Striped states in quantum Hall effect: Deriving a low-energy theory from Hartree-Fock - art. no. 155301

There is growing experimental and theoretical evidence that very clean two- dimensional electron systems form unidirectional charge density waves (UCDW ) or "striped" states at low temperatures and at Landau level filling fract ions of the form nu = M + x with 4 < M < 10 an integer and 0.4 less than or similar tox less than or similar to0.6. Following previous work, we model the striped state using a Hartree-Fock approach. We construct the low-energ y excitations of the system by making smooth deformations of the stripe edg es analogous to the construction of edge state excitations of quantum Hall droplets. These low-energy excitations are described as a coupled Luttinger liquid theory, as discussed previously by MacDonald and Fisher [Phys. Rev. B 61, 5724 (2000)]. Here, we extend that work and explicitly derive all of the parameters of this low energy theory using a Hartree-Fock approach, We also make contact with the equivalent low-energy hydrodynamic approach of Fogler and Vinokur [Phys. Rev. Lett. 84, 5828 (2000)] and similarly derive the parameters of this theory. As examples of the use of these results, we explicitly calculate the low-energy excitation spectrum and study tunneling into the striped state.