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

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.