Issue
EPL
Volume 86, Number 3, May 2009
Article Number 37010
Number of page(s) 6
Section Condensed Matter: Electronic Structure, Electrical, Magnetic and Optical Properties
DOI http://dx.doi.org/10.1209/0295-5075/86/37010
Published online 19 May 2009
EPL, 86 (2009) 37010
DOI: 10.1209/0295-5075/86/37010

Effect of inter-edge Coulomb interactions on transport through a point contact in a $\nu$ = 5/2 quantum Hall state

Sourin Das1, 2, Sumathi Rao3 and Diptiman Sen4

1   Institut für Festkörper-Forschung - Theorie 3, Forschungszentrum Jülich - 52425 Jülich, Germany, EU
2   Institut für Theoretische Physik A, RWTH Aachen - 52056 Aachen, Germany, EU
3   Harish-Chandra Research Institute - Chhatnag Road, Jhusi, Allahabad 211 019, India
4   Centre for High Energy Physics, Indian Institute of Science - Bangalore 560 012, India

s.das@fz-juelich.de
sumathi@hri.res.in
diptiman@cts.iisc.ernet.in

received 11 February 2009; accepted in final form 17 April 2009 ; published May 2009
published online 19 May 2009

Abstract
We study transport across a point contact separating two line junctions in a $\nu$ = 5/2 quantum Hall system. We analyze the effect of inter-edge Coulomb interactions between the chiral bosonic edge modes of the half-filled Landau level (assuming a Pfaffian wave function for the half-filled state) and of the two fully filled Landau levels. In the presence of inter-edge Coulomb interactions between all the six edges participating in the line junction, we show that the stable fixed point corresponds to a point contact that is neither fully opaque nor fully transparent. Remarkably, this fixed point represents a situation where the half-filled level is fully transmitting, while the two filled levels are completely backscattered; hence the fixed point Hall conductance is given by $G_H=\frac{1}{2} e^2/h $. We predict the non-universal temperature power laws by which the system approaches the stable fixed point from the two unstable fixed points corresponding to the fully connected case $(G_H=\frac{5}{2} e^2/h)$ and the fully disconnected case (GH = 0).

PACS
73.43.-f - Quantum Hall effects.
73.43.Jn - Tunneling.
71.10.Pm - Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.).

© EPLA 2009