First-Principles Density-Functional Theory Calculations of Thermomagnetic Properties

Conventional active coolers including water heat pumps and air conditioning have moving
components that can cause mechanical failure and fatigue over time. They cannot be
down-scaled to micron sizes and cannot be integrated into on-chip small-scale designs.
Thermomagnetic and thermoelectric cooling systems emerged as an alternative to conventional
active cooling systems. Thermomagnetic cooling systems are based on the Nernst-
Ettingshausen effect that was observed in Bismuth for the first time. In the presence of an
electric current and a perpendicular magnetic field, electrons and holes are pushed to opposite
sides due to the Lorentz force. The migration of charge carriers develops a temperature
gradient across the material, perpendicular to both electric current and magnetic field. Hence,
heat can be pumped across the sample, this is the basis of Ettingshausen coolers. Similarly,
applying a magnetic field perpendicular to a temperature gradient generates a transverse
voltage difference, the so-called Nernst Voltage.
The primary objective of this dissertation is to develop a code to calculate the response of
a system to the simultaneous presence of a magnetic field and a temperature gradient using
first-principles density functional theory. First, I obtained the Nernst coefficient within constant
relaxation time approximation to establish an insight into the Nernst effect and how it is
related to the details of the band-structure. The aforementioned method is, however, unable
to reconstruct the experimentally measured values as the Nernst coefficient is sensitive to
the details of the relaxation times and in particular, it is proportional to the carrier mobility.
Therefore, I implement the charge carrier relaxation time due to various scattering mechanisms
including electron-phonon and electron-ionized impurity scattering in our theory.
Experimental data of germanium, silicon, indium antimonide, and bismuth in a wide range
of temperatures and doping concentrations were successfully reproduced. Furthermore, with
the help of analytical models, I obtained a simplified model for the Nernst coefficient in order
to find the material descriptors to predict the Nernst coefficient which turned out to be
effective mass.
Lastly, I propose an approach to evaluate anomalous Nernst transport within the density functional
theory framework. The semi-classical Boltzmann transport was modified by adding
the effect of Berry curvature. Once the formalism was completed, the approach was implemented on the basis set of maximally localized Wannier functions and applied to Fe3Sn to
replicate the experimental data.