Second harmonics of magnetic quantum oscillations in layered metals

We find expressions for the second harmonics of magentic quantum oscillations of interlayer magnetoconductivity and magnetization in quasi-two-dimensional metals. The expressions obtained are useful, since in some experiments with quasi-twodimensional metals, the second harmonic of magnetic quantum oscillations is also observed. We analyze the effect of magnetic oscillations of the real part of electron self-energy part ReΣ on the shape of the quantum magnetization oscillations and on the magnetoresistance of quasi-two-dimensional conductors. In the limit of strong quantum oscillations, which is possible only in two-dimensional or quasi-twodimensional metals, the real part of electron self-energy function ReΣ also oscillates strongly. Usually it is neglected, taking into account only its imaginary part ImΣ, since it is assumed that ReΣ only shifts the chemical potential and does not affect the observed properties. However, ReΣ cannot be neglected if it also oscillates. As our calculations show, ReΣ oscillations affect the observed properties, since they shift the chemical potential relative to the Landau level even on average over the period of quantum oscillations. Oscillations of ReΣ affect the shape of the quantum magnetization oscillations [1], which is used to experimentally determine the regime of quantum oscillations: constant chemical potential or a constant electron density [2]. This question is not only of great practical importance for the analysis of numerous experiments, but also of substantial interest for the development of the theory of magnetic quantum oscillations. T. I. M. acknowledges the RFBR grants 19-02-01000, 21-52-12027.