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

Abstract

The field dependence of the power factor for a layered thermoelectric material with a closed Fermi surface in a quantizing magnetic field and at helium temperatures has been studied in the geometry where the temperature gradient and the magnetic field are perpendicular to the material layers. The calculations are carried out in the constant relaxation time approximation. In weak magnetic fields, the layered-structure effects are shown to manifest themselves in a phase retardation of power factor oscillations, increase of their relative contribution, and certain reduction of the power factor in whole. In high magnetic fields, there exists an optimal range, where the power factor reaches its maximum, with the corresponding value calculated for the chosen parameters of the problem in the effective mass approximation being by 12% higher than that for real layered crystals. Despite low temperatures, the power factor maximum obtained with those parameters in a magnetic field of 1 T has a value characteristic of cuprate thermoelectric materials at 1000 K. For this phenomenon to take place, it is necessary that the ratio between the free path of charge carriers and the interlayer distance should be equal to or larger than 30,000. However, in ultraquantum magnetic fields, the power factor drastically decreases following the dependence P ∝ T −3 B −6 . The main reason for this reduction is a squeeze of the Fermi surface along the magnetic field in the ultraquantum limit owing to the condensation of charge carriers on the bottom of a single filled Landau subband. K e y w o r d s: power factor, thermoelectric coefficient, quantizing magnetic field, Landau's subband, Fermi surface squeeze.

Can layered-structure effects be observed, if the Fermi surface is closed?

“…Moreover, the consideration was carried out in the approximation ζ 0 /(µ * B) ≫ 1. The result obtained in work [5] for the constant component of the conductivity at low temperatures, when ζ 0 /(kT ) ≫ 1, practically coincides with our one presented in work [11] for the case of a constant relaxation time. However, the dependence of the oscillating part of the longitudinal conductivity on the magnetic field is slightly different.…”

“…In work [11], a detailed derivation was given for the equation of chemical potential in the electron gas in a quantizing magnetic field, as well as the formulas for components of the longitudinal electroconductivity, in the case of an arbitrary function W (x) and provided that the relaxation time τ of charge carriers is either a constant or a function of the longitudinal quasimomentum only, i.e. τ = τ (x).…”

“…As the magnetic field grows, both curves approach each other, because, in the case of closed FS, Eq. ( 13) has the following asymptotic solution in strong quantizing magnetic fields [11]:…”

“…Now let us calculate the total longitudinal conductivity in a magnetic field. As was already mentioned in work [11], one has to consider the narrowing of the single filled Landau subband. Therefore, the substitution γ = (ζ − µ * B) /∆ has to be done in formulas ( 8) and ( 9) with regard for Eqs.…”

“…perpendicularly to the layers) is described by the strongcoupling law rather than the effective mass one. At the same time, in the works published earlier [6][7][8][9], the analysis of the diamagnetic susceptibility of an electron gas showed that the layered-structure effects can manifest themselves, if the FS is closed too, provided that the level of the filling of a miniband is high. This work aimed at studying the influence of layered-structure effects on the longitudinal conductivity of layered crystals with closed FSes in a strong quantizing magnetic field.…”