Effects of surface roughness on the paramagnetic response of small unconventional superconductors

We theoretically study effects of surface roughness on the magnetic response of small unconventional superconductors by solving the Eilenberger equation for the quassiclassical Green function and the Maxwell equation for the vector potential simultaneously and self-consistently. The paramagnetic phase of spin-singlet $d$-wave superconducting disks is drastically suppressed by the surface roughness, whereas that of spin-triplet $p$-wave disks is robust even in the presence of the roughness. Such difference derives from the orbital symmetry of paramagnetic odd-frequency Cooper pairs appearing at the surface of disks. The orbital part of the paramagnetic pairing correlation is $p$-wave symmetry in the $d$-wave disks, whereas it is $s$-wave symmetry in the $p$-wave ones. Calculating the free-energy, we also confirm that the paramagnetic state is more stable than the normal state, which indicates a possibility of detecting the paramagnetic effect in experiments. Indeed our results are consistent with an experimental finding on high-$T_c$ thin films.Comment: 11 pages, 10 figure

Quantization of Conductance Minimum and Index Theorem

We discuss the minimum value of the zero-bias differential conductance $G_{\textrm{min}}$ in a junction consisting of a normal metal and a nodal superconductor preserving time-reversal symmetry. Using the quasiclassical Green function method, we show that $G_{\textrm{min}}$ is quantized at $(4e^2/h) N_{\mathrm{ZES}}$ in the limit of strong impurity scatterings in the normal metal. The integer $N_{\mathrm{ZES}}$ represents the number of perfect transmission channels through the junction. An analysis of the chiral symmetry of the Hamiltonian indicates that $N_{\mathrm{ZES}}$ corresponds to the Atiyah-Singer index in mathematics.Comment: 5 pages, 1 figur

Effects of the phase coherence on the local density of states in superconducting proximity structures

We theoretically study the local density of states in superconducting proximity structure where two superconducting terminals are attached to a side surface of a normal-metal wire. Using the quasiclassical Green's function method, the energy spectrum is obtained for both of spin-singlet $s$-wave and spin-triplet $p$-wave junctions. In both of the cases, the decay length of the proximity effect at the zero temperature is limited by a depairing effect due to inelastic scatterings. In addition to the depairing effect, in $p$-wave junctions, the decay length depends sensitively on the transparency at the junction interfaces, which is a unique property to odd-parity superconductors where the anomalous proximity effect occurs.Comment: 11 pages, 9 figure

Supercurrent reversal in Zeeman-split Josephson junctions

We study theoretically the shape of the current-phase relation in a Josephson junction comprising the Zeeman-split superconductors (ZSs) and a normal metal (N). We show that at low temperatures the Josephson current in the ZS/N/ZS junctions exhibits an additional reversal in direction at a certain phase difference $\varphi_c \in (0, \pi)$. Calculating the spectral Josephson current, the band-splitting due to the Zeeman interaction is shown to cause the level crossing in the spectra of the Andreev bound states and the sign reversal in the Josephson current. Additionally, we propose an alternative method to electrically control the critical phase difference $\varphi_c$ by tuning the Rashba spin-orbit coupling, eliminating the need for manipulating magnetizations.Comment: 8 pages, 10 figure

Fulde-Ferrell-Larkin-Ovchinnikov state in a superconducting thin film attached to a ferromagnetic cluster

We study theoretically the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states appearing locally in a superconducting thin film with a small circular magnetic cluster. By solving the Eilenberger equation in two dimensions, we calculate the pair potential, pairing correlations, free-energy density, and quasiparticle density of states for various cluster sizes and exchange potentials. Increasing the exchange potential and cluster size leads to a higher number of nodes in the pair potential. Although the free-energy density beneath the ferromagnet locally exceeds the normal-state value, the FFLO states are stabilized by the superconducting condensate away from the magnetic cluster. Analyzing the pairing-correlation functions, we show that the spatial variation of the spin-singlet s-wave pair potential generates p-wave Cooper pairs. These odd-frequency Cooper pairs play a dominant role in governing the inhomogeneous subgap spectra observed in the local density of states. Furthermore, we propose an experimental method for the detection of local FFLO states by analyzing the quasiparticle density of states.</p

Incisional atrial reentrant tachycardia: experimental study on the conduction property through the isthmus

AbstractBackgroundIncisional atrial reentrant tachycardia is a life-threatening tachyarrhythmia after surgery for congenital heart disease. Slow conduction through an isthmus between anatomical barriers, such as a right atriotomy or the sites for cannulation, has been shown to be a prerequisite for perpetuation of the incisional atrial reentrant tachycardia. However, the conduction property through the isthmus has not been examined in detail.MethodsTo examine the conduction property, 2 tandem incisions were made on the lateral right atrium with various distances (3 to 20 mm) between the incisions in 16 canines. Four weeks after the surgery, the lateral right atrium was mapped epicardially during pacing to examine the conduction property through the isthmus. The conduction property was characterized by approximated curves of the conduction velocity through the isthmus in accordance with the pacing cycle lengths. The atrial tissue at the isthmus was examined microscopically.ResultsThe approximated curves of the conduction velocity were classified into 3 different types. Decremental conduction was observed only in the isthmi between 5 and 15 mm in width. A small amount of surviving myocardium between the scars formed the critical isthmus microscopically (decremental type). In the isthmi wider than 15 mm in width, slow conduction was not seen at any paced cycle length (nondecremental type). In the extremely narrow isthmi less than 5 mm in width, all of the atrial myocardium at the isthmus was replaced by fibrous tissue. Conduction was blocked at the isthmus and the activation detoured around the incisions (block type). There was a statistically significant difference in the approximated curves between the 3 different types of conduction properties (P < .01).ConclusionThe width of the isthmus determines the conduction property through the isthmus that contributes to the development of the incisional atrial reentrant tachycardia. Thus, the incisional atrial reentrant tachycardia may be preventable by leaving a sufficient amount of surviving myocardium between the incisions or by connecting the incisions by an ablative procedure