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 {Δ}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 becomes {∂}n/{∂}{μ}{∝}ec^-Δω/2T[1 +[A({η})/({η}-1)]({Δ}ωc{)}^{2/(1+{{η}})}/T] for TΔ{{{ω}}}c, where Δ{{{ω}}}c=eΔB/mc. Here we assume that the interaction between the fermions is given by v(q)={V}₀$/${q}^{2{{-}}{{η}}}$ (1{≤}{η}{≤}2), where A({η}) is an {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.