Correlated tunneling and the instability of the fractional quantum Hall edge

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July 21, 2009
Correlated tunneling and the instability of the
fractional quantum Hall edge
Dror Orgad Oded Agam
PRL 100,156802 (2008)
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Outline
The system Historical overview of theory and
experiments The model A toy model Solution
implications
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Fractional quantum Hall effect
Incompressibility (gap)
Landau levels
Interaction
Edges
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Integer quantum Hall effect
Wens theory
Landau levels
Interaction
?
Edges
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Chern-Simons theory
Composite fermions
Electron correlations built into the bulk are
assumed to extend all the way to the edge
mean field
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Tunneling into the edge of a FQHE droplet
(A sharp cleaved edge)
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Tunneling into the edge of a FQHE droplet Wens
theory
Tunneling into the edge of a FQHE droplet
Experimental results
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Tunneling into the edge of a FQHE droplet
Experimental results
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Tunneling into the edge of a FQHE droplet back
to Theory
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Tunneling into the edge of a FQHE droplet
additional experiments
Tunneling into the edge of a FQHE droplet
Theory again
Chang et al., 2001
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Tunneling into the edge of a FQHE droplet More
experiments
Tunneling into the edge of a FQHE droplet
Numerics
Mandal Jain, 2002
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The edge tunneling puzzle Non-universality ?!
Wens 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)
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Landau levels of Composite Fermions
Edge states
The interaction Hamiltonian
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Correlated tunneling A toy model
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Landau levels of Composite Fermions
The Chiral Luttinger Model for the edge states
Can be diagonalized exactly.
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Diagonalization
Tunneling density of states
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Tunneling density of states
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Diagonalization
1. Transformation to new bosonic fields
2. Refermionization
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Diagonalization
1. Transformation to new bosonic fields
2. Refermionization
3. Transformation to new fermionic fields
4. Bosonization
5. Diagonalization
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The diagonalized action
Is the new rotated auxiliary field with velocity
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Regularization
Edge dispersion
functions of
Two additional (counter propagating) edge states
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Comments
Benjamin-Ono type regularization
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Summery

1. Instability due to correlated tunneling.
2. A similar behavior for and .
3. Edge reconstruction.
4. Universality of ?

Thank You!