Thermoelectric transport properties of an apparent Fermi liquid: Relation to an analytic anomaly in the density of states and application to hole-doped delafossites

Abstract

Through the motivation of the recent discovery of dispersionless regions in the band structure of the delafossites, a model density of states of free fermions including a discontinuity as analytical anomaly is studied. The resulting temperature dependence of the chemical potential is obtained both exactly and by different approximation schemes which are then discussed thoroughly. This includes the introduction of an approximation of the polylogarithm difference which is capable of accessing a parameter range neither covered by Sommerfeld expansion nor by Boltzmann approximation. It is found that the Fermi temperature and several other temperature scales may be very low, giving rise to experimentally observable behaviours differing from the one described by Fermi liquid theory. In particular, two kinds of apparent Fermi liquid behaviour emerge at intermediate temperatures. This behaviour is related to recent transport data reported for CuCr(1-x)MgxO2 [A. Maignan et. al, Solid State Commun. 149, 962 (2009)] and CuRh(1-x)MgxO2 [A. Maignan et. al, Phys. Rev. B 80, 115103 (2009)] by means of the temperature independent correlation functions ratio approximation. In this way an effective density of states as well as the effective charge carrier density of these materials are determined. Furthermore, conclusions about the specific heat of the latter material are drawn which presents particular effects of the analytical anomaly.