Analytical treatment of the de Haas–van Alphen frequency combination due to chemical potential oscillations in an idealized two-band Fermi liquid

Abstract

de Haas-van Alphen oscillation spectrum is studied for an idealized two-dimensional Fermi liquid with two parabolic bands in the case of canonical (fixed number of quasiparticles) and grand canonical (fixed chemical potential) ensembles. As already reported in the literature, oscillations of the chemical potential in magnetic field yield frequency combinations that are forbidden in the framework of the semiclassical theory. Exact analytical calculation of the Fourier components is derived at zero temperature and an asymptotic expansion is given for the high temperature and low magnetic field range. A good agreement is obtained between analytical formulae and numerical computations.

Random walks and magnetic oscillations in compensated metals

“…However, the above-mentioned type of Fermi surface yields quantum-oscillations spectra with numerous frequency combinations that cannot be accounted for by this semiclassical model. This phenomenon which has raised a great interest [6][7][8][9][10][11][12] is generally attributed to either the formation of Landau bands or ͑and͒ oscillations of the chemical potential in magnetic field.…”

“…The inset compares the ratio / 0 behavior for two compensated orbits ͑solid line͒ and two electron-type orbits ͑dashed line͒ of same area ͑or frequency͒ F 0 =5/ 7 with effective masses m 0 ‫ء‬ = 1 and m 1 ‫ء‬ = 2.5, in the absence of magnetic breakdown ͑b 0 → ϱ͒. The chemical potential for two electron orbits is computed from Ref 12,. Eq.…”

Frequency combinations in the magnetoresistance oscillations spectrum of a linear chain of coupled orbits with a high scattering rate

“…Oppositely, analytical calculations of the effective masses related to the frequency combinations induced by the oscillation of the chemical potential in dHvA spectra of an ideal two-band electronic system yield [22]:…”

Combination quantum oscillations in canonical single-band Fermi liquids

“…In particular, there are combination frequencies in dHvA and/or SdH oscillations of a 2D multiband metal with fixed electron density n e ͑canonical ensemble͒, predicted by Alexandrov and Bratkovsky ͑AB͒, 6 and studied numerically [6][7][8][9][10][11] and analytically. [12][13][14] The effect has been experimentally observed in different low-dimensional systems. 3,15,16 Obviously, there are no mixing of the fundamental single-band frequencies, if the chemical potential is fixed by a reservoir ͑grand-canonical ensemble͒.…”