Identifying diverging-effective mass in MOSFET and $^3$He systems

Emerging devices such as a neuromorphic device and a qubit can use the Mott transition phenomenon, but in particular, the diverging mechanism of the phenomenon remains to be clarified. The diverging-effective mass near Mott insulators was measured in strongly correlated Mott systems such as a fermion $^3$He and a Si metal-oxide-semiconductor-field-effect transistor, and is closely fitted by the effective mass obtained by the extension of the Brinkman-Rice(BR) picture, $m^*/m=1/[1-(U/U_c)^2]=1/(1-κ^2_{BR}ρ^4)$ when $κ^2_{BR}{\approx}1({\neq}$1), where $0<U/U_c=κ_{BR}ρ^2<1$, correlation strength is $κ_{BR}$, band-filling is $ρ$. Its identification is a percolation of a constant mass in the Brinkman-Rice picture. Over $κ_{BR}{\approx}0.96$ is evaluated.

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