Fermi-surface mean free path from sheet resistivity (${\ell }_F=\hslash k_F/(n{e}^2{\rho }_{\square })$)

For a spin-degenerate parabolic two-dimensional band, the Drude model gives $\tau =m^{\ast }/(n{e}^2{\rho }_{\square })$ and $v_F=\hslash k_F/m^{\ast }$. Their product is the displayed mass-independent mean free path. A Fermi-surface transport interpretation requires a sufficiently degenerate electron gas; a quantum lifetime need not equal the transport relaxation time.