Kondo effect in multi-dirac and weyl fermions

Abstract

In the present thesis we study the quantum magnetic impurity inserted in single and multi Dirac and Weyl hosts. We start by reproducing well known cases in literature, such as the Dirac and Weyl semimetals, manipulating the model Hamiltonian to change break symmetries at the emergence of the Kondo effect. By changing symmetries and the chemical potential, we explore various combinations of systems such as Dirac semimetal, Dirac metal, Weyl semimetal and Weyl semimetal for linear ($J=1$) and non-linear ($J>1$) behavior in dispersion relation. $J$ is also called topological charge of the system and influence for Kondo to emerge as well as the symmetries we choose to break, such as Time Reversal and Inversion symmetry. We will explore the numerical method that allows us to calculate the Kondo physics properties that emerge in such systems. We also describe the process throughout the work and how we evolved from a simple system to a more complete one. We conclude that for some specific combination of parameters and breaking inversion symmetry of these exotic systems, Kondo physics emerges. We also analyze the behavior of the magnetization in the dispersion relation for Weyl semimetals.