Fermi-liquid theory for thin arbitrarily polarized ~3He films

摘要

We study the thermodynamic response, effective masses, and collective excitations for thin (submonolayer) ~3He films as a function of density and polarization using Fermi liquid theory. The Landau parameters f~(↑↑), f~(↑↓), f~(↓↓) are obtained to quadratic order in the low-density s-wave and p-wave T-matrix interaction parameters. Values for the effective interaction components are determined by fitting zero-polarization experimental data for the cases of thin ~3He films on graphite and also thin ~3He films in surface states of thin superfluid ~4He films. By fitting the interaction parameters, we can calculate the Landau parameters to all orders, and we show results for the behavior of F_e~(↑↑) for e ≤ 30. With knowledge of the Landau parameters we calculate the polarization dependence of the state-dependent effective masses, compressibility, spin susceptibility, and zero-sound spectra for the mobile submonolayer range of areal densities. Our results predict a dramatic decrease in the effective masses for ~3He on graphite as a function of polarization at higher coverages. At fixed density, the compressibility is shown to decrease monotonically with increasing polarization. At small polarization the inverse spin susceptibility is largest for small density whereas at large polarization it is largest for large density. We show that zero sound will propagate at all densities and polarizations whereas spin zero sound does not propagate in these systems. The condition for thermodynamic stability in an arbitrarily polarized Fermi liquid film is derived and discussed. We show explicitly the Fermi surface distortion due to the presence of a zero-sound mode. A table of predicted values for the zero polarization Fermi liquid parameters F_0~s and F_0~a is provided.