We study the properties of the normal modes of a chain of Josephson junctions in the simultaneous presence of disorder and absorption. We consider the superconducting regime of small phase fluctuations and focus on the case where the effects of disor
der and absorption can be treated additively. We analyze the frequency shift and the localization length of the modes. We also calculate the distribution of the frequency-dependent impedance of the chain. The distribution is Gaussian if the localization length is long compared to the absorption length; it has a power law tail in the opposite limit.
We apply the quantum jump approach to address the statistics of work in a driven two-level system coupled to a heat bath. We demonstrate how this question can be analyzed by counting photons absorbed and emitted by the environment in repeated experim
ents. We find that the common non-equilibrium fluctuation relations are satisfied identically. The usual fluctuation-dissipation theorem for linear response applies for weak dissipation and/or weak drive. We point out qualitative differences between the classical and quantum regimes.
We investigate heat and charge transport through a diffusive SIF1F2N tunnel junction, where N (S) is a normal (superconducting) electrode, I is an insulator layer and F1,2 are two ferromagnets with arbitrary direction of magnetization. The flow of an
electric current in such structures at subgap bias is accompanied by a heat transfer from the normal metal into the superconductor, which enables refrigeration of electrons in the normal metal. We demonstrate that the refrigeration efficiency depends on the strength of the ferromagnetic exchange field h and the angle {alpha} between the magnetizations of the two F layers. As expected, for values of h much larger than the superconducting order parameter Delta, the proximity effect is suppressed and the efficiency of refrigeration increases with respect to a NIS junction. However, for h sim Delta the cooling power (i.e. the heat flow out of the normal metal reservoir) has a non-monotonic behavior as a function of h showing a minimum at h approx Delta. We also determine the dependence of the cooling power on the lengths of the ferromagnetic layers, the bias voltage, the temperature, the transmission of the tunneling barrier and the magnetization misalignment angle {alpha}.
We investigate the subgap transport properties of a S-F-Ne structure. Here S (Ne) is a superconducting (normal) electrode, and F is either a ferromagnet or a normal wire in the presence of an exchange or a spin- splitting Zeeman field respectively. B
y solving the quasiclassical equations we first analyze the behavior of the subgap current, known as the Andreev current, as a function of the field strength for different values of the voltage, temperature and length of the junction. We show that there is a critical value of the bias voltage V * above which the Andreev current is enhanced by the spin-splitting field. This unexpected behavior can be explained as the competition between two-particle tunneling processes and decoherence mechanisms originated from the temperature, voltage and exchange field respectively. We also show that at finite temperature the Andreev current has a peak for values of the exchange field close to the superconducting gap. Finally, we compute the differential conductance and show that its measurement can be used as an accurate way of determining the strength of spin-splitting fields smaller than the superconducting gap.
We study quantum phase-slip (QPS) processes in a superconducting ring containing N Josephson junctions and threaded by an external static magnetic flux. In a such system, a QPS consists of a quantum tunneling event connecting two distinct classical s
tates of the phases with different persistent currents [K. A. Matveev et al., Phys. Rev. Lett. 89, 096802 (2002)]. When the Josephson coupling energy EJ of the junctions is larger than the charging energy EC = e2/2C where C is the junction capacitance, the quantum amplitude for the QPS process is exponentially small in the ratio EJ/EC. At given magnetic flux each QPS can be described as the tunneling of the phase difference of a single junction of almost 2pi, accompanied by a small harmonic displacement of the phase difference of the other N-1 junctions. As a consequence the total QPS amplitude nu is a global property of the ring. Here we study the dependence of nu on the ring size N taking into account the effect of a finite capacitance C0 to ground which leads to the appearance of low-frequency dispersive modes. Josephson and charging effects compete and lead to a nonmonotonic dependence of the ring critical current on N. For N=infty, the system converges either towards a superconducting or an insulating state, depending on the ratio between the charging energy E0 = e2/2C0 and the Josephson coupling energy EJ.
We discuss the theoretical framework to describe quasiparticle electric and heat currents in NIS tunnel junctions in the dirty limit. The approach is based on quasiclassical Keldysh-Usadel equations. We apply this theory to diffusive NISS tunnel junc
tions. Here N and S are respectively normal metal and superconductor reservoirs, I is an insulator layer and S is a nonequilibrium superconducting lead. We calculate the quasiparticle electric and heat currents in such structures and consider the effect of inelastic relaxation in the S lead. We find that in the absence of strong relaxation the electric current and the cooling power for voltages $eV < Delta$ are suppressed. The value of this suppression scales with the diffusive transparency parameter. We ascribe this suppression to the effect of backtunneling of nonequilibrium quasiparticles into the normal metal.
