Spin dephasing due to a random Berry phase

We investigate relaxation and dephasing of an electron spin confined in a semiconductor quantum dot and subject to spin-orbit coupling. Even in vanishing magnetic field, B = 0, slow noise coupling to the electron's orbital degree of freedom leads to dephasing of the spin due to a random, in general non-Abelian Berry phase acquired by the spin. For illustration we first present a simple quasiclassical description, then consider a model with 2 orbital states only, and finally present a perturbative quantum treatment appropriate for an electron in a realistic (roughly parabolic, not too strongly confining) quantum dot. We further compare the effect of different sources of noise. While at large magnetic fields phonons dominate the relaxation processes, at low fields electron-hole excitations and possibly 1/f noise may dominate.