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Quantum Phase Diagram of Helium Three Monolayer on HD Plated Graphite

雅博 鎌田

Published Mar 22, 2018• 0 citations
Publisher

Abstract

At low densities (ρ ≲ 4.2 nm -2 ), measured heat capacities satisfy the C = γT dependence at low T , which is characteristic of the degenerate Fermi liquid.With increasing density effective mass of a 3 He quasiparticle, deduced from γ, shows the divergence up to m * /m = 4.4 ± 0.3 until 4.2 nm -2 .At the lowest densities (0.1 ≲ ρ ≲ 0.7 nm -2 ), we observed the formation of the self-condensed liquid, judging from the γ coefficient smaller than the value of the noninteracting Fermi gas.Its critical density (0.7 nm -2 ) is quantitatively consistent with that of 1 -3 layers on graphite [1], but contradict recent Monte Carlo studies which claims that the potential corrugation play an essential role to stabilize the self-condensed liquid.

DOI
10.15083/00077878

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At low densities (ρ ≲ 4.2 nm -2 ), measured heat capacities satisfy the C = γT dependence at low T , which is characteristic of the degenerate Fermi liquid.With increasing density effective mass of a 3 He quasiparticle, deduced from γ, shows the divergence up to m * /m = 4.4 ± 0.3 until 4.2 nm -2 .At the lowest densities (0.1 ≲ ρ ≲ 0.7 nm -2 ), we observed the formation of the self-condensed liquid, judging from the γ coefficient smaller than the value of the noninteracting Fermi gas.Its critical density (0.7 nm -2 ) is quantitatively consistent with that of 1 -3 layers on graphite [1], but contradict recent Monte Carlo studies which claims that the potential corrugation play an essential role to stabilize the self-condensed liquid.
We report clear experimental signatures of the theoretically unexpected gas-liquid transition in the first three monolayer systems of 3He^{3}\mathrm{He}3He adsorbed on graphite. The transition is inferred from the linear density dependence of the gamma coefficient of the heat capacity measured in the degenerate region ($2\ensuremath{\le}T\ensuremath{\le}80\text{ }\text{ }\mathrm{mK}$) below a critical liquid density (${\ensuremath{\rho}}_{c0}$). Surprisingly, the measured ${\ensuremath{\rho}}_{c0}$ values ($0.6--0.9\text{ }\text{ }{\mathrm{nm}}^{\ensuremath{-}2}$) are nearly the same for all these layers in spite of their quite different environments. We conclude that the ground state of 3He^{3}\mathrm{He}3He in strictly two dimensions is not a dilute quantum gas but a self-bound quantum liquid with the lowest density ever found.
The nuclear magnetic susceptibility of 3He^{3}\mathrm{He}3He adsorbed on the surface of graphite, plated with a monolayer of solid 4He^{4}\mathrm{He}4He, has been measured at surface densities less than 0.055 \AA{} $^{\mathrm{\ensuremath{-}}2}$ and at temperatures down to 6 mK. A temperature-independent susceptibility is observed at low temperatures, which is strongly enhanced over the ideal-gas value, due to quasiparticle interactions. The inferred Landau-Fermi-liquid parameters allow a comparison with microscopic theories of interacting Fermi systems.
The two-dimensional (2D) nature of the high-Tc materials has lead to renewed interest in the properties of fermions in two dimensions. Calculations of the corrections to the leading Fermi-liquid (FL) behaviour of the single-particle self-energy Σ(p, E), and the specific heat have shown that the differences between 2D and three-dimensional FLs arise from the difference in phase space between two and three dimensions. Here we investigate the imaginary part Σ″(p, ξp) of Σ(p, E) on shell at a low density which has a (p - pF)2 In (p - pf) dependence in two dimensions where pF is the Fermi wavenumber. We find that both particle-hole (ph) and particle-particle (pp) contributions are important in this limit so that in principle no class of diagrams can be neglected in the low-density limit in two dimensions, and one is effectively limited to second order in the interaction for reliable quantitative results. This is in contrast with three dimensions where the ph contribution becomes negligible compared with the pp contribution at low densities and only pp ladder diagrams survive. We argue, however, that the density dependence of Σ(p, E) is unchanged by high orders in perturbation theory and that in the limit pF → 0 the form of the dependence of Σ(p, E) on p - pF is given by the second-order contribution. We find that the (p - pF)2 In (p - pf) behaviour is limited to a values of p - pf Λ; pF so that the region over which FL behaviour is evident shrinks with decreasing density.
In the one-dimensional (1D) nanopores of FSM-16 (2.8 nm in diameter) and the 3D pores of HMM-2 (2.7 nm, and 5.5 nm in 3D period), the 4 He films adsorbed on these nanopore walls show the properties of the Bose quantum fluid and superfluidity above 1.4 atomic layers at low temperatures. The boundary of the Bose fluid region was determined from the kink (peak) temperature T C of the heat capacity at each coverage n . The phase diagrams obviously show dependence on the 1D and 3D pore connections, respectively. In the 3D nanopores, the coverage (density) dependence of T C is well reproduced by the Bose-Einstein condensation temperature of the 3D ideal gas which is proportional to ( n - n c ) 2/3 , where n c is the onset coverage. In the case of the 1D pores (channels), T C is proportional to ( n - n c ) at 0.1 < T C < 1K. This T C is likely to correspond to the crossover temperature of the 2D ideal gas heat capacity from the constant heat capacity of the Boltzmann gas to the linear in T , with decreasing temperature. At T C , the thermal de Broglie wavelength of the free particle is still shorter than the pore diameter, while the thermal phonon wavelength is estimated to become longer than the diameter below T C , which indicates the 1D phonon state.
The appearance of the fermion condensation, which can be compared to the Bose-Einstein condensation, in different Fermi liquids is considered; its properties are discussed; and a large amount of experimental evidence in favor of the existence of the fermion condensate (FC) is presented. We show that the appearance of FC is a signature of the fermion condensation quantum phase transition (FCQPT), which separates the regions of normal and strongly correlated liquids. Beyond the FCQPT point, the quasiparticle system is divided into two subsystems, one containing normal quasiparticles and the other, FC, localized at the Fermi level. In the superconducting state, the quasiparticle dispersion in systems with FC can be represented by two straight lines, characterized by effective masses M FC * and M L * and intersecting near the binding energy E 0, which is of the order of the superconducting gap. The same quasiparticle picture and the energy scale E 0 persist in the normal state. We demonstrate that fermion systems with FC have features of a “quantum protectorate” and show that strongly correlated systems with FC, which exhibit large deviations from the Landau Fermi liquid behavior, can be driven into the Landau Fermi liquid by applying a small magnetic field B at low temperatures. Thus, the essence of strongly correlated electron liquids can be controlled by weak magnetic fields. A reentrance into the strongly correlated regime is observed if the magnetic field B decreases to zero, while the effective mass M* diverges as $$M^ * \propto {1 \mathord{\left/ {\vphantom {1 {\sqrt B }}} \right. \kern-\nulldelimiterspace} {\sqrt B }}$$ . The regime is restored at some temperature T∗∝BT^ * \propto \sqrt B T∗∝B​ . The behavior of Fermi systems that approach FCQPT from the disordered phase is considered. This behavior can be viewed as a highly correlated one, because the effective mass is large and strongly depends on the density. We expect that FCQPT takes place in trapped Fermi gases and in low-density neutron matter, leading to stabilization of the matter by lowering its ground-state energy. When the system recedes from FCQPT, the effective mass becomes density independent and the system is suited perfectly to be conventional Landau Fermi liquid.
The behavior of Fermi systems that approach the fermion condensation quantum phase transition (FCQPT) from the disordered phase is considered. We show that the quasiparticle effective mass M * diverges as M * ∝ 1/¦ x − x FC ¦, where x is the system density and x FC is the critical point at which FCQPT occurs. Such behavior is of general form and takes place in both three-dimensional (3D) and two-dimensional (2D) systems. Since the effective mass M * is finite, the system exhibits the Landau Fermi liquid behavior. At ¦ x − x FC ¦/ x FC ≪1, the behavior can be viewed as highly correlated, because the effective mass is large and strongly depends on the density. In the case of electronic systems, the Wiedemann-Franz law is valid and the Kadowaki-Woods ratio is preserved. Beyond the region ¦ x – x FC ¦/ x FC ≪1, the effective mass is approximately constant and the system becomes a conventional Landau Fermi liquid.