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 $\nu=1/2$. 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 $\nu=1/2$ filling fraction in the rotating BEC shows no roton minimum. We have investigated this using composite fermion theory with the P$\ddot{o}$schl-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.