Collective Mode in a Superconductor with Mixed-Symmetry Order Parameter Components

Abstract

We consider a superconducting state with mixed-symmetry order parameter components, e.g., $d+is$ or ${d+id}^{\prime }$ with $d^{\prime }{=d}_{\mathrm{xy}}$. We argue for the existence of a new orbital magnetization mode which corresponds to oscillations of relative phase $\phi$ between two components around an equilibrium value of $\phi =\frac{\pi }{2}$. It is similar to the “clapping” mode in superfluid ${}^3\mathrm{He}-A$. We estimate the frequency of this mode ${\omega }_0(B,T)$ depending on the field and temperature for the specific case of magnetic field induced $d^{\prime }{=d}_{\mathrm{xy}}$ state. This mode is tunable with a magnetic field with ${\omega }_0(B,T)\propto B{\Delta }_0$, where ${\Delta }_0$ is the magnitude of the $d$-wave order parameter. We also estimate the velocity $s(B,T)$ of this mode.