Phonon drag and carrier diffusion contribution to heat transport of superconductor MgB₂

Abstract

The temperature variation of phonon drag thermoelectric power [Formula: see text] is computed within the relaxation time approximation for high temperature MgB2 superconductors. The phonon drag thermoelectric power ([Formula: see text] in normal state of MgB2 superconductors dominates and is an artifact of strong phonon-impurity and phonon scattering mechanism. The carrier diffusive thermoelectric power is explored when heat transfer is limited by the scattering of phonons from defects, grain boundaries, phonons and charge carriers. The carrier diffusion contribution to the thermoelectric power ([Formula: see text] is analyzed keeping in mind the inherent two energy gaps. The conductivity within the relaxation time approximation for [Formula: see text] and [Formula: see text] band carriers has been taken into account ignoring a possible energy dependence of the scattering rates. Such an estimate sets an upperbound on [Formula: see text] and is about 50% of total heat transfer at room temperature. Both these channels for heat transfer are added and [Formula: see text] starts departing from linear temperature dependence at about 150[Formula: see text]K, before increasing at higher temperatures weakly. It is shown that the behavior of the [Formula: see text] is determined by competition among the several operating scattering mechanisms for the heat carriers and a balance between carrier diffusion and phonon drag contributions. The numerical analysis of thermoelectric power in the metallic phase of MgB2 shows similar results as those revealed from experiments. The anomalies reported experimentally are well accounted in terms of the scattering mechanism by phonon drag and carrier scattering with impurities.

Band filling and disorder effects on the normal state thermoelectric behavior in MgB2

“…On the whole, the sign change of the diffusive Seebeck is a signature of electron filling in the  band (see figure 6b). In summary, our calculations show that in undoped clean MgB 2 the diffusive term S diff is dominated by the  band contribution, which has lower Fermi energy and higher effective mass as compared to the  band 20,21 , hence the positive sign of S is accounted for in terms of  holes. The mixed electron/hole character of the  band, which entails mutually opposite contributions to S from antibonding  holes and bonding  electrons, also contributes to the much lower S the  band as compared to the  band 19 .…”

“…A phenomenological approach in term of physical parameters is reported in ref. 21 . Here we just summarize some key qualitative aspects.…”

“…To account for this discrepancy it is necessary to consider the phonon drag contribution. Several experimental works have indeed claimed the presence of phonon drag contribution on the basis of the temperature dependence of S curve [2,19,20,21]. In the presence of a temperature gradient, the phonons are not in thermal equilibrium and there is a net phonon flux from the hot to the cold side of the sample.…”

“…A quantitative modelling of S drag is out of the scope of this work. A phenomenological approach in term of physical parameters is reported in [21]. Here we just summarize some key qualitative aspects.…”

“…Thereby, the overall curve shape appears as a broad bump around above 150 K, superimposed to a roughly linear temperature dependence. The most accredited qualitative interpretation of this S(T) behavior is that the measured S results from phonon-drag S drag and diffusive S diff contributions of comparable magnitude [2,[19][20][21], the former associated to a broad maximum at T ≈ Θ D /5 − Θ D /4 (Θ D Debye temperature) and the latter associated to a roughly linear behavior. Seebeck anisotropy S ab /S c measured on single crystals was found to be ≈3-4 in the whole temperature range from T c to room temperature [19].…”