On the electron spectrum of a type-II superconductor in magnetic field. The magnetization oscillations

A damping of the de Haas van Alphen oscillations in the superconducting state

“…Outside this region we expect to set |∆(y)| = 0 but, since from (4), any choice in the range 0 ≤ ∆(y) ≤ |∆| for y −hk x /2eB > d makes little difference, we can for simplicity still take |∆(y)| = |∆|. Taking all these observations into account the constant energy orbits corresponding to these relations are the same as those studied by Burmistrov and Dubovskii [13]. Firstly we investigate the orbits and spectrum for P x = 0.…”

“…Less obviously, P x , also behaves like an orbit centre (see below). It is natural Taking all these observations into account the constant energy orbits corresponding to these relations are the same as those studied by Burmistrov and Dubovskii [13]. Firstly we investigate the orbits and spectrum for P x = 0.…”

“…degeneracy within a cell is lifted. On the other hand, translations of such an orbit by lattice vectors (different choices of k x ) leave Taking all these observations into account the constant energy orbits corresponding to these relations are the same as those studied by Burmistrov and Dubovskii [15]. Firstly we investigate the orbits and spectrum for P x = 0.…”

“…However, as was pointed out in ref. [13] P x = 0 changes the spectra drastically because, as is clear from (2) 'Landau level' energies depend upon P x . The rest of this paper deals with these complications.…”

“…Evidently this would be of particular importance in connection with anisotropic superconductors where (k) can have lines of zeroes on the Fermi surface [5]. Unfortunately at this stage there is no consensus concerning the mechanism of how the experimentally observed oscillations of the diamagnetic response of a type II superconductor come about [6][7][8][9][10][11][12][13][14][15][16][17] (see [7] for a recent review of the various theoretical approaches). Using our recently developed very general semiclassical theory of quasiparticles in the superconducting state [18], in what follows we develop a semiclassical picture of Landau-like orbits of quasiparticles suggested by the simple model calculation of Miller and Györffy [8].…”