3D simulations of the electrothermal and THz emission properties of   Bi$_2$Sr$_2$CaCu$_2$O$_8$ intrinsic Josephson junction stacks
  We used 2D coupled sine-Gordon equations combined with 3D heat diffusion equations to numerically investigate the thermal and electromagnetic properties of a $250 \times 70\,\mu\mathrm{m}^2$ intrinsic Josephson junction stack. The 700 junctions are grouped to 20 segments; we assume that in a segment all junctions behave identically. At large input power a hot spot forms in the stack. Resonant electromagnetic modes, oscillating either along the length ((0, $n$) modes) or the width (($m$, 0) modes) of the stack or having a more complex structure, can be excited both with and without a hot spot. At fixed bath temperature and bias current several cavity modes can coexist in the absence of a magnetic field. The (1, 0) mode, considered to be the most favorable mode for THz emission, can be stabilized by applying a small magnetic field along the length of the stack. A strong field-induced enhancement of the emission power is also found in experiment, for an applied field around 5.9 mT. 
Fabian Rudau, Raphael Wieland, Julian Langer, Xianjing Zhou, Min Ji,   Nickolay Kinev, Luyao Hao, Ya Huang, Jun Li, Peiheng ...
cond-mat.supr-con