Consequences of a possible adiabatic transition between \nu=1/3 and \nu=1 quantum Hall states in a narrow wire

TL;DR

This paper explores the theoretical possibility of adiabatically connecting different quantum Hall states in a narrow wire, proposing potential applications like a DC voltage step-up transformer, while discussing experimental challenges.

Contribution

It introduces a theoretical analysis of adiabatic transitions between /3 and  quantum Hall states using composite fermion and Luttinger liquid models, suggesting novel device applications.

Findings

Adiabatic junctions could enable a DC step-up transformer.

Theoretical models predict feasible adiabatic transitions between /3 and  states.

Experimental implementation faces significant challenges.

Abstract

We consider the possibility of creating an adiabatic transition through a narrow neck, or point contact, between two different quantized Hall states that have the same number of edge modes, such as \nu=1 and \nu=1/3. We apply both the composite fermion and the Luttinger liquid formalism to analyze the transition. We suggest that using such adiabatic junctions one could build a DC step-up transformer, where the output voltage is higher than the input. Difficulties standing in the way of an experimental implementation of the adiabatic junction are addressed.