Theoretical study on manifestation of geometric phase of Dirac fermions in 2+1 dimension through transport

Abstract

We understand our universe in terms of elementary particles and interactions among them. The elementary particles refer to the elementary excitations on the ground state, which is so-called vacuum. Likewise, a natural approach to understanding phases of condensed matters is to search for elementary excitations and their behaviors on the ground state of condensed matters. For example, most of metals are comprehended by electrons having renormalized mass, magnetic moment, and etcetera. Moreover, electrons at the Fermi energy in a graphene behaves like relativistic Dirac fermions in the 2+1 dimension. To find out what is the elementary excitation of condensed matters is not only important to grasp the phase of them but is interesting in the sense that we can utilize the brand-new particles and their properties on a table in laboratory.

Especially, the surface of topological insulators and single layer of graphene have attracted a massive interest as electrons in the matters can be coined relativistic. Differently from non-relativistic electrons, relativistic electrons have a property that directions of momentum and spin are parallel, called chirality. By the chirality, it is known that the wave function of relativistic electrons acquires the geometric phase(Berry phase) by $\pi$ when they are in the cyclotron motion. The phenomenon has draw interests as it is shown in quantum Hall experiments. However, reseaches related to the chirality of relativistic Dirac fermions have been limited to when the direction of spin is changed on a plane in the adiabatic way.

This research stems from the idea that the direction of spin will be changed according to the sudden scattering of electrons at junctions or edges. It is found that the scattered relativistic electrons acquire continuous values of quantum phase but the geometric phase $\pi$, and studied transport phenomena as manifestation of them. The findings suggest that topological number of insulators under the metal-insulator and insulator-metal-insulator setup is detectable. And a spin transistor is suggested as an application. In addition, the geometric phase acquired during a sudden scattering is essential for a understanding of scattering process at graphene edges. To demonstrate it, band structure and interference patterns of electrons in graphene nano-ribbons is studied.