Correlated tunneling and the instability of the fractional quantum Hall edge

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

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

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

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

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

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

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

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

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

Hilke et al., 2001 for Tunneling into the edge of a FQHE droplet: More experiments Tunneling into the edge of a FQHE droplet: Numerics 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)

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

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

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

Diagonalization Tunneling density of states:

Tunneling density of states:

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

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

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

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

Correlated tunneling and the instability of the fractional quantum Hall edge