Static and dynamic properties of Josephson weak links with singlet and triplet coupling
AbstractWe theoretically study static and dynamic properties of short Josephson junctions (JJs) with singlet and triplet Josephson coupling. In singlet Josephson weak links, two singlet superconductors S are connected with each other by a normal film (N) or wire. Triplet JJs, which we denote Sm-N(F)-Sm, are formed by two singlet BCS superconductors covered by a thin layer of a weak ferromagnet Fw. These superconductors Sm are separated from the N (or F) layer by spin filters, which pass electrons with only one spin orientation. The triplet Cooper pairs propagating from the left (right) superconductors Sm differ from each other not only in polarizations, but also in chiralities. The latter is determined by the magnetization orientation in weak ferromagnets Fw. We obtain analytical formulas for the critical Josephson current in both types of JJs. If the chiralities of the triplet Cooper pairs penetrating into the N film in Sm-N(F)-Sm JJs from the left and right Sm are different, the Josephson current is not 0 in the absence of the phase difference (spontaneous Josephson current). We also calculate the admittance Y(Ω) for arbitrary frequencies Ω in the case of singlet JJs and for low frequencies in the case of triplet JJs. At low temperatures T, the real part of the admittance Y′(Ω) in singlet JJs starts to increase from 0 at ℏΩ≥Δsg, but at T≥Δsg, it has a peak at low frequencies the magnitude of which is determined by inelastic processes. The subgap Δsg depends on the transparencies of the S/N interfaces and on the phase difference 2χ0. The low-frequency peak in Y′(Ω) in triplet JJs disappears.