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

Abstract

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 $ΔB = B - 2 n_e hc/e$ ($n_e$ is the density of electrons) near the half-filled state. It is shown that, after including the lowest order gauge field correction, the compressibility goes as ${\partial n \over \partial μ} \propto e^{- Δω_c / 2 T} \left ( 1 + {A (η) \over η- 1} {(Δω_c)^{2 \over 1 + η} \over T} \right )$ for $T \ll Δω_c$, where $Δω_c = {e ΔB \over mc}$. Here we assume that the interaction between the fermions is given by $v ({\bf q}) = V_0 / q^{2 - η} \ (1 \le η\le 2)$, 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.