Collective excitations of quantum Hall states under tilted magnetic field

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.

Figure 1

Comparison between the dispersion computed from the electron density (blue circles) that obtained from the preferred density (green triangles). The number of CF LLs used for ${\rho }_e$ is 20, which guaranties the unphysical mode (red squares) to remain at zero energy up to $ql\sim 2.2$, while for ${\rho }_p$ 7 LLs is used. The activation gap (black line) is computed using ${\rho }_p$.

Figure 2

Dispersion of the collective excitations at different fillings and $\theta$ for (a) $\theta =0.7, \nu =1/3$; (b) $\theta =1.2, \nu =1/3$; (c) $\theta =0.7, \nu =2/5$; and (d) $\theta =1.2, \nu =2/5$. Due to computational difficulty, we only calculate the anisotropic dispersion up to the first minimum corresponding to the magnetoroton gap: $ql\simeq 1.4$ for $\nu =1/3$ and $ql\simeq 0.8$ for $\nu =2/5$. The isotropic dispersion (red lines) is obtained by considering merely the influence of the tilt on the isotropic component $V_0$ of the interaction potential, while the dispersion in the $x$ (black lines) and $y$ (blue liens) directions take into account the $V_{n\ne 0}$ components.