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 {Delta}{ital B}={ital B}{minus}2{ital n}{sub {ital e}}{ital hc}/{ital e} ({ital n}{sub {ital e}} 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 {partial_derivative}{ital n}/{partial_derivative}{mu}{proportional_to}{ital e}{sup {minus}{Delta}{omega}}{sub {ital c}}/2{ital T}[1 +[{ital A}({eta})/({eta}{minus}1)]({Delta}{omega}{sub {ital c}}){sup 2/(1+{eta})}/{ital T}] for {ital T}{much_lt}{Delta}{omega}{sub {ital c}}, where {Delta}{omega}{sub {ital c}}={ital e}{Delta}{ital B}/{ital mc}. Here we assume that the interaction between the fermions is given by {ital v}({bold q})={ital V}{sub 0}/{ital q}{sup 2{minus}{eta}} (1{le}{eta}{le}2), where {ital A}({eta}) is an {eta}-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.