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

TL;DR

This paper investigates how gauge-field fluctuations influence the compressibility and effective mass of composite fermions near the half-filled state at finite temperatures, revealing divergence behaviors linked to interactions.

Contribution

It provides a theoretical analysis of gauge-field fluctuation effects on composite fermions, including a specific formula for compressibility and insights into divergence phenomena.

Findings

Compressibility exhibits exponential decay with temperature.

Divergent correction to the activation energy gap.

Consistent with divergent effective mass renormalization.

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