Possible Dynamic States in Inductively Coupled Intrinsic Josephson Junctions of Layered High-$T_c$ Superconductors

Based on computer simulations and theoretical analysis, a new dynamic state is found in inductively coupled intrinsic Josephson junctions in the absence of an external magnetic field. In this state, the plasma oscillation is uniform along the $c$ axis with the fundamental frequency satisfying the ac Josephson relation. There are $(2m+1)\pi$ phase kinks around the junction center, with $m$ being an integer, periodic and thus nonuniform in the $c$ direction. In the $IV$ characteristics, the state manifests itself as current steps occurring at all cavity modes. Inside the current steps, the plasma oscillation becomes strong, which generates several harmonics in frequency spectra at a given voltage. The recent experiments on terahertz radiations from the mesa of a ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ single crystal can be explained in terms of this state.

Figure 1

Simulated $IV$ characteristics under the boundary conditions (a) without and (b) with radiation with $C=0.000177$ and $R=707.1$. The vertical dashed lines correspond to the voltage at cavity modes $V=n{\Phi }_0/(2\sqrt{{\epsilon }_c}L)$. Inset: geometry of the mesa of BSCCO single crystal.

Figure 2

Typical configurations of the static term in the phase difference [the second term in Eq. (2)]: (a) period of 2 layers and (b) period of 4 layers, corresponding to the first current step, and (c) corresponding to the second current step.

Figure 3

Comparison between the theory and simulations on the dc part of Josephson current $⟨\sin P_l{⟩}_t$ in two neighboring layers for the configuration in Fig. 2b: (a) off resonance at $J_{\mathrm{ext}}=0.12$, (b) at the middle of the first step with $J_{\mathrm{ext}}=0.35$, (c) at the top of the first step with $J_{\mathrm{ext}}=0.53$. The solid curves are results by numerical simulations and the symbols are derived by the analytic expressions. (d) Current dependence of voltage (red) and $J_{\mathrm{net}}$ (blue) at the first current step. Green symbols are for the theoretical estimate $J_{\mathrm{ext}}-\omega \beta$. (e) $⟨{\Delta }^{(2)}\sin P_l{⟩}_t$ at $J_{\mathrm{ext}}=0.35$ (dashed red line) and at $J_{\mathrm{ext}}=0.53$ (dashed green line).

Figure 4

Time evolutions of the magnetic field and electric field and the frequency spectrum. The dc part of the electric field has been subtracted. Left/right: at the bottom/top of the first current step.

Figure 5

Dependence of radiation power evaluated by the Poynting vector at the edges of IJJs (a) on $|Z|$ (in unit of $1/\sqrt{{\epsilon }_c}$) and (b) on $\theta$ inside the first current step at $J_{\mathrm{ext}}=0.27$. (c) Radiation power at all current steps.