Inhomogeneous state in nonequilibrium superconductor/normal-metal tunnel structures: A Larkin-Ovchinnikov-Fulde-Ferrell-like phase for nonmagnetic systems

We analyze nonequilibrium states in a tunnel superconductor-normal-metal (N/S/N) structure in the presence of a tunnel current $I$. We use an approximation of an effective temperature $T$ and calculate the current-voltage $I\text{−}V$ characteristics. It is shown that the $I\text{−}V$ dependence may have an S-shaped form. We determine nonuniform current $I\left(x\right)$ and temperature $T\left(x\right)$ distributions that arise as a result of instability of the uniform state with negative differential conductance $\left(dI/dV<0\right)$. We discuss an analogy with equilibrium superconductors with an exchange field in which nonuniform states predicted by Larkin/Ovchinnikov and Fulde/Ferrell are possible.

Figure 1

(Color online) (a) The system under consideration. (b) The proposed system in which an inhomogeneous distribution of the energy gap can be probed with a point-contact spectroscopy.

Figure 2

(Color online) (a) Normalized effective temperature and (b) energy gap as functions of the applied voltage $V$ for $\gamma /{\Delta }_0=0.01$ and different temperatures $T_0=1/\left(2{\beta }_0\right)$ (shown in the inset).

Figure 3

(Color online) (a) The CVC of the system in the homogeneous state for $\gamma /{\Delta }_0=0.01$ and different temperatures. The part of the CVC corresponding to an inhomogeneous state (a broad high-temperature domain) is shown by the dashed vertical line. (b) The CVC in the homogeneous state for different damping $\gamma$. The temperature $T_0$ is chosen so that ${\Delta }_0{\beta }_0=15$.

Figure 4

(Color online) (a) The potential $W\left(\theta \right)$ for different $V:V=V_0$ (solid line); $V<V_0$ (dashed line), and $V>V_0$ (dashed-dotted line). (b) Phase trajectories $\left(T,dT/dx\right)$. Solid line shows a separatrix [a domain wall in $T\left(x\right)$ distribution]; dashed and dotted lines show domainlike structure of $T\left(x\right)$ distribution; (c) spatial dependence of the effective temperature corresponding to a domainlike structure (arbitrary units).