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Progress of Theoretical Physics

Fermi Liquid Theory of Dilute Submonolayer 3He on Thin 4He II Film: Dimer Bound State and Cooper Pairs

Kazumasa Miyake

Published Jun 1, 1983• 185 citations
Publisher

Abstract

A degenerate dilute Fermi system, with a shallow dimer bound state, is discussed with attention to the possibility of Fermi superfluidity. (Necessary information on interaction is expressed through the bound state energy of the dimer.) A relevant system may be dilute submonolayer 3He on a thin 4He II film just above the onset of the apparent gas-liquid phase separation of 3He.

DOI
10.1143/ptp.69.1794

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A degenerate dilute Fermi system, with a shallow dimer bound state, is discussed with attention to the possibility of Fermi superfluidity. (Necessary information on interaction is expressed through the bound state energy of the dimer.) A relevant system may be dilute submonolayer 3He on a thin 4He II film just above the onset of the apparent gas-liquid phase separation of 3He.
We study the dilute-gas expansion for a two-dimensional Fermi system with arbitrary short-range repulsive interactions. In contrast with the three-dimensional case, we find an unusual pole in the vertex part in the particle-particle channel, for all center-of-mass momenta q2kF{\mathit{k}}_{\mathit{F}}kF​. We show that this represents an excitation consisting of bound hole pairs, which disperses down to zero energy at q=2kF{\mathit{k}}_{\mathit{F}}kF​. We study the effect of these bound states on the single-particle self-energy and find that the quasiparticles are well defined. Thus in the low-density regime, there is no breakdown of Fermi-liquid theory. In the Appendix we discuss the two-particle phase shift in the dilute Fermi gas, its connection with bound states, and the analogy with the potential scattering phase shift.
We study the thermodynamic response, effective masses, and collective excitations for thin (submonolayer) 3{}^{3}3He films as a function of density and polarization using Fermi liquid theory. The Landau parameters ${f}^{\ensuremath{\uparrow}\ensuremath{\uparrow}},{f}^{\ensuremath{\uparrow}\ensuremath{\downarrow}},{f}^{\ensuremath{\downarrow}\ensuremath{\downarrow}}$ are obtained to quadratic order in the low-density sss-wave and ppp-wave TTT-matrix interaction parameters. Values for the effective interaction components are determined by fitting zero-polarization experimental data for the cases of thin 3{}^{3}3He films on graphite and also thin 3{}^{3}3He films in surface states of thin superfluid 4{}^{4}4He films. By fitting the interaction parameters, we can calculate the Landau parameters to all orders, and we show results for the behavior of ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{F}}_{\ensuremath{\ell}}^{\ensuremath{\uparrow}\ensuremath{\uparrow}}\phantom{\rule{4.pt}{0ex}}\text{for}\phantom{\rule{4.pt}{0ex}}\ensuremath{\ell}\ensuremath{\leqslant}30$. 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 3{}^{3}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 F0sandF1a{F}_{0}^{\text{s}}\phantom{\rule{4.pt}{0ex}}\text{and}\phantom{\rule{4.pt}{0ex}}{F}_{1}^{\text{a}}F0s​andF1a​ is provided.
We examine the thermodynamics of a two-dimensional Fermi gas model describing adsorbed 3{}^{3}3Hein a thin superfluid 4{}^{4}4Hefilm. The 3{}^{3}3Hesystem is characterized by both a hydrodynamic effective mass and a set of discrete transverse single-particle states that model the effects of the interaction with the substrate that supports the film. We show that the magnetization steps seen in experiment are a simple manifestation of the T=0KT=0\mathrm{K}T=0K equation of state. We prove that perfectly horizontal magnetization steps rigorously disappear at any finite temperature. We show that the thermal stability of the steps is determined by the larger of $\ensuremath{\Delta}\ensuremath{\epsilon}/2,$ one-half of the level spacing, and ${\ensuremath{\mu}}_{m}{\mathcal{H}}_{0},$ the magnetic energy. We derive the conditions under which there exist points in the phase space (termed invariant points) through which all low-temperature isotherms pass exponentially close. The invariant points appear for magnetization versus 3{}^{3}3Hecoverage, chemical potential versus magnetization, magnetic susceptibility versus coverage, and speed of sound squared versus coverage. We compare our calculated invariant points for the magnetization versus coverage with experiment and find good agreement. We show that there exist small regions of thermodynamic phase space in which the temperature derivative of the pressure is negative. We explain these anomalous regions as the result of 3{}^{3}3Heatoms ``spilling over'' from a full Fermi sea to an empty Fermi sea upon the application of a small increase in temperature. Through a Maxwell relation, this behavior can also be seen as in the appearance of a local peak in low-temperature entropy isotherms versus coverage. In the limit of a two state model, we calculate the specific heat and show that a Schottky peak develops in the low 3{}^{3}3Hecoverage limit. We calculate the magnetic susceptibility and predict that it should exhibit a steplike structure versus 3{}^{3}3Hecoverage similar to that of the magnetization. We calculate the speed of sound and show that it should exhibit zero-temperature discontinuities at the points where new Fermi seas begin to be occupied. Both the steplike structure in the magnetic susceptibility and the discontinuity-type structure in the speed of sound persist to temperatures on the order of 100 mK, and are analyzed in terms of invariant points in their respective phase diagrams. We show explicitly that, in the Fermi gas limit, the zero-field magnetic susceptibility is simply proportional to the isothermal compressibility.
The last five years have seen a burst of activity leading to the current view that 3He atoms dissolved in superfluid liquid 4He show remarkable resemblance to a weakly-interacting Fermi gas. This is because the solvent 4He, having vanishingly small entropy, specific heat, viscosity and magnetic susceptibility, behaves almost as if it were a massive vacuum, in which 3He atoms float. So at last a real Fermi ‘gas’ is available and can readily be cooled to temperatures well below its Fermi degeneracy temperature. This model of solute 3He, with its weaknesses and strengths, is the basis of this article.
Abstract Very dilute solutions of 3He in superfluid 4He behave as an almost ideal Fermi gas at millikelvin temperatures, which can be strongly polarized in high magnetic fields. This has enabled studies of their equilibrium, transport, and dynamical spin properties to be made over a wide range of temperatures, concentrations, and polarizations covering systems that are highly degenerate to those that are non-degenerate. This chapter discusses polarized Fermi gas, model theories, equilibrium theories, transport properties, and spin dynamics.
We study the finite temperature-density phase diagram of an attractive fermionic system that supports two-body (dimer) and three-body (trimer) bound states in free space. Using interactions characteristic for nuclear systems, we obtain the critical temperature Tc2{T}_{c2}Tc2​ for the superfluid phase transition and the limiting temperature Tc3{T}_{c3}Tc3​ for the extinction of trimers. The phase diagram features a Cooper-pair condensate in the high-density, low-temperature domain which, with decreasing density, crosses over to a Bose condensate of strongly bound dimers. The high-temperature, low-density domain is populated by trimers whose binding energy decreases toward the density-temperature domain occupied by the superfluid and vanishes at a critical temperature Tc3>Tc2{T}_{c3}>{T}_{c2}Tc3​>Tc2​.