Collective modes in the electronic polarization of double-layer systems in the superconducting state

TL;DR

This paper investigates collective excitations in the superconducting state of double-layer systems, revealing new mode couplings and their temperature evolution, with implications for understanding interlayer interactions and c-axis conductivity.

Contribution

The study derives analytical expressions for collective mode frequencies considering interlayer pairing and hopping, uncovering a coupling between amplitude and phase fluctuations at finite momentum.

Findings

Two collective modes can appear below the pair-breaking threshold.

Amplitude and phase fluctuations are coupled at finite momentum due to interlayer hopping.

A plasmon mode evolves with temperature in the normal state.

Abstract

Standard weak coupling methods are used to study collective modes in the superconducting state of a double-layer system with intralayer and interlayer interaction, as well as a Josephson-type coupling and single particle hopping between the layers by calculating the electronic polarization function perpendicular to the layers. New analytical results are derived for the mode frequencies corresponding to fluctuations of the relative phase and amplitude of the layer order parameters in the case of interlayer pairing and finite hopping $t$. A new effect is found for finite $k$-dependent hopping: then the amplitude and phase fluctuations are coupled. Therefore two collective modes may appear in the dynamical c-axis conductivity below the threshold energy for breaking Cooper pairs. With help of numerical calculations we investigate the temperature dependence of the collective modes and show how a plasmon corresponding to charge fluctuations between the layers evolves in the normal state.