In-plane dissipation as a possible synchronization mechanism for terahertz radiation from intrinsic Josephson junctions of layered superconductors

Strong terahertz radiation from the mesa structure of a ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ single crystal has been observed recently, where the mesa intrinsically forms a cavity. For a thick mesa of a large number of junctions, there are many cavity modes with different wave vectors along the $c$ axis corresponding to almost the same bias voltages. The mechanism responsible for exciting the uniform mode which radiates coherent terahertz waves in experiments is unknown. In this paper, we show that the in-plane dissipation selects the uniform mode. For perturbations with nonzero wave numbers along the $c$ axis, the in-plane dissipations are significantly enhanced, which prevents the excitation of corresponding cavity modes. Our analytical results are confirmed by numerical simulations.

Figure 1

Stability diagram for the homogeneous solution along the $ab$ plane. In the filled region, the homogeneous solution is unstable and the cavity mode $(k_m,q)$ is excited. Inset is a schematic view of the setup for THz radiation.

Figure 2

Snapshots of the electric field (first row), magnetic field (second row), and Josephson current $\sin \left({\varphi }_l\right)$ (third row) without the in-plane dissipation ${\beta }_{\text{ab}}=0$ [(a)–(d)] and with the in-plane dissipation ${\beta }_{\text{ab}}=0.2$ [(e)–(f)]. When ${\beta }_{\text{ab}}=0$, various cavity modes $(m,n)=(7,5)$ in (a), $(m,n)=(9,3)$ in (b), $(m,n)=(7,2)$ in (c) and $(m,n)=(4,1)$ in (d) are excited when the bias current is swept. For ${\beta }_{\text{ab}}=0.2$, only the modes with $n=0$, [$(m,n)=(1,0)$ in (e), other cavity modes with $m>1$ are not shown here] are excited for $N={10}^3$. For $N={10}^4$, irregular patterns of the EM fields are excited even with the in-plane dissipation ${\beta }_{\text{ab}}=0.2$. The supercurrent forms blocks with alternating sign between neighboring blocks indicating $\pm \pi$ phase jumps at the interface of each block. We use $L_x=0.4{\lambda }_c$, $\zeta =7.1\times {10}^4$ in simulations.

Figure 3

$\mathit{IV}$ curve obtained with ${\beta }_{\text{ab}}=0.2$ and $N={10}^3$. Other parameters are the same as those in Fig. 2. The radiation power is estimated using $S_r=|E_{ac}^2|/(2\left|Z\right|)$ and ${\epsilon }_d=1$ where $E_{ac}$ is the averaged ac electric field at edges.[28] The maximal power at the first cavity mode $m=1$ is about $2800\mathrm{W}/{\mathrm{cm}}^2$. The experimental measured $\mathit{IV}$ deviates significantly from the theoretical one in the high bias region due to the strong self-heating effect.

Figure 4

Schematic view of the numerical grids.

Figure 5

Snapshots of the Josephson current $\sin \left({\varphi }_l\right)$ in the flux-flow region with the in-plane dissipation ${\beta }_{\text{ab}}=0.2$. Here the applied magnetic field is $B_a=1\mathrm{T}$, $L_x=0.1{\lambda }_c$, $N=500$, $\zeta =7.1\times {10}^4$. The core of Josephson vortex is located at $\varphi =(2m+1)\pi$.