1. 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

2. 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

3. 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

4. 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

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

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

7. transport through a point contactV

8. V V

9. weak backscattering

10. 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)

11. 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 ,,,,,

12. 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 !

13. 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

14. Tunneling in the Jain sequenceV

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

16. noise
quasiparticle charge
Chung et al PRL03

17. 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

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

19. charge
statistics

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

21. weak backscattering only charge modes in the dynamicsV
down up
only charge modes in the dynamics
charge and neutral modes in the dynamics
always only charge mode in the dynamics

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

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

24. shot noise

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