The spin relaxation due to the spin-orbit interaction (SOI) is studied theoretically in a quantum well with electrons occupying only the ground subband. First, it is shown that the coefficient of the Rashba SOI is proportional to b off − 1, in which the parameter b off , determined by the band offsets and the band gaps, passes through unity, for example, by changing x in Ga 0.47 In 0.53 As(well)/Al x Ga 1−x As y Sb 1−y (barrier). Second, it is derived that the transition matrix element of each

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... pin-flip phonon scattering has the same proportionality factor b off − 1, in addition to the impurity scattering previously studied by the same authors [Phys. Rev. B 89, 075314 (2014)]. These findings suggest the possibility of strongly suppressing the spin-relaxation rate by choosing appropriate materials.