Fitting of m*/m with Divergence Curve for He$_{3}$ Fluid Monolayer using Hole-driven Mott Transition

The electron-electron interaction for strongly correlated systems plays an important role in formation of an energy gap in solid. The breakdown of the energy gap is called the Mott metal-insulator transition (MIT) which is different from the Peierls MIT induced by breakdown of electron-phonon interaction generated by change of a periodic lattice. It has been known that the correlated systems are inhomogeneous. In particular, He$_{3}$ fluid monolayer [1] and La$_{1-x}$Sr$_{x}$TiO$_{3}$ [2] are representative strongly correlated systems. Their doping dependence of the effective mass of carrier in metal, m*/m, indicating the magnitude of correlation (Coulomb interaction) between electrons has a divergence behavior. However, the fitting remains unfitted to be explained by a Mott-transition theory with divergence. In the case of He$_{3}$ regarded as the Fermi system with one positive charge (2 electrons + 3 protons), the interaction between He$_{3}$ atoms is regarded as the correlation in strongly correlated system. In this presentation, we introduce a Hole-driven MIT with a divergence near the Mott transition [3] and fit the m*/m curve in He$_{3}$ [1] and La$_{1-x}$Sr$_{x}$TiO$_{3}$ systems with the Hole-driven MIT with m*/m=1/(1-$\rho ^{4})$ where $\rho $ is band filling. Moreover, it is shown that the physical meaning of the effective mass with the divergence is percolation in which m*/m increases with increasing doping concentration, and that the magnitude of m*/m is constant.\\[4pt] [1] Phys. Rev. Lett. 90, 115301 (2003).\\[0pt] [2] Phys. Rev. Lett. 70, 2126 (1993).\\[0pt] [3] Physica C 341-348, 259 (2000); Physica C 460-462, 1076 (2007).