D. Ferraro N. Magnoli M. Merlo Tunneling of multiple-quasiparticles between fractional quantum Hall edges Maura Sassetti Università di Genova A. Braggio D. Ferraro N. Magnoli M. Merlo

Outline LL exponents in the Laughlin series (universal vs non-universal) Measurements in p.c. for the Jain sequence Tunneling of multiple-quasiparticles current and noise

gapped bulk excitations Quantum Hall effect Tsui, Stormer, Gossard incompressible fluid gapped bulk excitations Von Klitzing, Dorda, Pepper PRL80 ; Tsui, Stormer, Gossard PRL82 , Laughlin PRL 83

FQH edge states boundary restriction of the bulk theory Hall liquid chiral excitations with no gap low-energy sector of the incompressible fluid Wen, PRL 90, PRB90,91; Cappelli, Dunne, Trugenberger, Zemba Nucl. Phys. 93 Lopez, Fradkin PRB 99 ....

Laughlin series quasiparticle excitations charge statistics Laughlin PRL 83; Arovas, Schrieffer, Wilczek PRL 84.

chiral Luttinger liquids fractional charge fractional statistics dynamics (LL exponents) Wen 90

transport through a point contact V

V V

weak backscattering

weak backscattering mode dynamics general solutions at any order in Moon, Yi, Kane, Fisher PRL 93 (MC simulations) Yue, Matveev, Glazman PRB 94 (weak interaction expansion ) Fendley, Ludwig, Saleur PRL 95, 96 (thermodinamic Bethe Ansatz) Weiss, Egger, Sassetti PRB 95 (real time P.I. ) Aristov, Woelfle EPL 08 (fermionic representation, RG equation)

extremely weak backscattering Chung, Heiblum, Umansky PRL 03 extremely weak backscattering theory negative slope non-universal power law exponent ! Other experimental deviations Chang et al., PRL 96; Grayson et al. PRL 98; Glattli et al. Physica E 00; Chang et al. PRL 01; Grayson et al. PRL 01; Hilke PRL 01, Roddaro PRL03, 04 ,,,,,

several proposals non universal ! e-ph coupling (Heinonen & Eggert PRL 96, Rosenow & Halperin PRL 02) e-e interaction (Mandal & Jain PRL 02; Papa & Mac Donald PRL 05) edge reconstruction (Mac Donald et al. J. Phys 93, Chamon & Wen PRB 94, Wan et al. PRL 02,Yang PRL 03) local filling factor (Sandler et al PRB 98, Roddaro et al. PRL 05, Lal EPL 07) non universal !

shot noise weak backscattering Poissonian process for rubust! Chung et al PRL03 De-Picciotto et al. Nature 97 for Kane & Fisher, PRL 94; Fendley, Ludwig, Saleur PRL 95 rubust! De-Picciotto et al. Nature 97 Saminadayar et al. PRL 97 Reznikov et al. Nature 99 ...

Tunneling in the Jain sequence V

extremely weak backscattering Chung, Heiblum, Umansky PRL 03 positive slope change in the power-law scaling

noise quasiparticle charge Chung et al PRL03

Chamon, Fradkin, Lopez PRL07 Hall liquid charged mode neutral mode topological dynamical Lopez, Fradkin PRB 99 Chamon, Fradkin, Lopez PRL07 Lee, Wen 98 Kane Fisher PRB 95

excitations charge statistics quasiparticle agglomerate electrons Haldane PRL 83, Halperin PRL 84, Jain PRL 89

charge statistics

tunneling processes most relevant operators for (scaling dimension) Ferraro Braggio, Merlo Magnoli, Sassetti arXiv:08053435; similar to: Wen; Kane, Fisher PRB 95 single quasiparticle p-agglomerate

weak backscattering only charge modes in the dynamics V down up only charge modes in the dynamics charge and neutral modes in the dynamics always only charge mode in the dynamics

positive slope Chung et al. PRL 03 relevance of p-agglomerate

fitting of the experimental data Ferraro Braggio, Merlo Magnoli, Sassetti arXiv:08053435

shot noise

Conclusions tunneling experiments in the Jain sequence relevance of neutral mode dynamics at low temperatures relevance of multiple-quasiparticle tunneling at extremely low temperatures