Collective Modes in Two-band Superconductors

TL;DR

This paper investigates collective modes in two-band superconductors in the dirty limit, revealing their temperature dependence, spectrum characteristics, and how they can be experimentally detected via Josephson junction measurements.

Contribution

It provides a detailed analysis of the existence, spectrum, and conditions for collective modes in two-band superconductors across all temperatures below T_c.

Findings

Collective modes exist at all T < T_c if their frequency exceeds inelastic scattering rate and is below the energy gaps.

At low T, modes are related to counterphase oscillations of condensate currents in each band.

The spectrum includes gapless and gapped branches, with the gapless mode being sound-like.

Abstract

We analyze collective modes in two-band superconductors in the dirty limit. It is shown that these modes exist at all temperatures $T$ below $T_{c}$ provided the frequency of the modes is higher than the inelastic scattering rate and lower than the energy gaps $\Delta_{a,b}$. At low temperatures these modes are related to counterphase oscillations of the condensate currents in each band. The spectrum of the collective oscillations is similar to the spectrum of the Josephson ''plasma'' modes in a tunnel Josephson junction but the velocity of the mode propagation in the case under consideration is much lower. At higher temperatures ($\Delta_{b}<T<T_{c}$) the spectrum consists of two branches. One of them is gapless (sound-like) and the second one has a threshhold that depends on coupling between the bands. We formulate the conditions under which both types of collective modes can exist. The spectrum of the collective modes can be determined by measuring the I-V characteristics of a Josephson junction in a way as it was done by Carlson and Goldman.