Abstract
We study the neutral excitations of fractional quantum Hall states in electronic systems of finite width where an external anisotropy is introduced by tilting the magnetic field. As in the isotropic case, the neutral collective excitation can be worked out through the conserving method of composite fermions in the Hamiltonian theory because the interaction potential has a natural cutoff due to the quantum well width. We show how such a computation can be carried out perturbatively for an anisotropic interaction. We find that unlike the charge gap, the neutral collective gap is much more sensitive to the tilt and can thus, for certain fractional quantum Hall states, be easily destroyed by the parallel component of the magnetic field. We also discuss the convergence of the collective spectrum to the activation gap in the large-momentum limit.
Highlights
Fractional quantum Hall (FQH) states of two-dimensional (2D) systems in a strong perpendicular magnetic field are protected by their intrinsic topological order
We show that the time-dependent Hartree-Fock (TDHF) formalism based on the electron density needs an infinite number of composite fermion (CF) LLs to remain numerically valid in the large-momentum limit, while the physical constraint in the Hamiltonian theory makes the CF Landau levels (CF LLs) increasingly coupled
The radial expansion corresponds to different electronic angular-momentum states, but here, the angular expansion is enough because we study CFs that have a different magnetic length from electrons and we are mainly interested in their inter-LL physics
Summary
Fractional quantum Hall (FQH) states of two-dimensional (2D) systems in a strong perpendicular magnetic field are protected by their intrinsic topological order. Within the Hamiltonian theory, which is directly related to Jain’s original picture, and standard flux-attachment proc√edure [17] in the long-wavelength limit ql 1, where l = h/eB is the magnetic length, one may use the time-dependent Hartree-Fock (TDHF) approximation to study the collective excitations of CF states. In this case, the CF IQH state with p filled CF LLs can be viewed as the mean-field ground state.
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