Multiple-quasiparticle tunneling between edge states in the FQHE

1. LAMIA-INFM-CNR Multiple-quasiparticle tunneling between edge states in the FQHE Dario Ferraro Università di Genova Matteo Merlo Nicodemo Magnoli Maura Sassetti Alessandro Braggio

2. Outline FQHE, edge states Point Contact and quasiparticles tunneling Puzzling experiments Our model and results

3. FQHE, edge states incompressibility gapped excitations with fractional charge and statistics Stormer et al., RMP 98

4. FQHE, edge states Hall liquid Low-energy sector of an incompressible liquid Boundary restriction of bulk theory Wen, PRB 90 Lopez, Fradkin PRB 99 Excitations with no gap

5. FQHE, edge states Hall liquid Lopez, Fradkin PRB 99 charged mode topologicalmode

6. Vertex operator m-agglomerate vertex statistics charge Not fixed for the periodicity of the statistical angle Completely fixed by charge condition

7. Vertex operator We consider the value of that gives the most relevant scaling dimension of the vertex operator p-agglomerate Single quasiparticle Most relevant operators!

8. Quantum Point Contact Backscattering current Shot Noise

9. Experiments Chung et al., PRL 03 Change in slope around low T high T

10. Our model and results Our tunneling hamiltonian not strictly zero

11. Our model and results: conductance Fitting of the experimental data Relevance of p-agglomerates

12. Our model and results: shot noise Width of transition depends on the ratio of scaling dimentions between single qp and p-agglomerates Fano factor with Effective charge

13. Conclusions Extending Fradkin-Lopez to finite propagation velocity of neutral mode we proofed • The change in power laws of conductance • The relevance of p-agglomerate at low energy and low backscattering • The shot noise behaviour at low energy The physics of the p-agglomerate need further theoretical and experimental investigation Thank you for your attention

17. FQHE Edge States Hall liquid ( odd) Wen, Int.J.Mod.Phys. 92

19. Our model and results Propagating neutral mode Lee, Wen condmat 9809169v2 not strictly zero Neutral modes have dynamics and influence the single quasiparticle, but not of the p-agglomerate New energy scale

20. Point Contact at , theory vs. experiment Different slopes Bunching of p-quasiparticles Complete for Incomplete for Chung et al., PRL 03 These observations suggest the existence of ‘‘low’’ and ‘‘high’’ temperature backscattering states, each with its characteristic charge and energy. Chung et al., PRL 03

21. charge fields electrons quasi-particles local tunneling DOS of quasi-particle

22. q-particletunnelingin QPC Roddaro et al. PRL 03, PRL 04 weak qp backscattering theory: maximum experiments: minimum at low temperatures Kane & Fisher PRL 92 Moon et al. PRL 93 Fendley et al. PRL 95

23. experimental deviations also with electron tunneling in between edge-metal and edge-edge Renormalized non-universal exponent in the TDOS 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.... e-ph coupling (Heinonen & Eggert PRL 96) dissipative environment (Rosenow & Halperin PRL 02) edge reconstruction (Mac Donald et al. J. Phys 93, Chamon & Wen PRB 94, Wan et al. PRL 02,Yang PRL 03) edge interaction (Mandal & Jain PRL 02; Papa & Mac Donald PRL 05)

24. Fractional charge in QPC weak q-particle backscattering Poissonian process for Kane & Fisher, PRL 94 De-Picciotto et al. Nature 97 Saminadayar et al. PRL 97 Reznikov et al. Nature 99 ...

25. different geometry with a different statistics of the process fractional charges ? Luttinger exponents ?

26. electron tunneling 3DEG edge-edge tunneling bulk-edge tunneling Kane & Fisher, PRL ’97

27. charge’s fields electrons quasi-particles local tunneling DOS