Cavity phenomena in mesas of cuprate high-$T_c$ superconductors under voltage bias

TL;DR

This paper models cavity phenomena in cuprate high-$T_c$ superconductor mesas, revealing how phase kinks and geometry influence terahertz wave emission, with potential applications in waveguide resonators.

Contribution

It introduces a theoretical model of cavity effects in cuprate superconductor mesas, highlighting the role of $ ext{±} ext{π}$ phase kinks and annular geometry for enhanced terahertz emission.

Findings

Neumann boundary conditions approximate small mesas effectively.

$ ext{±} ext{π}$ phase kinks stabilize coherence across thousands of junctions.

Annular geometry improves frequency tuning and reduces heating.

Abstract

Modeling a single crystal of cuprate high-$T_c$ superconductor, such as $\rm{Bi_2Sr_2CaCu_2O_{8+\delta}}$, as a stack of intrinsic Josephson junctions, we formulate explicitly the cavity phenomenon of plasma oscillations and electromagnetic (EM) waves in mesas of cylindrical and annular shapes. When the mesa thickness is small compared with the EM wavelength, the boundary condition for the inductively coupled sine-Gordon equations is the Neumann-type one to a good approximation, addressed first theoretically and verified in a recent experiment. This renders the superconductor mesa a cavity. Biasing a dc voltage in the $c$ direction, a state with $\pm\pi$ kinks in the superconductivity phase difference piled up alternatively along the c axis is stabilized. The $\pm\pi$ phase kinks provide inter-lock between superconductivity phases in adjacent junctions, taking the advantage of huge inductive couplings inherent in the cuprate superconductors, which establishes the coherence across the whole system of more than $\sim 600$ junctions. They also permit a strong coupling between the lateral cavity mode and the transverse Josephson plasma, enhance the plasma oscillation significantly at the cavity modes which radiates EM waves in the terahertz band when the lateral size of mesa is set to tens of micrometers. In order to overcome the heating effect, we propose to use annular geometry. The dependence of frequency on the aspect ratio is analyzed, which reveals that the shape tailor is quite promising for improving the present technique of terahertz excitation. The annular geometry may be developed as a waveguide resonator, mimic the fiber lasers for visible lights.