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

Quantum Annealing Effect on Entropic Slowing Down in Frustrated Decorated Bond System

We propose that the importance of the quantum annealing procedure to find the ground state of frustrated decorated bond systems where 'entropic slowing down' happens due to peculiar density of states. Here, we use the time dependent Schr\"odinger equation to analyze the real time dynamics of the process. It is found that the quantum annealing is very efficient comparing to the thermal annealing for searching the ground state of the systems. We analyze the mechanism of quantum annealing from a view point of adiabatic process.Comment: 2 pages, 4 figures, proceedings of ICM200

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