Roton minimum at ν = 1∕2 filled fractional quantum Hall effect of Bose particles

Abstract

We have studied the collective excitation of fractional quantum Hall effect (FQHE) in the rotating Bose-Einstein condensate (BEC) using CF theory at the filling fraction ν = 1/2. The roton type of excitation in the FQHE of electron system is established over the years for all the filling fraction, whereas the collective excitation at ν = 1/2 filling fraction in the rotating BEC shows no roton minimum. We have investigated this using composite fermion theory with the Pöschl-Teller interaction potential between the particles. We have seen that the long range interaction will give the roton, whereas short range interaction gives no roton minimum.

Collective spin density excitation of fractional quantum Hall states in dilute ultra-cold Bose atoms

“…Using δ function potential it is not possible to calculate the energy spectra for large number of particles. To avoid this difficulty and to access the system size in the thermodynamic limit we have considered Pöschl-Teller interaction potential (V P T ) [21,24].…”

“…In the small wave vector limit (k → 0), Larmor's as function of separation distance (r) of two particles in unit of magnetic length (l) for different values of µ in unit of inverse of l (data taken from Ref. [21]). theorem stipulates that the SW energy is precisely equal to the bare Zeeman, for a conventional ferromagnet, such as the one at ν = 1 [19] or at ν = 1/3 [20], SW has positive dispersion with energy that increases monotonically with wave vector reaching a large wave vector asymptotic limit of particle and hole seperation energy with opposite spin.…”

“…al. have studied the collective charge density excitation of FQH states of rotating BEC using CF theory for filling fraction ν = 1/2 [21]. But best of our knowledge, spin density excitation (SDE) of FQHE of Bose particles has not been studied till date.…”

“…In the small wave vector limit (k → 0), Larmor's as function of separation distance (r) of two particles in unit of magnetic length (l) for different values of µ in unit of inverse of l (data taken from Ref. [21]).…”

Double roton-minima in bosonic fractional quantum Hall states

“…As we raise the μ-value, then the essence of PT-interaction goes well with δ-function. But for smaller values of μ the nature of PT potential differs from the contact interaction, as the range of interaction increases with decrease of μ [27,28]. That's why we have considered μ-values between a specific range in our calculation.…”