Collective modes of a spin density wave superconductor

Abstract

The properties of the coexistent state of the spin density wave (SDW) and superconductivity (SC) are considered within a mean field description. A four component Nambu formalism is adopted, which allows for a SDW state with wave vector Q, as well as singlet and triplet pairing of the superconducting state. However, explicit calculations reveal that the order parameter for the triplet pairing vanishes. It is also shown that the SDW and SC mutually inhibit each other. The collective modes of the coexistent state are calculated using the linear response theory. In the coexistent phase the collective modes corresponding to the oscillations of the amplitudes of the SDW and SC gap ( G and δ, respectively) couple to each other. Similarly, the SC phase mode and the charge density oscillations get coupled as in a normal superconductor; leaving behind the SDW phase mode which retains its individuality. In the limit of zero wave vector, it was shown that there exist two amplitude modes with frequencies 2 ( G ± δ) for the coexistent phase. This behaviour is in contrast with that of a charge density wave superconductor, where only one amplitude mode exists. The generalization of the calculation of the collective modes using a random phase approximation allows for the evaluation of their spectral density functions, which clearly shows a two peak structure. The possibility of the observation of these amplitude modes by Raman scattering and its relevance in the interpretation of the observed superconducting gap of the high- T c materials by Raman spectroscopy is discussed.