Interband Phase Modes and Nonequilibrium Soliton Structures in Two-Gap Superconductors

We predict a new dynamic state in current-carrying superconductors with a multicomponent order parameter. If the current density $J$ exceeds a critical value $J_t$, an interband breakdown caused by charge imbalance of nonequilibrium quasiparticles occurs. For $J>J_t$, the electric field penetrating from current leads gives rise to various static and dynamic soliton phase textures, and voltage oscillations similar to the nonstationary Josephson effect. We propose experiments to observe these effects which would probe the multicomponent nature of the superconducting order parameter.

Figure 1

Geometries in which the interband phase breakdown could occur. Here N labels normal electrodes, gray domains show phase solitons moving along thin arrows, and block arrows indicate current directions. Static phase textures form in microbridges (a) and point contacts (b), while in the 4-terminal geometry (c) the solitons and antisolitons continuously annihilate in the center.

Figure 2

Formation of a static phase soliton in $\theta (x)$ near the bridge edge after the current density was instantaneously turned on from $0$ to $J=0.99J_t$ at $t=0$. Times and distances from the center $(x=0)$ are taken in the units of ${\tau }_{\theta }$ and $a$, respectively, $L_e=a/10$, $L_{\theta }=0.1L_e$.

Figure 3

Dynamics of formation of a static soliton chain in the bridge of length $2a$ after $J(t)$ was instantaneously turned on from $0$ to $1.025J_t$ at $t=0$. Only the right half $(0<x<a)$ is shown, and the rest is the same as in Fig. 2.

Figure 4

Moving soliton shuttle along the right half of the horizontal leg $(0<x<a)$ in the 4-terminal geometry shown in Fig. 1c. $J(t)$ was instantaneously turned on from 0 to $1.012J_t$ at $t=0$, and the rest is the same as in Fig. 2.