Longitudinal conductivity of layered charge-ordered crystals in a high quantizing magnetic field

Abstract

The longitudinal Seebeck coefficient of the charge-ordered layered crystals in a strong quantizing magnetic field normal to layers plane has been determined.The conditions whereby charge ordering parameter and chemical potential of charge carriers are the oscillating functions of the magnetic field induction are considered. The longitudinal Seebeck coefficient has been calculated for two models of the relaxation time: i) constant relaxation time and ii) the relaxation time proportional to the longitudinal velocity. It has been shown that in a quasi-classical region of magnetic fields for the case of the relaxation time proportional to the longitudinal velocity the longitudinal Seebeck coefficient is less than for the case of constant relaxation time. In this region, for selected problem parameters it does not exceed 4.37μV/K. In the strong quantizing magnetic fields for both models of the relaxation time the longitudinal Seebeck coefficient is virtually the same. For selected problem parameters its maximal modulus is 2033μV/K. At the same time, in the disordered layered crystals, in a quasiclassical region, the Seebeck coefficient is approximately one order of magnitude less than for the charge ordered crystals. In the strong magnetic fields, the Seebeck coefficient for the disordered layered crystals is factor of 7 to 9 less than for the charge-ordered crystals. However, in super strong magnetic fields, under current carriers concentration in the only filled Landau sub-band, for both models of the relaxation time the modulus of the Seebeck coefficient tends to zero according to asymptotic law 2   B zz  . IntroductionAt the present time much attention is given to the development and study of the properties of new thermoelectric materials. The objects of experimental investigation are metals, alloys, semiconductors [1, 2], fullerenes [3], composites [4], including biomorphic [5], etc.Theory of thermoelectric properties of materials, including nanosystems, is being actively developed as well [6,7]. One of the first works on the theory of transverse Seebeck coefficients of metals in quantizing magnetic fields was performed by Kosevich and Andreyev [8].Many of the investigated materials, for instance, semiconductor systems of A II B VI C VII class, intercalated graphite compounds, synthetic metals, graphene, etc. belong in their crystal structure to layered materials. At the same time, the overwhelming majority of theoretical works dedicated to behaviour of such layered systems in quantizing magnetic fields are mainly concerned with the transverse galvanomagnetic effects. The author of this paper is aware of only one work which deals with the thermal conductivity of graphene in a quantizing magnetic field [9]. In so doing, its Fermi surface is considered to be open, that is, such which occupies the entire one-dimensional Brillouin zone and, with a periodic continuation, is a connected one, that is, represents a continuous corrugated cylinder.

Power Factor for Layered Thermoelectric Materials with a Closed Fermi Surface in a Quantizing Magnetic Field

“…On the other hand, in the previous works, the author showed that, if the behavior of charge carriers in the direction perpendicular to the layers is studied, the layered-structure effects can be well pronounced in the case of a closed FS as well [12] or if the topological transition from the open FS to a closed one takes place [13].…”

“…For the calculation of the power factor, we also need an expression for the relaxation time τ 0 . For any γ 0 , this quantity can be determined in the same way as in works [12,13], namely, by the formula…”