Path Integral Two Dimensional Models of P– and D–Wave Superconductors and Collective Modes

The main parameter, which describes superfluids and superconductors and all their main properties is the order parameter. After discovery the high temperature superconductors (HTSC) and heavy fermion superconductors (HFSC) the unconventional pairing in different superconductors is studied very intensively. The main problem here is the type of pairing: singlet or triplet, orbital moment of Cooper pair value L, symmetry of the order parameter etc. Recent experiments in Sr2RuO4 renewed interest in the problem of the symmetry of the order parameters of the HTSC. The existence of CuO2 planes – the common structural factor of HTSC – suggests we consider two-dimensional (2D) models. A 2D– model of p–pairing using a path integration technique has been developed by Brusov and Popov. A 2D model of d–pairing within the same technique has been developed by Brusov et al. All properties of 2D–superconductors (for example, of CuO2 planes of HTSC) and, in particular, the collective excitations spectrum, are determined by these functionals. We consider all superconducting states, arising in symmetry classification of p-wave and d-wave 2D–superconductors, and calculate the full collective modes spectrum for each of these states. This will help to identify the type of pairing and the symmetry of the order parameter in HTSC and HFSC.