  We predict the enhancement of the spin-rotation coupling due to the interband
mixing. The Bloch wavefunctions in the presence of mechanical rotation are
constructed with the generalized crystal momentum which includes a gauge
potential arising from the rotation. Using the eight- band Kane model, the
renormalized spin-rotation coupling is explicitly obtained. As a result of the
renormalization, the rotational Doppler shift in electron spin resonance and
the mechanical torque on an electron spin will be strongly modulated.
