Study on Electronic Transport Properties via Boltzmann Transport Equation Pohang University of Science and Technology

Abstract

The Boltzmann transport equation (BTE) is the one of fundamental and commonly used methodology investigating the electronic transport properties of solid system. BTE describes distribution function of electrons in momentum space, therefore, the electronic transport properties depend on low-energy elec- tronic structure. Especially, geometry of Fermi surface and group velocity on fermi surface determine electronic conductivity. The size effect of solid system increases electronic resistivity. The scattering on the surface of solid system is not negligible in the thin film or nanowire system. The longer mean free path of electrons leads to larger increase of resistivity with respect to bulk system. The grain-boundary scattering is additional factor of the thin film or nanowire. Fuchs-Sondheimer (FS)-model and Mayadas-shatzkes (MS)-model are conven- tional method to introduce surface and grain-boundary scatterings. The external magnetic field can be crucial role of transport properties. Movement of charged particle under magnetic field generates the Lorentz force on a moving particle perpendicular to magnetic field and velocity of particle motion Magnetic field. This yields cyclotronic motion of the particle, hence change of resistivity. The change of resistivity by magnetic field is estimated by magnetoresistance (MR). In spite of lots of studies of transport properties in decades, Several transport phe- nomenon have not been explained clearly. The first case is thin film or nanowire with anisotropy of bulk conductivity. As the conventional FS- and MS- modes consider isotropic system, the interplay between anisotropy of bulk conductivity and boundary condition has not been studied analytically. The second one is MR of complex Fermi surface. For the simplest Fermi surface such as sphere, ellipsoid and cylinder, the magnetotransport properties have been investigated based on BTE. In contrast, non-equalibrium physics of complex Fermi surfaces are more quantitive, as analogy of simpler systems. Moreover, the studies on Hall conductivity under the magnetic field are less developed then that of longitudi- nal conductivity. The doctoral dissertion consists of the following componants: In chapter I, I review general background of transport theory focusing on BTE. The semiclassical modelling approach is used to describe electronic motion and scattering mechanism. In chapter II, I construct modified model for anisotropic nanowire with rect- angular cross-section. I derive the conductivity with rectangular boundary condi- tions with anisotropic mean free path of charge carriers. Then, I include external surface scattering and grain boundary scattering as perturbations. This is ex- cellent application of Boltzmann transport theory. In chapter 3.1, I introduce computation code for magnetotransport calculations. I show that MR results of the simplest Fermi surfaces well reproduce the previous results. Furthermore, my code can calculate MR tensor components of real materials by analyzing wan- nier bands from the first-principles calculation. I exhibit MR of PdCoO2 as an example of real materials. Computational results of PdCoO2 show interesting features of colaboration between longitudinal or Hall resistivity and direction or strength of external magnetic field. Additionally, in chapter 3.5, I show my earlier investigation on electronic structure of square-net materials with P4/nmm space group. The Tight-binding Hamiltonian formalism well describes the low-energy electronic structures and Fermi surfaces. I demonstrated the distant-neighbor hopping parameters has crucial role determining topology of Fermi surface, by extension electronic transports. The exotic angle-dependence of square-net ma- terials is attracting topic, and the motivation of my later studies on transport theory.