Positions of the magnetoroton minima in the fractional quantum Hall effect

Abstract

The multitude of excitations of the fractional quantum Hall state are very accurately understood, microscopically, as excitations of composite fermions across their Landau-like Λ levels. In particular, the dispersion of the composite fermion exciton, which is the lowest energy spin conserving neutral excitation, displays filling-factor-specific minima called "magnetoroton" minima. Simon and Halperin employed the Chern-Simons field theory of composite fermions [Phys. Rev. B 48, 17368 (1993)] to predict the magnetoroton minima positions. Recently, Golkar et al. [Phys. Rev. Lett. 117, 216403 (2016)] have modeled the neutral excitations as deformations of the composite fermion Fermi sea, which results in a prediction for the positions of the magnetoroton minima. Using methods of the microscopic composite fermion theory we calculate the positions of the roton minima for filling factors up to 5/11 along the sequence s/(2s + 1) and find them to be in reasonably good agreement with both the Chern-Simons field theory of composite fermions and Golkar et al.'s theory. We also find that the positions of the roton minima are insensitive to the microscopic interaction in agreement with Golkar et al.'s theory. As a byproduct of our calculations, we obtain the charge and neutral gaps for the fully spin polarized states along the sequence s/(2s ± 1) in the lowest Landau level and the n = 1 Landau level of graphene.

Quench Dynamics of Collective Modes in Fractional Quantum Hall Bilayers

“…For large kℓ B (ideally in the kℓ B → ∞) we expect the energy of the modes to be independent of k and the dispersions to flatten out. This is because in this limit the constituent CF excitons are far away from each other and do not interact [78][79][80]. Therefore, in this regime, we anticipate that the energy of the symmetric and anti-symmetric modes should approach each other.…”

Gaffnian and Haffnian: Physical relevance of nonunitary conformal field theory for the incompressible fractional quantum Hall effect

“…To further motivate the physical relevance of the Gaffnian and Haffnian phases to the gapped FQH systems, we look at the familiar Laughlin phase at ν = 1 3 , and focus on its gapped elementary excitations (namely, the neutral and quasielectron excitations). Such excitations are well studied in the composite fermion picture and the Jack polynomial formalism [40][41][42][43][44][45]. The elementary low-lying neutral excitation is the magnetoroton mode.…”

Microscopic theory for nematic fractional quantum Hall effect

“…It is instructive to first go over the elementary neutral excitations for the Laughlin phase. The low-lying neutral excitations of the Laughlin phase have been well studied [15,[23][24][25][26]33,36]. In the long wavelength limit, the neutral excitations are quadrupole excitations well approximated by the projected density mode, or the single mode approximation [29].…”

“…In the long wavelength limit, the neutral excitations are quadrupole excitations well approximated by the projected density mode, or the single mode approximation [29]. The model wave functions of the entire branch of the neutral excitations (also called the magnetoroton mode, with quadrupole excitations at small momenta and dipole excitations at large momenta) can be constructed either using the Jack polynomial formalism [15] and the corresponding first quantized wave functions [26], or using exciton states in the composite fermion picture [23][24][25]. At large momenta, a magnetoroton mode is a neutral excitation that consists of a pair of well separated quasielectron and quasihole.…”

“…This is true from numerical calculations for all accessible system sizes, and is expected to be true in the thermodynamic limit. The Jack polynomial formalism, the composite fermion picture, and the first quantized form of the neutral excitations are also constructed to shed more insights on the nature of such many-body states [15,[23][24][25][26][27]. Numerical studies have tentatively shown that short range interactions can lead to instability of the intrinsic guiding center metric, and such "squeezed" Laughlin states can harbor uniform nematic order [14].…”