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${\mathit{n}}_{\mathit{e}}$hc/e (${\mathit{n}}_{\mathit{e}}$ 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 ∂n/∂μ∝${\mathit{e}}_{\mathit{c}}^{\mathrm{-}\mathrm{\Delta }\mathrm{\omega }}$/2T[1 +[A(η)/(η-1)](Δ${\mathrm{\omega }}_{\mathit{c}}$${)}^{2/(1+\mathrm{\eta })}$/T] for T≪Δ${\mathrm{\omega }}_{\mathit{c}}$, where Δ${\mathrm{\omega }}_{\mathit{c}}$=eΔB/mc. Here we assume that the interaction between the fermions is given by v(q)=${\mathit{V}}_0$/${\mathit{q}}^{2\mathrm{-}\mathrm{\eta }}$ (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.

• Received 21 November 1994

DOI:https://doi.org/10.1103/PhysRevB.51.10779