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

Abstract

Abstract. -Deploying a recently developed semiclassical theory of quasiparticles in the superconducting state we study the de Haas-van Alphen effect. We find that the oscillations have the same frequency as in the normal state but their amplitude is reduced. We find an analytic formulae for this damping which is due to tunnelling between semiclassical quasiparticle orbits comprising both particle-like and hole-like segments. The quantitative predictions of the theory are consistent with the available data.The revival of interest [1][2][3] in studying the de Haas-van Alphen (dHvA) effect in the superconducting state [4] is driven by the hope that this would provide new k-vector dependent information about the superconducting gap ∆(k). Evidently this would be of particular importance in connection with anisotropic superconductors where ∆(k) can have lines of zero's on the Fermi surface [5]. Unfortunately at this stage there is no concensus 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]. Using our recently developed very general semiclassical theory of quasiparticles in the superconducting state [16], 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]. Clearly the long term aim of a semiclassical theory is to provide an analogue of the Lifshitz-Kosevich formulae for superconductors. Hopefully such a formulae would allow the interpretation of experiments in terms of the Fermi surface and the variation of ∆(k) on the Fermi surface. At this stage we only deal with conventional superconductors with the usual s-wave pairing. As it happens this is the only case for which reliable data already exists. Within the limits of a number of simplifying assumptions the above semiclassical theory provides for Bohr-Sommerfeld like quantisation rules for quasiparticles. In particular it allows for the analogue of magnetic breakdown which involves tunnelling between distinct semiclassical orbits. We show that there are orbits which enclose areas that are precisely the same size as the Landau orbits in the normal state, but involve such tunnelling. As will be seen the consequence of these tunnelling events is a damping factor in the Lifshitz-Kosevich formulae in agreement with experiments [1][2][3].The theory we wish to use seeks the semiclassical spectrum of the following Bogoliubov-de c EDP Sciences

Damping of the de Haas–van Alphen oscillations in the superconducting state ofMgB2

“…The most recent theoretical work 50,58 however, suggests that the Miyake theory should seriously overestimate the damping and that the Maki model should provide an accurate quantitative estimate of the average gap on the dHvA orbit. Our data is in serious disagreement with this as the gap values found from the Maki model fits are more than a factor 10 times larger than the expected zero field π band gap.…”

“…Close to H c2 , for H ab, we find that the numerical data can be approximated by ∆ Recently, there has been further theoretical work on the dHvA effect in superconductors. Duncan and Györffy 58 have extended the work in Ref. 55 and given a new formula for R SC .…”