1. Sep. 23, 2008
Correlated tunneling and the instability of the fractional quantum Hall edge
Dror Orgad Oded Agam
PRL 100, (2008)

2. Outline The system Historical overview of theory and experiments
The model
A toy model
Solution & implications

3. Incompressibility (gap)
Fractional quantum Hall effect
Incompressibility (gap)
Landau levels
Interaction
Edges

4. Integer quantum Hall effect
Wen’s theory
Landau levels
Landau levels
Interaction ?
Edges

5. Chern-Simons theory Composite fermions mean field
Electron correlations built into the bulk are assumed to extend all the way to the edge
mean field

6. Tunneling into the edge of a FQHE droplet
(A sharp cleaved edge)
Landau levels

7. Tunneling into the edge of a FQHE droplet: Experimental results
Tunneling into the edge of a FQHE droplet: Wen’s theory
for

8. Tunneling into the edge of a FQHE droplet: Experimental results
Grayson et al., PRL 1998:
for
Cang et al., PRL 1996
for

9. Non-propagating modes
Tunneling into the edge of a FQHE droplet: back to Theory
Conti & Vinagle, 1998
Han & Thouless, 1997
Zülicke & MacDonald, 1999
Hydrodynamical Theory
The nature of the underlying quasiparticles is ignored
Alexeev et al., 2000
Tunneling via impurity states sharply located at the Fermi level
Lee & Wen, 1998
Lopez & Fradkin, 1999
Non-propagating modes

10. Levitov, Shytov & Halperin,1998, 2001
Tunneling into the edge of a FQHE droplet: additional experiments
Tunneling into the edge of a FQHE droplet: Theory again
Chang et al., 2001
Levitov, Shytov & Halperin,1998, 2001
Smearing of Wen’s original result due to finite value of

11. Tunneling into the edge of a FQHE droplet: More experiments
Tunneling into the edge of a FQHE droplet: Numerics
Hilke et al., 2001
for
Mandal & Jain, 2002

12. The edge tunneling puzzle: Non-universality ?!
Wen’s theory - is it complete ?
We show:
“Correlated tunneling” may lead to an edge instability towards a new configuration with reconstructed edge.
Similar behavior has been observed in the numerical studies of Tsiper & Goldman (2001), and Wan ,Yang & Rezayi, (2002/3)

13. Correlated tunneling terms
Landau levels of Composite Fermions
Edge states
The interaction Hamiltonian:
Hartree term
Correlated tunneling terms
Fock term

14. Correlated tunneling: A toy model
Eigenvalues:
Ground state

15. Can be diagonalized exactly.
Landau levels of Composite Fermions
The Chiral Luttinger Model for the edge states:
Can be diagonalized exactly.

16. Tunneling density of states:
Diagonalization

17. Tunneling density of states:

18. 1. Transformation to new bosonic fields:
Diagonalization
1. Transformation to new bosonic fields:
2. Refermionization

19. Diagonalization 1. Transformation to new bosonic fields:
2. Refermionization
3. Transformation to new fermionic fields
4. Bosonization
5. Diagonalization

20. Instability: The diagonalized action: when becomes negative, i.e.
Is the new rotated auxiliary field with velocity
Instability:
when becomes negative, i.e.
Neguyen, Joglekar & Murthy, 2004))

21. Two additional (counter propagating) edge states
Regularization
Edge dispersion:
functions of
Two additional (counter propagating) edge states

22. Comments: Benjamin-Onno type regularization:
(Wiegmann & Zabrodin, Shytov, Orgad)
Extreme cases: Wigner Crystal – Fermi liquid
Other possible effects of the regularization
and
and
respectively
Noise measurements (Misha Reznikov)

23. Thank You! Summery Instability due to correlated tunneling.
A similar behavior for and
Edge reconstruction.
Universality of ?
Thank You!