A method of distinction of a mixed dx2-y2+idxy state of HTSC from the pure d-wave state

Recent experiments and theoretical considerations show that in HTSC the mixture of different d-wave states is realized. We calculate for the first time the collective mode spectrum in a mixed state d(x)(-y)(2)(2) + id(xy) of HTSC. We use the model of d-pairing for superconductive and superfluid fermi-systems (HTSC, HFSC, etc., developed by P.N. Brusov and N.P. Brusova within path integration technique earlier. There are 10 collective modes in considered state: five of them are high frequency and five others seem to be Goldstone-like ones. In spite of the fact that spectra in both states d(x)(-y)(2)(2) and d(xy) are identical the spectrum in mixture d(x)(-y)(2)(2) + id(xy) state turns out to be quite different from them. Thus the probe of the spectrum in ultrasound and/or microwave absorption experiments could be used to distinguish the mixture - of two d-wave states from pure d-wave state. (C) 2000 Elsevier Science B.V. All rights reserved.