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 $\Delta B=B-2n_{e}hc/e$ ($n_e$ 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 $\frac{\partial n}{\partial \mu }\propto e^{-\Delta {\omega }_c/2T}\left(1+\frac{A(\eta )}{\eta -1}\frac{(\Delta {\omega }_c{)}^{\frac{2}{1+\eta }}}{T}\right)$ for $T\ll \Delta {\omega }_c$, where $\Delta {\omega }_c=\frac{e\Delta B}{mc}$. Here we assume that the interaction between the fermions is given by $v(\mathbf{q})=V_0/q^{2-\eta }(1\le \eta \le 2)$, where $A(\eta )$ is a $\eta$ 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.

Plain Tex, 24 pages, 5 figures available upon request