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 d-f hybridization on the Josephson current through Eu-chalcogenides

A superconducting ring with a pi junction made from superconductor/ferromagnetic-metal/superconductor (S-FM-S) exhibits a spontaneous current without an external magnetic field in the ground state. Such pi ring provides so-called quiet qubit that can be efficiently decoupled from the fluctuation of the external field. However, the usage of the FM gives rise to strong Ohmic dissipation. Therefore, the realization of pi junctions without FM is expected for qubit applications. We theoretically consider the possibility of the pi coupling for S/Eu-chalcogenides/S junctions based on the d-f Hamiltonian. By use of the Green's function method we found that pi junction can be formed in the case of the finite d-f hybridization between the conduction d and the localized f electrons.Comment: 4 pages, 4 figure

Influence of impurity-scattering on tunneling conductance in d-wave superconductors with broken time reversal symmetry

Effects of impurity scattering on tunneling conductance in dirty normal-metal/insulator/superconductor junctions are studied based on the Kubo formula and the recursive Green function method. The zero-bias conductance peak (ZBCP) is a consequence of the unconventional pairing symmetry in superconductors. The impurity scattering in normal metals suppresses the amplitude of the ZBCP. The degree of the suppression agrees well with results of the quasiclassical Green function theory. When superconductors have $d$+is-wave pairing symmetry, the time-reversal symmetry is broken in superconductors and the ZBCP splits into two peaks. The random impurity scattering reduces the height of the two splitting peaks. The position of the splitting peaks, however, almost remains unchanged even in the presence of the strong impurity scattering. Thus the two splitting peaks never merge into a single ZBCP.Comment: 12 pages, 5 figures, using jpsj2.cls and overcite.st

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

Josephson current in s-wave superconductor / Sr_2RuO_4 junctions

The Josephson current between an s-wave and a spin-triplet superconductor Sr$_2$RuO$_4$ (SRO) is studied theoretically. In spin-singlet / spin-triplet superconductor junctions, there is no Josephson current proportional to $\sin \phi$ in the absence of the spin-flip scattering near junction interfaces, where $\phi$ is a phase-difference across junctions. Thus a dominant term of the Josephson current is proportional to $\sin 2\phi$ . The spin-orbit scattering at the interfaces gives rise to the Josephson current proportional to $\cos\phi$, which is a direct consequence of the chiral paring symmetry in SRO