Thermal and electromagnetic properties of Bi$_2$Sr$_2$CaCu$_2$O$_8$ intrinsic Josephson junction stacks studied via one-dimensional coupled sine-Gordon equations

TL;DR

This study uses coupled sine-Gordon and heat diffusion equations to numerically analyze the thermal and electromagnetic behavior of long intrinsic Josephson junction stacks, revealing hot spot formation and standing wave patterns.

Contribution

It introduces a numerical approach combining sine-Gordon and heat equations to study large Josephson junction stacks with segmentation, highlighting thermal-electromagnetic interactions and vortex states.

Findings

Hot spot formation at high bias currents.

Presence of standing wave patterns in current and electric field.

Vortex/antivortex lines associated with $c$ kink states.

Abstract

We used one-dimensional coupled sine-Gordon equations combined with heat diffusion equations to numerically investigate the thermal and electromagnetic properties of a $300\,\mu\mathrm{m}$ long intrinsic Josephson junction stack consisting of $N = 700$ junctions. The junctions in the stack are combined to $M$ segments where we assume that inside a segment all junctions behave identically. Most simulations are for $M = 20$. For not too high bath temperatures there is the appearence of a hot spot at high bias currents. In terms of electromagnetic properties, robust standing wave patterns appear in the current density and electric field distributions. These patterns come together with vortex/antivortex lines across the stack that correspond to $\pi$ kink states, discussed before in the literature for a homogeneous temperature distribution in the stack. We also discuss scaling of the thermal and electromagnetic properties with $M$, on the basis of simulations with $M$ between 10 and 350.