Stability and Josephson effect of time-reversal-symmetry-broken multicomponent superconductivity induced by frustrated intercomponent coupling

A time-reversal-symmetry-broken (TRSB) superconductivity can be induced by sign-reversed intercomponent couplings in superconductors with three components or above. Here we derive stability conditions for this TRSB state using the Ginzburg-Landau (GL) theory. We find that there are multiple divergent lengths of superconductivity coherence, and that the GL parameter cannot be used to categorize this novel superconductivity. We reveal that the critical Josephson current of a constriction junction between two different TRSB states is suppressed significantly from that for the same state. This effect provides a unique way to verify experimentally the TRSB state in multiband superconductors.

Figure 1

TRSB states with intrinsically complex order parameters of a three-component superconductor in a Josephson junction of constriction structure.

Figure 2

Schematic temperature dependence of determinant of the coupling matrix of the linearized GL equations [see Eqs. (2) and (3)]. The doubly degenerated root at $T_c$ is a necessary condition for a stable TRSB state, whereas the single-root case is associated with a conventional TRSR state similar to single-component systems.

Figure 3

Phase diagram for a three-component superconductor with stable TRSB superconductivity at the central part and TRSR one at the corners.

Figure 4

Distortions in the complex order parameters in the TRSB state with equal bulk amplitude for the three order parameters. (a) Definitions of distortions in order parameters. (b) and (c) Characteristic distortions of mode I and mode II, respectively, for the case of equal effective mass.