Charge fractionalization on quantum Hall edges

Abstract

We discuss the propagation and fractionalization of localized charges on the edges of quantum Hall bars of variable widths, where interactions between the edges give rise to Luttinger liquid behavior with a non-trivial interaction parameter g. We focus in particular on the separation of an initial charge pulse into a sharply defined front charge and a broader tail. The front pulse describes an adiabatically dressed electron which carries a non-integer charge, which is √ g times the electron charge. We discuss how the presence of this fractional charge can, in principle, be detected through measurements of the noise in the current created by tunneling of electrons into the system. The results are illustrated by numerical simulations of a simplified model of the Hall bar.

Transient dynamics of spin-polarized injection in helical Luttinger liquids

“…Since their non-Fermi liquid behavior was observed in a variety of transport experiments, in good agreement with theoretical predictions, they have been proposed as ideal playgrounds to explore the phenomenon of charge fractionalization [10,11]. Alternative setups can be created by exploting the chiral edge states of integer quantum Hall bars: if the boundaries of the bar are close enough, electron interactions between the counter-propagating edge states are not negligible, and the full system can be viewed as a non-chiral LL [12,13,14,15]. Most of the theoretical works studying charge fractionalization have focused on noise measurements in carbon nanotubes and quantum Hall bars.…”

“…The functionρ(x, t) is the time evolution, obtained by means of Eqs. (11)(12)(13), of an initial wave packetρ (0) (x) with normalized shape ( ρ (0) (x) dx = 1). Identifying the current I (inj) (n ∆t) = Q n /∆t and considering the limit ∆t → 0 one obtains from Eq.…”

Charge Fractionalization in the Integer Quantum Hall Effect

“…Interchannel interaction can be monitored in a direct fashion. In v ¼ 2, Coulomb interaction between electrons in the two adjacent edge channels is expected to modify the noninteracting channels [19,20,[28][29][30][31][32][33]. An electron injected selectively into the "hot" channel, while the other channel is "cold," is predicted to decompose into two modes-"fast" and "slow."…”

“…An electron injected selectively into the "hot" channel, while the other channel is "cold," is predicted to decompose into two modes-"fast" and "slow." Each is shared between the two original channels, and each carries a fraction of an electron charge [28][29][30][31][32][33][34]. Indeed, a recent rf transmission measurement investigated the detailed dispersion of the slow mode and its separation from the fast mode [34].…”

Luttinger liquids, Fermi liquids, and fractional statistics

“…The fractionalization is linked to chiral separation of charges that are introduced in the system 11,12 , so that fractions of a unit charge move to the right and the left, respectively. There has in particular been interest in the study of this effect for edge excitations in quantum Hall systems, where interactions between edge modes give rise to the charge fractionalization [7][8][9][10] . However, one should note the important difference between the charge fractionalization effect in the bulk of the quantum Hall system and at the edges.…”