Strain-induced gradients of local electric fields in semiconductor quantum dots can couple to the quadrupole moments of nuclear spins. We develop a theory describing the influence of this quadrupolar coupling (QC) on the spin correlators of electron and hole "central" spins localized in such dots. We show that when the QC strength is comparable to or larger than the hyperfine coupling strength between nuclei and the central spin, the relaxation rate of the central spin is strongly enhanced and can be exponential. We demonstrate a good agreement with recent experiments on spin relaxation in hole-doped (In,Ga)As self-assembled quantum dots.
PACS numbers:The spin of an electron or a hole in a semiconductor quantum dot is the main component of numerous proposed spintronic and quantum computing devices 1 . Spin decoherence and finite spin lifetimes are currently the major factors that limit our ability to control spin states in dots. A single "central" (i.e., electron or hole) spin in a dot interacts via hyperfine coupling with a large number (10 4 − 10 6 ) of nuclear spins. The net effect of this coupling to the nuclear spin bath can be characterized by an effective Overhauser magnetic field B n that acts upon the central spin. Within a quantum dot ensemble, each central spin precesses around a different B n . If B n is time-independent, such precession alone cannot lead to complete relaxation of the central spin polarization. This is evidenced from the observation of spin echoes 2 that can be used to cancel the dephasing of central spins in an ensemble of dots with different constant B n . However, stochastic dynamics of the Overhauser field B n induces irreversible relaxation of the central spin and loss of coherence 3,4 . The physics that leads to changes of B n and its corresponding influence on central spin relaxation are the subject of considerable theoretical debate 1,4-8 .It was suggested that, at microsecond time scales, the dynamics of the Overhauser field is dominated by hyperfine-mediated nuclear co-flips, which originate from unequal strengths of the hyperfine couplings of the central spin to different nuclear spins inside the same dot 4 . Numerical simulations by Al-Hassanieh et al. 1 showed that such co-flips generally lead only to a logarithmically slow central spin relaxation. In contrast, recent experimental studies with hole-doped (In,Ga)As quantum dots reported a nearly ideal Lorentzian shape of the spin noise power spectrum, indicating exponential relaxation of central hole spins rather than a power-law or logarithmic relaxation 10 .Here we show that quadrupolar couplings (QC) of nuclear spins to the strain induced electric field gradients inside typical semiconductor quantum dots can induce relatively fast dynamics of the Overhauser field B n , and consequently accelerated relaxation of electron and hole spins in weak external fields. Our model directly applies to InGaAs self-assembled quantum dot systems, which are among the most popular platforms for spin memories and qubits 11,12 ; however, ...
