Correlated tunneling and the instability of the fractional quantum Hall edge Dror Orgad Oded Agam July 21, 2009 PRL 100, (2008)

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

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

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

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

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

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

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

9 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 Tunneling into the edge of a FQHE droplet: additional experiments Chang et al., 2001 Tunneling into the edge of a FQHE droplet: Theory again 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 Hilke et al., 2001 for Tunneling into the edge of a FQHE droplet: Numerics 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 Landau levels of Composite Fermions The interaction Hamiltonian: Hartree term Fock term Correlated tunneling terms Edge states

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

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

16 Diagonalization Tunneling density of states:

17 Tunneling density of states:

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

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

22 Comments: Benjamin-Ono type regularization: Extreme cases: Wigner Crystal – Fermi liquid Noise measurements (Misha Reznikov) and respectively

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