Momentum Distribution Function of a Narrow Hall Bar in the FQHE Regime

Abstract

The momentum distribution function ($n(k)$) of a narrow Hall bar in the fractional quantum Hall effect regime is investigated using Luttinger liquid and microscopic many-particle wavefunction approaches. For wide Hall bars with filling factor $\nu =1/M$, where $M$ is an odd integer, $n(k)$ has singularities at $\pm M{k}_F$. We find that for narrow Hall bars additional singularities occur at smaller odd integral multiples of $k_F$: $n(k)\sim A_p\mid k\pm p{k}_F{\mid }^{2{\Delta }_p-1}$ near $k=\pm p{k}_F$, where $p$ is an odd integer $M,M-2,M-4,...,1$. If inter-edge interactions can be neglected, the exponent $2{\Delta }_p=(1/\nu +p^2\nu )/2$ is independent of the width ($w$) of the Hall bar but the amplitude of the singularity $A_p$ vanishes exponentially with $w$ for $p\ne M$.

Conference paper published in J. Korean Phys. Soc. Vol29, S10 (1996)