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 $ν=1/M$, 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 pk_{F} \mid ^{2Δ_{p}-1}$ near $k=\pm pk_{F}$, where $p$ is an odd integer $M,M-2,M-4,...,1$. If inter-edge interactions can be neglected, the exponent $2 Δ_{p}= (1/ ν+p^{2} ν)/2$ is independent of the width ($w$) of the Hall bar but the amplitude of the singularity $A_p$ vanishes exponentially with $w$ for $p\not=M$.