Geometrical Spin Dephasing in Quantum Dots

We study spin-orbit mediated relaxation and dephasing of electron spins in quantum dots. We show that higher order contributions provide a relaxation mechanism that dominates for low magnetic fields and is of geometrical origin. In the low-field limit relaxation is dominated by coupling to electron-hole excitations and possibly $1/f$ noise rather than phonons.

Figure 1

Left: Single electron lateral quantum dot in a magnetic field, which lifts the ground state degeneracy. Virtual transitions to excited states are induced by weak fluctuations of the external fields $\delta E_x(t)$, $\delta E_y(t)$. Right: Graphical representation of the evolution operator. Virtual transitions to excited states $n$ (wavy lines) are integrated out to yield an effective Hamiltonian within the doublet subspace.

Figure 2

Spin relaxation rates for a GaAs quantum dot with level spacing ${\omega }_0=1\mathrm{K}$ as a function of the Zeeman field. We chose a temperature $T=100\mathrm{mK}$ and Ohmic coupling ${\lambda }_{\Omega }=0.05$. Below $B^{*}\approx 1\mathrm{T}$ spin relaxation is dominated by coupling to Ohmic fluctuations. For $B<B^{**}\approx 15\mathrm{mT}$ geometrical spin relaxation due to coupling to Ohmic fluctuations dominates. For all $B$ values plotted, the Bloch-Redfield consistency requirement, $B_{\mathrm{eff}}\gg 1/T^{(i)}$, is satisfied.