Effective Hamiltonian for striped and paired states at the half-filled Landau level

Abstract

We study a pairing mechanism for the quantum Hall system using a mean field theory with a basis on the von Neumann lattice, on which the magnetic translations commute. In the Hartree-Fock-Bogoliubov approximation, we solve the gap equation for spin-polarized electrons at the half-filled Landau levels. We obtain an effective Hamiltonian which shows a continuous transition from the compressible striped state to the paired state. Furthermore, a crossover occurs in the pairing phase. The energy spectrum and energy gap of the quasiparticle in the paired state is calculated numerically at the half-filled second Landau level.

14 pages, 10 figures, revised version, to be published in Nucl. Phys. B

References in corpus (13)

• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Strongly Anisotropic Transport in Higher Two-Dimensional Landau Levels
• Incompressible paired Hall state, stripe order and the composite fermion liquid phase in half-filled Landau levels
• Exact Quantization of Even-Denominator Fractional Quantum Hall State at $\nu$=5/2 Landau Level Filling Factor
• Anisotropic States of Two-Dimensional Electron Systems in High Landau Levels: Effect of an In-Plane Magnetic Field
• Strongly Anisotropic Electronic Transport at Landau Level Filling Factor $\nu =9/2$ and $\nu =5/2$ Under Tilted Magnetic Field
• Charge Density Wave Ordering in Half Filled High Landau Levels
• Field-tilt Anisotropy Energy in Quantum Hall Stripe States
• Observation of Induced Chern-Simons Term in P- and T- violating Superconductors
• Finite Temperature Density Instability at High Landau Level Occupancy
• Landau-Ginzburg Theories for Non-Abelian Quantum Hall States
• Compressible Anisotropic States around the Half-Filled Landau Levels
• Stability of the compressible quantum Hall state around the half-filled Landau level

Cited by in corpus (4)

• Experimental Evidence for a Spin-Polarized Ground State in the ν=5/2 Fractional Quantum Hall Effect
• Energy Spectrum of Neutral Collective Excitations in Striped Hall States
• Induced Chern-Simons term of a paired electron state in the quantum Hall system
• Paired and Stripe States in the Quantum Hall System