The de Haas-van Alphen effect in canonical and grand canonical multiband Fermi liquid.pdf

a r X i v : m t r l - t h / 9 5 0 9 0 0 4 v 1 2 1 S e p 1 9 9 5 The de Haas-van Alphen effect in canonical and grand canonical multiband Fermi liquid A.S. Alexandrov1 and A.M. Bratkovsky2 1 Department of Physics, Loughborough University of Technology, Loughborough, Leics. LE11 3TU, U.K. 2 Department of Materials, University of Oxford, Oxford OX1 3PH, U.K. (August 4, 1995) Abstract A qualitatively different character of dHvA oscillations has been found in a multiband (quasi)two dimensional Fermi liquid with a fixed fermion density ne (canonical ensemble) compared with an open system where the chemical potential μ is kept fixed (grand canonical ensemble). A new fundamental period Pf appears when ne is fixed, a damping of the Landau levels is relatively small and a background density of states is negligible. Pf is determined by the total density rather than by the partial densities of carriers in different bands: Pf = 1/(2neφ) for spin-split Landau levels and Pf = 1/(neφ) in the case of spin degenerate levels where φ is the flux quantum. 71.25.H Typeset using REVTEX 1 The de Haas-van Alphen oscillations of susceptibility as a function of the inverse magnetic field 1/H are well studied both experimentally and theoretically [1]. The frequency of the oscillations is proportional to the extremal cross section of the Fermi surface. Therefore, in the multiband metals one would expect several different dHvA periods corresponding to the independent contributions of different bands. [1–3] The dHvA effect in closed and open systems was analysed by Dingle back in 1951 [4] with the conclusion that there is practically no difference because the dependence of the chemical potential on the magnetic field, in the case of fixed ne, is very weak. In this Letter we show that while this is true for three dimensions and(or) for the relatively large damping of Landau levels, the dHvA effect is qualitatively different in the near two-dimensional (2D) canonical Fermi liquid compared with