Spin Qubits in Germanium Structures with Phononic Gap

We propose qubits based on shallow donor electron spins in germanium structures with phononic gap. We consider a phononic crystal formed by periodic holes in Ge plate or a rigid cover / Ge layer / rigid substrate structure with gaps approximately a few GHz. The spin relaxation is suppressed dramatically, if the Zeeman frequency omegaZ is in the phononic gap, but an effective coupling between the spins of remote donors via exchange of virtual phonons remains essential. If omegaZ approaches to a gap edge in these structures, a long-range (limited by detuning of omegaZ) resonant exchange interaction takes place. We estimate that ratio of the exchange integral to the longitudinal relaxation rate exceeds 10(exp 5) and lateral scale of resonant exchange 0.1 mm. The exchange contribution can be verified under microwave pumping through oscillations of spin echo signal or through the differential absorption measurements. Efficient manipulation of spins due to the Rabi oscillations opens a new way for quantum information applications.