Geometric Phases in Graphitic Cones

TL;DR

This paper investigates geometric phases in graphitic cones using a topological approach, revealing a holonomy-induced phase analogous to the Aharonov-Bohm effect, extended to systems with multiple cones and effective defects.

Contribution

It introduces a geometric framework to analyze topological phases in graphitic cones and extends the analysis to complex configurations with multiple cones.

Findings

Spinor acquires a phase around the cone apex due to holonomy

Topological phases are analogous to the Aharonov-Bohm effect

Extension of analysis to systems with multiple cones and defects

Abstract

In this article we use a geometric approach to study geometric phases in graphitic cones. The spinor that describes the low energy states near the Fermi energy acquires a phase when transported around the apex of the cone, as found by a holonomy transformation. This topological result can be viewed as an analogue of the Aharonov-Bohm effect. The topological analysis is extended to a system with $n$ cones, whose resulting configuration is described by an effective defect.