Edge Current of FQHE and Aharanov-Bhom Type Phase

TL;DR

This paper explores how Aharonov-Bohm type phases influence edge currents in the fractional quantum Hall effect, linking topological phases with observable current phenomena.

Contribution

It introduces the role of relative AB type statistical phases in the development of edge currents in FQHE, emphasizing topological phase transformations.

Findings

Edge currents are connected to AB type phases via the Shift quantum number.

Topological phases influence the physics of current flow in FQHE.

The study highlights the importance of Berry's phase in edge current development.

Abstract

When two non-identical quasi-particles in the Hall fluid encircle each other, relative AB type phase developes.As the quasi-particles advance towards the edge in a similar circular way, the developed current should have connection with this AB type phase through the {\it Shift} quantum number or Berry's topological phase. We have pointed out the role of relative AB type statistical phase in the development of edge current.In fact,the physics of the current flow in FQHE is sketched here from the topological point of phase transformation.