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

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.