Theory of box-model hyperfine couplings and transport signatures of long-range nuclear-spin coherence in a quantum-dot spin valve

We have theoretically analyzed coherent nuclear-spin dynamics induced by electron transport through a quantum-dot spin valve. The hyperfine interaction between electron and nuclear spins in a quantum dot allows for the transfer of angular momentum from spin-polarized electrons injected from ferromagnetic or half-metal leads to the nuclear spin system under a finite voltage bias. Accounting for a local nuclear-spin dephasing process prevents the system from becoming stuck in collective dark states, allowing a large nuclear polarization to be built up in the long-time limit. After reaching a steady state, reversing the voltage bias induces a transient current response as the nuclear polarization is reversed. Long-range nuclear-spin coherence leads to a strong enhancement of spin-flip transition rates (by an amount proportional to the number of nuclear spins) and is revealed by an intense current burst, analogous to superradiant light emission. The crossover to a regime with incoherent spin flips occurs on a relatively long-time scale, on the order of the single-nuclear-spin dephasing time, which can be much longer than the time scale for the superradiant current burst. This conclusion is confirmed through a general master equation. For the two limiting regimes (coherent/incoherent spin flips), the general master equation recovers our simpler treatment based on rate equations, but is also applicable at intermediate dephasing. Throughout this work, we assume uniform hyperfine couplings, which yield the strongest coherent enhancement. We propose realistic strategies, based on isotopic modulation and wave-function engineering in core-shell nanowires, to realize this analytically solvable "box-model" of hyperfine couplings.