Three-dimensional phase-kink state in a thick stack of Josephson junctions and terahertz radiation

The dynamics of superconductivity phase in thick stack of Josephson junctions with strong inductive coupling, such as the one realized in layered high-$T_c$ cuprates and possibly the recently discovered FeAs-based superconductors, is investigated under a $c$-axis bias voltage and in the absence of an external magnetic field. The kink state found previously by the present authors is extended to three dimensions for both rectangular and cylindrical geometries. The $IV$ characteristics are calculated and the distributions of electromagnetic field inside the samples are clarified. The solution for a cylindrical mesa exhibits a higher resonating frequency than that of a square mesa with the same linear size by a factor of $\sim 2.4$. More importantly, from the radius dependence of the resonance frequency for the cylinder geometry it is possible to confirm directly the kink state and thus to reveal the mechanism of the strong radiation discovered in recent experiments.

Figure 1

(Color online) 2D phase kink for the (1,1) cavity mode of a rectangular mesa obtained by numerical integration on Eq. (10).

Figure 2

(Color online) $IV$ curves derived by Eqs. (11, 12, 13) presuming a step-function phase kink (red symbols) and by Eq. (14) (blue lines) for the (1,1) mode of a rectangular mesa with $L_x=0.4$ and $L_y=1.5$. The cavity frequency is $\omega =8.128$, which corresponds to 0.62 THz approximately.

Figure 3

(Color online) Distribution of (a) ac electric field and (b) ac magnetic field in for the (1,1) cavity mode of the rectangular mesa.

Figure 4

(Color online) Distribution of static Josephson current for the (1,1) cavity mode of a rectangular mesa.

Figure 5

(Color online) (a) Phase kink and (b) radial dependence of phase in a cylinder sample obtained by numerical integration on Eq. (16).

Figure 6

(Color online) $IV$ curves derived by Eqs. (17, 18, 19) presuming a step-function phase kink (red symbols) and by Eq. (20) (blue lines) for the (0,1) mode of a cylinder sample of $a=0.4$. The cavity frequency is $\omega =9.579$, which corresponds to 0.73 THz approximately.

Figure 7

(Color online) Distribution of ac electric field [(a) and (b)] and magnetic field [(c) and (d)] in a cylinder sample.

Figure 8

(Color online) (a) Distribution and (b) radial dependence of Josephson current for the (0,1) mode of a cylinder sample.