Dynamical interactions in (2+1)D Dirac systems

Abstract

In this thesis we study the full relativistic and dynamical interaction in (2+1)D Dirac systems. First, we briefly introduce condensed-matter realizations of such systems and discuss some of their key properties. After this, following work by Marino, we project Quantum Electrodynamics (QED) onto a plane, and show that the (2+1)D Pseudo-QED Lagrangian is equivalent to this projection. The properties of this Lagrangian are discussed, and it is shown that it describes unscreened Coulomb interaction in the static limit. A review is made of results of Pseudo-QED in the literature, focusing on obtaining the transverse conductivity. We reproduce results in the literature showing that a quantum valley Hall current may be generated by dynamical interactions for both the massive and massless case, and a quantum Hall current in the massive case. We then couple massive Pseudo-QED to a massive scalar field via a quartic interaction to study the effect on the generated transverse currents. We find that the quantum valley Hall current obtains a non-universal correction dependent on the ratio of the fermionic and scalar field masses. We also consider massless Pseudo-QED coupled to a scalar field and calculate the divergent Feynman diagrams involving the scalar field. These could be used for a renormalization group (RG) analysis of the system to investigate how the RG-flow of massless Pseudo-QED changes under the influence of a scalar field. We end by briefly considering other applications of Pseudo-QED and other projections of QED in the outlook.