Effective mass of composite fermions: A phenomenological fit to the anomalous propagation of a surface acoustic wave

Abstract

We calculate the conductivity associated with the anomalous propagation of a surface acoustic wave above a two-dimensional electron gas at $\ensuremath{\nu}=1/2.$ Murthy-Shankar's middle representation is adopted, and a contribution to the response functions beyond the random-phase approximation is taken into account. We give a phenomenological fit for the effective mass of a composite fermion, with experimental data for the anomalous propagation of surface acoustic wave at $\ensuremath{\nu}=1/2,$ and find that the phenomenological value of the effective mass is several times larger than the theoretical value ${m}_{\mathrm{th}}^{*}=6\ensuremath{\varepsilon}{/e}^{2}{l}_{1/2}$ derived from the Hartree-Fock approximation. We compare the phenomenological value of the composite fermion effective mass with that measured in experiments for the activation energy and the Shubnikov-de Haas oscillations. It is found that the comparison is fairly good.