Abstract
We have focussed to study the even-denominator fractional quantum Hall (EDFQH) states observed in monolayer graphene. In this letter, we have studied polarization mainly for the two EDFQH states at filling fractions ν = 1/2, 1/4, which are observed in an experimental study [Nat. Phys. 14, 930 (2018)] a few years ago. We have applied Chern Simon's gauge field theory to explain the possible variational wave functions for different polarized states and calculated their ground state energies using the Coulomb potential. We have chosen the lowest energy states using suitable combinations of flux attached with the electrons for different polarized states of those EDFQH states.