Sep. 23, 2008 Correlated tunneling and the instability of the fractional quantum Hall edge Dror Orgad Oded Agam PRL 100,156802 (2008)

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

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

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

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

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

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

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

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

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

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

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)

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

Correlated tunneling: A toy model Eigenvalues: Ground state

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

Tunneling density of states: Diagonalization

Tunneling density of states:

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

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

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))

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

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)

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