{\deg}C. The c-axis length remarkably extended to 11.7317(4) {\AA} and superconductivity emerged at 12.1 K in the uncollapsed tetragonal La122. A cylindrical hole-like Fermi-surface around the {\Gamma} point that plays an important role for an s+-wave paring in iron-based superconductors was missing in the uncollapsed tetragonal La122 due to heavily electron-doping. Superconductivity in La122 may be closely related to that induced in CaFe2As2 under pressure., Comment: 8 pages, 7 figures, 1 table

We investigated quantized modes of kinks in the phase space of superconducting gaps in a superconductor with multiple gaps. The kink is described by the sine-Gordon model in a two-gap superconductor and by the double sine-Gordon model in a three-gap superconductor. A fractional-flux vortex exists at the edge of the kink, and a fractional-flux vortex will be stable in a three-gap superconductor with time-reversal symmetry breaking. The kink and fractional-flux vortex exhibit massless modes as a sliding motion. We show further that there are one zero-energy mode (massless mode) and quantized excitation modes in kinks, which are characteristic features of multi-gap superconductors. The equation of quantized modes for the double sine-Gordon model is solved numerically. The correction to the ground-state energy is calculated based on the renormalization theory., Comment: 9 pages, 8 figures

We present a theory of the isotope effect of the Curie temperature $T_{\rm c}$ in itinerant ferromagnets. The isotope effect in ferromagnets occurs via the electron-phonon vertex correction and the effective attractive interaction mediated by the electron-phonon interaction. The decrease of the Debye frequency increases the relative strength of the Coulomb interaction, which results in a positive isotope shift of $T_{\rm c}$ when the mass $M$ of an atom increases. Following this picture, we evaluate the isotope effect of $T_{\rm c}$ by using the Stoner theory and a spin-fluctuation theory. When $T_{\rm c}$ is large enough as large as or more than 100K, the isotope effect on $T_{\rm c}$ can be measurable. Recently, precise measurements on the oxygen isotope effect on $T_{\rm c}$ have been performed for itinerant ferromagnet SrRuO$_3$ with $T_{\rm c}\sim 160$K. A clear isotope effect has been observed with the positive shift of $T_{\rm c}\sim 1$K by isotope substitution ($^{16}O\rightarrow ^{18}O$). This experimental result is consistent with our theory., Comment: 6 pages, 7 figures

The crystal structure, superconducting properties, and electronic structure of a novel superconducting 122-type antimonide, BaPt$_2$Sb$_2$, have been investigated by measurements of powder X-ray diffraction patterns, electrical resistivity, ac magnetic susceptibility, specific heat as well as ab-initio calculations. This material crystallizes in a new-type of monoclinic variant of the CaBe$_2$Ge$_2$-type structure, in which Pt$_2$Sb$_2$ layers consisting of PtSb$_4$ tetrahedra and Sb$_2$Pt$_2$ layers consisting of SbPt$_4$ tetrahedra are stacked alternatively and Ba atoms are located between the layers. Measurements of electrical resistivity, ac magnetic susceptibility and specific heat revealed that BaPt$_2$Sb$_2$ is a superconducting material with a $T_{\rm c}$ of 1.8 K. The electronic heat capacity coefficient $\gamma_{\rm n}$ and Debye temperature $\theta_{\rm D}$ were 8.6(2) mJ/mol K$^2$ and 146(4) K, where the figures in parentheses represent the standard deviation. The upper critical field $\mu_{\rm 0}H_{\rm c2}(0)$ and the Ginzburg-Landau coherent length $\xi(0)$ were determined to be 0.27 T and 35 nm. Calculations showed that it has two three-dimensional Fermi surfaces (FSs) and two two-dimensional FSs, leading to anisotropic transport properties. The d-states of the Pt atoms in the Pt2Sb2 layers mainly contribute to $N(E_{\rm F})$. A comparison between experimental and calculated results indicates that BaPt$_2$Sb$_2$ is a superconducting material with moderate coupling., Comment: 24 pages, 9 figures

In $N$-band superconductors, the $U(1)^N$ phase invariance is spontaneously broken. We propose a model for $N$-band superconductors where the phase differences between gaps are represented by abelian gauge fields. This model corresponds to an $SU(N)$ gauge theory with the abelian projection. We show that there are massless modes as well as massive modes when the number of gaps $N$ is greater than 3. There are $N-3$ massless modes and two massive modes near a minimum of the Josephson potential when $N$ bands are equivalent and Josephson couplings are frustrated. The global symmetry $U(1)^{N-1}$ is broken down by the Josephson term to $U(1)^{N-3}$. A non-trivial configuration of the gauge field, that is, a monopole singularity of the gauge field results in a fractional quantum-flux vortex. The fractional quantum-flux vortex corresponds to a monopole in 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)

We investigate several important properties of multi-band superconductors. They are time-reversal symmetry breaking, chirality and fractional quantum flux vortices in three-band superconductors. The BCS (Bardeen-Cooper-Schrieffer) gap equation has a solution with time-reversal symmetry breaking in some cases. We derive the Ginzburg-Landau free energy from the BCS microscopic theory. The frustrating pairing interaction among Fermi surfaces leads to a state with broken time-reversal symmetry, that is, a chiral solution. The Ginzburg-Landau equation for three-component superconductors leads to a double sine-Gordon model. A kink solution exists to this equation as in the conventional sine-Gordon model. In the chiral region of the double sine-Gordon model, an inequality of Bogomol'nyi type holds, and fractional-$\pi$ kink solutions exist with the topological charge Q. This yields multi-vortex bound states in three-band 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.

We have performed x-ray photoemission spectroscopy on the system of noncentrosymmetric superconductor, Li$_2$(Pd$_x$Pt$_{1-x}$3)B. For Li$_2$Pt$_3$B, we found 2 major peaks with 2 other weak components, and the band calculations were in agreement with the observation. The assignment of valence band features using the calculated partial density of states determined that Pt 5d and B 2p contribute to the density of states at the Fermi level. The effect of antisymmetric spin-orbit coupling on the band structure might have been probed, and the analysis on the effect of Pt incorporation into the system indicates the smooth evolution of electronic structures. We presented the measurements of core levels (Pd 3d, Pt 4f, and B 1s) and discussed the chemical bonding states and electronic structures from them., Comment: 14 pages, 5 figures

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 figures

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.

First principle FLAPW band calculations of the new superconductor MgB2 were performed and the polarization function P12(Q) between the two p-bands mainly formed of boron pz-orbital was calculated. We found that P12(Q) is substantially enhanced around Q=(0,0,p/c), which supports the two-band mechanism of superconductivity for MgB2. P12(Q) peaks at Qz ~ 0.3(2p/c) and Qz \~ 0.5(2p/c). These two peaks are related to the nesting of these Fermi surfaces, but significantly deviates from the position expected from the simplest tight-binding bands for the p-bands. From the calculations for different lattice parameters, we have found significant dependences on the isotopic species of B and on the pressure effect of the polarization function in accordance with the respective changes of Tc in the above-mentioned framework., Comment: 15 pages, 7 graphs. to be published in J. Phys. Soc. Jpn. 70_, No.8