Influence of gauge-field fluctuations on composite fermions near the half-filled state.

Taking into account the transverse gauge field fluctuations, which interact with composite fermions, we examine the finite temperature compressibility of the fermions as a function of an effective magnetic field ∆B = B − 2nehc/e (ne is the density of electrons) near the half-filled state. It is shown that, after including the lowest order gauge field correction, the compressibility goes as ∂n ∂μ ∝ ec ( 1 + A(η) η−1 (∆ωc) 2 1+η T ) for T ≪ ∆ωc, where ∆ωc = e∆B mc . Here we assume that the interaction between the fermions is given by v(q) = V0/q 2−η (1 ≤ η ≤ 2), where A(η) is a η dependent constant. This result can be interpreted as a divergent correction to the activation energy gap and is consistent with the divergent renormalization of the effective mass of the composite fermions. PACS numbers: 73.40.Hm, 71.27.+a, 11.15.-q