Topological Aspect of high-$T_c$ Superconductivity, Fractional Quantum Hall Effect and Berry Phase

TL;DR

This paper explores the topological connections between high-temperature superconductivity, fractional quantum Hall states, and Berry phase, highlighting how non-Abelian Berry phases influence fractional statistics and superconducting mechanisms.

Contribution

It establishes a theoretical link between RVB states, FQH states, and Berry phases, emphasizing the role of topological effects in high-$T_c$ superconductivity.

Findings

Non-Abelian Berry phase characterizes 3D spinons and holons.

Fractional statistics emerge when particles are confined to planes.

Superconductivity mechanism is topologically analogous to FQH effect.

Abstract

We have analysed here the equivalence of RVB states with $\nu=1/2$ FQH states in terms of the Berry Phase which is associated with the chiral anomaly in 3+1 dimensions. It is observed that the 3-dimensional spinons and holons are characterised by the non-Abelian Berry phase and these reduce to 1/2 fractional statistics when the motion is confined to the equatorial planes. The topological mechanism of superconductivity is analogous to the topological aspects of fractional quantum Hall effect with $\nu=1/2$.