Boltzmann Equation with a Large Potential in a Periodic Box

The stability of the Maxwellian of the Boltzmann equation with a large amplitude external potential $\Phi$ has been an important open problem. In this paper, we resolve this problem with a large $C3-$potential in a periodic box $\mathbb{T}^d$, $d \geq 3$. We use [1] in $L^p-L^{\infty}$ framework to establish the well-posedness and the $L^{\infty}-$stability of the Maxwellian $\mu_E(x,v)=\exp\{-\frac{|v|^2}{2}-\Phi(x)\}$

Josephson effect in quasi one-dimensional unconventional superconductors

Josephson effect in junctions of quasi one-dimensional triangular lattice superconductors is discussed, where the theoretical model corresponds to organic superconductors (TMTSF)_2PF_6. We assume the quarter-filling electron band and p, d and f wave like pairing symmetries in organic superconductors. To realize the electronic structures in organic superconductors, we introduce the asymmetric hopping integral, (t') among second nearest lattice sites. At t'=0, the Josephson current in the d wave symmetry saturates in low temperatures, whereas those in the p and the f wave symmetries show the low-temperature anomaly due to the zero-energy state at the junction interfaces. The low-temperature anomaly appears even in the d wave symmetry in the presence of t', whereas the anomaly is suppressed in the f wave symmetry. The shape of the Fermi surface is an important factor for the formation of the ZES in the quarter-filling electron systems.Comment: 10 page

A phenomenological theory of zero-energy Andreev resonant states

A conceptual consideration is given to a zero-energy state (ZES) at the surface of unconventional superconductors. The reflection coefficients in normal-metal / superconductor (NS) junctions are calculated based on a phenomenological description of the reflection processes of a quasiparticle. The phenomenological theory reveals the importance of the sign change in the pair potential for the formation of the ZES. The ZES is observed as the zero-bias conductance peak (ZBCP) in the differential conductance of NS junctions. The split of the ZBCP due to broken time-reversal symmetry states is naturally understood in the present theory. We also discuss effects of external magnetic fields on the ZBCP.Comment: 12 page

Influence of magnetic impurities on charge transport in diffusive-normal-metal / superconductor junctions

Charge transport in the diffusive normal metal (DN) / insulator / $s$- and $d$-wave superconductor junctions is studied in the presence of magnetic impurities in DN in the framework of the quasiclassical Usadel equations with the generalized boundary conditions. The cases of $s$- and d-wave superconducting electrodes are considered. The junction conductance is calculated as a function of a bias voltage for various parameters of the DN metal: resistivity, Thouless energy, the magnetic impurity scattering rate and the transparency of the insulating barrier between DN and a superconductor. It is shown that the proximity effect is suppressed by magnetic impurity scattering in DN for any value of the barrier transparency. In low-transparent s-wave junctions this leads to the suppression of the normalized zero-bias conductance. In contrast to that, in high transparent junctions zero-bias conductance is enhanced by magnetic impurity scattering. The physical origin of this effect is discussed. For the d-wave junctions, the dependence on the misorientation angle $\alpha$ between the interface normal and the crystal axis of a superconductor is studied. The zero-bias conductance peak is suppressed by the magnetic impurity scattering only for low transparent junctions with $\alpha \sim 0$. In other cases the conductance of the d-wave junctions does not depend on the magnetic impurity scattering due to strong suppression of the proximity effect by the midgap Andreev resonant states.Comment: 11 pages, 13 figures;d-wave case adde

Effect of the Vortices on the Nuclear Spin Relaxation Rate in the Unconventional Pairing States of the Organic Superconductor (TMTSF)2_2PF6_6

This Letter theoretically discusses quasiparticle states and nuclear spin relaxation rates $T_1^{-1}$ in a quasi-one-dimensional superconductor (TMTSF)$_2$PF$_6$ under a magnetic field applied parallel to the conduction chains. We study the effects of Josephson-type vortices on $T_1^{-1}$ by solving the Bogoliubov de Gennes equation for $p$-, $d$- or $f$-wave pairing interactions. In the presence of line nodes in pairing functions, $T_1^{-1}$ is proportional to $T$ in sufficiently low temperatures because quasiparticles induced by vortices at the Fermi energy relax spins. We also try to identify the pairing symmetry of (TMTSF)$_2$PF$_6$.Comment: 4+ pages, 4 figure

Observability of surface Andreev bound states in a topological insulator in proximity to an s-wave superconductor

To guide experimental work on the search for Majorana zero-energy modes, we calculate the superconducting pairing symmetry of a three-dimensional topological insulator in combination with an s-wave superconductor. In analogy to the case of nanowires with strong spin-orbit coupling we show how the pairing symmetry changes across different topological regimes. We demonstrate that a dominant p-wave pairing relation is not sufficient to realize a Majorana zero-energy mode useful for quantum computation. Our main result of this paper is the relation between odd-frequency pairing and Majorana zero energy modes by using Green functions techniques in three-dimensional topological insulators in the so-called Majorana regime. We discuss thereafter how the pairing relations in the different regimes can be observed in the shape of the tunneling conductance of an s-wave proximized three-dimensional topological insulator. We will discuss the necessity to incorporate a ferromagnetic insulator to localize the zero-energy bound state to the interface as a Majorana mode.Comment: Accepted for publication in Journal of Physics: Condensed Matte

Elementary Excitations in Quantum Antiferromagnetic Chains: Dyons, Spinons and Breathers

Considering experimental results obtained on three prototype compounds, TMMC, CsCoCl3 (or CsCoBr3) and Cu Benzoate, we discuss the importance of non-linear excitations in the physics of quantum (and classical) antiferromagnetic spin chains.Comment: Invited at the International Symposium on Cooperative Phenomena of Assembled Metal Complexes, November 15-17, 2001, Osaka, Japa