To identify the superconducting gap symmetry in ${\mathrm{CeCoIn}}_{5}$ (${T}_{c}=2.3\text{ }\text{ }\mathrm{K}$), we measured angle-resolved specific heat (${C}_{\ensuremath{\phi}}$) a field rotated around $c$ axis down to very low temperature, $0.05{T}_{c}$, and made detailed theoretical calculations. In of 1 T, sign reversal fourfold angular oscillation ${C}_{\ensuremath{\phi}}$ was observed at $T\ensuremath{\simeq}0.1{T}_{c}$ upon entering quasiclassical regime where maximum corresponds...

In this article, we give a comprehensive review of recent progress in research on symmetry-protected topological superfluids and crystalline superconductors, their physical consequences such as helical chiral Majorana fermions. We start article with the minimal model that captures essence materials. The central part is devoted to superfluid $^3$He, which serves rich repository novel quantum phenomena originating from intertwining symmetries topologies. particular, it emphasized fluid...

Focusing on a quantum-limit behavior, we study single vortex in clean $s$-wave type-II superconductor by self-consistently solving the Bogoliubov--de Gennes equation. The discrete energy levels of bound states quantum limit are discussed. core radius shrinks monotonically up to an atomic-scale length lowering temperature $T$, and shrinkage stops saturate at lower $T$. pair potential, supercurrent, local density around exhibit Friedel-like oscillations. has particle-hole asymmetry induced...

We study the vortex structure and its field dependence within framework of quasi-classical Eilenberger theory to find difference between d_{x^2-y^2}- s-wave pairings. clarify effect d_{x^2-y^2}-wave nature lattice on pair potential, internal local density states. The pairing introduces a fourfold-symmetric around each core. With increasing field, their contribution becomes significant whole state, depending lattice's configuration. It is reflected in form factor which may be detected by...

It is proposed that the spatially modulated superfluid phase, or Fulde-Ferrell-Larkin-Ovchinnikov state could be observed in resonant fermion atomic condensates which are realized recently. We examine optimal experimental setups to achieve it by solving Bogoliubov-de Gennes equation for both idealized one-dimensional and realistic three-dimensional cases. The spontaneous modulation of this shown directly imaged as density profiles either optical absorption Stern-Gerlach experiments.

Generic features of the low-energy excitations in vortex lattice state are examined by comparatively studying self-consistent solutions quasiclassical Eilenberger theory both for ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave and s-wave pairings. This physics associated with a core, nodal structure, quasiparticle transfer between vortices governs physical properties such as field dependences zero-energy density states, internal distribution, shrinkage core radius. Eminent differences two pairings...

Vortex structure of pure $d_{x^2-y^2}$-wave superconductors is microscopically analyzed in the framework quasi-classical Eilenberger equations. Selfconsistent solution for $d$-wave pair potential obtained first time case an isolated vortex. The vortex core structure, i.e., potential, supercurrent and magnetic field, found to be fourfold symmetric even that mixing $s$-wave component absent. detailed temperature dependences these quantities are calculated. symmetry becomes clear when...

It is shown by microscopic calculations for trapped imbalanced Fermi superfluids that the gap function has always sign changes, i.e., Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state like, up to a critical imbalance $P_c$, beyond which normal becomes stable, at temperature T=0. A phase diagram constructed in $T$ vs $P$, where BCS without change stable only $T\neq 0$. We reproduce observed bimodality density profile identify its origin and evaluate $P_c$ as functions of coupling strength. These...

Using quasiclassical theory, we analyze the vortex structure of strong-paramagnetic superconductors. There, induced paramagnetic moments are accumulated exclusively around core. We quantitatively evaluate significant effect in $H$ dependence various quantities, such as low temperature specific heat, Knight shift, magnetization, and flux line lattice (FLL) form factor. The anomalous FLL factor observed by small angle neutron scattering $\mathrm{Ce}\mathrm{Co}{\mathrm{In}}_{5}$ is attributable...

The visualization of chiral p-wave superfluidity in Fermi gases near Feshbach resonances is theoretically examined. It proposed that the becomes detectable entire BCS-BEC regimes through (i) vortex by density depletion inside core and (ii) intrinsic angular momentum vortex-free states. revealed both are closely connected with Majorana zero energy mode edge mode, which survive until strong coupling BCS regime approached from weak limit vanish Bose-Einstein condensation regime.

We report the $^{75}$As-NQR and NMR studies on iron arsenide superconductor Li$_{x}$FeAs with $T_{\rm c} \sim 17$ K. The spin lattice relaxation rate, $1/T_{1}$, decreases below c}$ without a coherence peak, can be fitted by gaps s$^{\pm}$-wave symmetry in presence of impurity scattering. In normal state, both $1/T_{1}T$ Knight shift decrease decreasing temperature but become constant $T \leq 50 K$. Estimate Korringa ratio shows that correlations are weaker than other families arsenides,...

We investigate the topological aspect of spin-triplet $f$-wave superconductor UPt$_3$ through microscopic calculations edge- and vortex-bound states based on quasiclassical Eilenberger Bogoliubov-de Gennes theories. It is shown that a gapless linear dispersion exists at edge $ab$-plane. This forms Majorana valley, protected by mirror chiral symmetry. also demonstrate that, with increasing magnetic field, quasiparticles undergo phase transition from topologically trivial in double-core vortex...

Spin pumping refers to the microwave-driven spin current injection from a ferromagnet into adjacent target material. We theoretically investigate superconductors by fully taking account of impurity spin-orbit scattering that is indispensable describe diffusive transport with finite diffusion length. calculate temperature dependence signal and show pronounced coherence peak appears immediately below superconducting transition ${T}_{\mathrm{c}}$, which survives even in presence scattering. The...

Within a framework of two-component Ginzburg-Landau theory as model superconducting FeSe, we study the spatial structure vortex states in presence nematic twin boundary an s ± d wave superconductor.The result shows that orientation core is rotated 90 • across boundary, and just at becomes two fractional vortices with topological nature core-down core-up merons.The exotic may be confirmed by observing time evolution flow when are trapped escape from boundary.

It is shown theoretically that the Sommerfeld coefficient $\gamma(B)$ in mixed state contains useful information on gap topology a superconductor. We accurately evaluate against magnetic induction $B$ by using microscopic quasi-classical theory. The linear portion {$\gamma(\propto B)$} relative to $B_{\rm c2}$ and its slope low field faithfully corresponds anisotropy, so we can distinguish nodal anisotropic full gap, estimate magnitude of anisotropy.

To identify the superconducting gap structure in ${\mathrm{URu}}_{2}{\mathrm{Si}}_{2}$, we perform field-angle-dependent specific heat measurements for two principal orientations addition to field rotations, and a theoretical analysis based on microscopic calculations. The Sommerfeld coefficient $\ensuremath{\gamma}(H)$'s mixed state exhibit distinctly different dependence. This comes from point nodes substantial Pauli paramagnetic effect of ${\mathrm{URu}}_{2}{\mathrm{Si}}_{2}$. These...

We report the first ^{75}As-NMR study on a single crystal of hole-doped iron-pnictide superconductor Ba_{0.7}K_{0.3}Fe_2As_{2} (T_c = 31.5 K). find that Fe antiferromagnetic spin fluctuations are anisotropic and weaker compared to underdoped copper-oxides or cobalt-oxide superconductors. The lattice relaxation rate 1/T_1 decreases below T_c with no coherence peak shows step-wise variation at low temperatures, which is indicative multiple superconducting gaps, as in electron-doped...

The magnetic field $(H)$ dependence of the Sommerfeld coefficient $\ensuremath{\gamma}(H)$ low-temperature specific heat in ${\text{Sr}}_{2}{\text{RuO}}_{4}$ is analyzed by numerically solving microscopic Eilenberger equation. By taking account strong Pauli-paramagnetic effect, we find that exhibits a systematic change from concave function $\sqrt{H}$ to convex ${H}^{\ensuremath{\alpha}}(\ensuremath{\alpha}>1)$ at high fields when orientation varied, explaining experimental results....

Motivated by experiments on the superfluid $^{3}\mathrm{He}$ confined in a thin slab, we design concrete experimental setup for observing Majorana surface states. We solve quasiclassical Eilenberger equation, which is quantitatively reliable, to evaluate several quantities, such as local density of states (LDOS), mass current $A$ phase, and spin $B$ phase. In connection with realistic slab samples, consider upper lower surfaces side edges including corners thicknesses. Consequently,...

The electronic structure of vortices in a type II superconductor is analyzed within the quasi-classical Eilenberger framework. possible origin sixfold ``star'' shape local density states, observed by scanning tunneling microscope experiments on NbSe$_2$, examined light three effects; anisotropic pairing, vortex lattice, and states at Fermi surface. Outstanding features split parallel rays this star are well explained terms an $s$-wave pairing. This reveals rich internal associated with core.

The physics behind the $\mathrm{\text{rhombic}}\ensuremath{\rightarrow}\mathrm{\text{square}}\ensuremath{\rightarrow}\mathrm{\text{rhombic}}$ flux line lattice transformation in increasing fields is clarified on basis of Eilenberger theory. We demonstrate that this reentrance observed ${\mathrm{L}\mathrm{u}\mathrm{N}\mathrm{i}}_{2}{\mathrm{B}}_{2}\mathrm{C}$ due to intrinsic competition between superconducting gap and Fermi surface anisotropies. calculations not only reproduce it but also...

Orientational field dependence of the zero-energy density states (ZEDOS) is calculated for superconductors with polar state (line node), axial (point and three-dimensional d-wave state. Depending on gap topology relative direction dependencies ZEDOS sensitively differ, providing us a useful practical method to identify topology. It also demonstrated that rotation in basal plane shows sizable oscillation $(\ensuremath{\sim}3%)$ ZEDOS. This directly measurable low-T specific heat experiment mixed

The vortex structure is studied in light of MgB 2 theoretically based on a two-band superconducting model by means Bogoliubov-de Gennes framework. field dependence the electronic specific heat coefficient γ( H ) focused. exponent α )∝ shown to become smaller adjusting gap ratio two gaps major and minor bands. observed extremely small value α∼0.23 could be reasonable this with ∼0.3.

Despite intense studies the exact nature of order parameter in superconducting Sr2RuO4 remains unresolved. We have used small-angle neutron scattering to study vortex lattice with field applied close basal plane, taking advantage transverse magnetization. measured intrinsic anisotropy between c axis and Ru-O plane (~60), which greatly exceeds upper critical (~20). Our result imposes significant constraints on possible models triplet pairing raises questions concerning direction zero spin...

The temperature dependence of the site-dependent nuclear spin relaxation time ${T}_{1}$ around vortices is studied in $s$-wave and $d$-wave superconductors. Reflecting low-energy electronic excitations associated with vortex core, dependences deviate from those zero-field case, becomes faster when approaching core. In core region, ${T}_{1}^{\ensuremath{-}1}$ has a new peak below ${T}_{c}$. NMR study by resonance field may be method to prove spatial resolved structure various