Two-Dimensional Quantum Properties of Monolayer Helium Three Adsorbed on ZYX Graphite

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We investigated strong correlation effects in two-dimensional Fermion systems by measuring hear capacities and magnetization of monolayer ^3He physisorbed on ^4He preplated graphite surfaces. Four distinct regions including so far unknown new quantum fluid phases were observed as a function of areal density, which indicates a rather complicated phase diagram for this system.At low densities (Region-I), the low temperature properties can be described well by the Fermi fluid theory where the quasi-particle effective mass is enhanced by ten times of the bare mass. Upon increasing density towards that (6.9 nm^<-2>) for the 4/7 phase which is commensurate against the underlayer, the behavior of heat capacity and magnetization deviates from the Fermi fluid theory and shows anomalous spin-mass separation like tendency (Region-II). This region should be a new quantum fluid, for which we proposed a hypothesis of the 4/7 phase (Mott localized phase) doped with the zero-point vacancies (holes). With further increasing density, there appears another region where both heat capacity and magnetization do not change appreciably (Region-III). And then above 8.3 nm^<-2> the system undergoes a two-phase coexistence region (Region-IV) between the Region-III and a ferromagnetic phase. Region-III would be also a new quantum fluid with different properties from those of Region-II. It is desired to clarify whether its fluidity comes from the liquid phase promoted to the overlayer or from the 4/7 phase doped with excess particles in the near future.We verified our previous claim of the gapless quantum spin-liquid for the magnetic ground state of the 4/7 phase. Importantly, no gapped behavior was observed at temperatures down to 0.07 mK in the whole density range we studied. This is consistent with the path integral renormalization group calculation for the Hubbard model on a triangular lattice, and would be a general property of the strongly correlated fermions with frustration.