Clapping Modes in Unconventional Superconductors

We consider a superconducting state with a mixed symmetry order parameter components, e.g. d + is or d + id ′ with d ′ = dxy. We argue for the existence of the new orbital magnetization mode which corresponds to the oscillations of relative phase φ between two components around an equilibrium value of φ = π 2. It is similar to the so called " clapping " mode in superfluid 3 He − A. We estimate the frequency of this mode ω0(B, T) depending on the field and temperature for the specific case of magnetic field induced d ′ state. We find that this mode is tunable with an applied magnetic field with ω0(B, T) ∝ B∆0, where ∆0 is the magnitude of the d-wave order parameter. We argue also that similar filed induced clapping mode should be present in an organic p-wave superconductors. Clapping mode in High-Tc superconduc-tor. The order parameter in high-Tc supercon-ductors is widely believed [1] to be of a d x 2 −y 2 symmetry. However more careful consideration indicates that the symmetry of the state in high-Tc might be lower in a number of cases. The symmetry allows the secondary components to be generated whenever there is a perturbing field. These secondary components (is or id xy) generation has been addressed in recent literature for the case of inhomogeneity due to wall scattering [2] or due to vortex texture [3]. Similarly, the generated id ′ component near magnetic impurity and spontaneous violation of time reversal symmetry with global d + id ′ has also been discussed [4]. Another possibility for a global d + id ′ phase has been pointed out[5–7] where the external magnetic field applied to two-dimensional d-wave su-perconductor generates id ′. We present here [7] an excitation which constitutes a direct test of the induced component of the order parameter. This excitation is uniquely tied to the existence of the secondary out of phase component of the order parameter. Consider the most general situation of a complex order parameter which can be generally written as ∆ 0 + i∆ 1 where ∆ 0 is the original d x 2 −y 2 component and ∆ 1 is the induced s or d xy component which is orthogonal to the initial d x 2 −y 2 state. Define the global (Josephson) phase of the order parameter ν and the relative phase φ as: …