# Universal power law decay of spin polarization in double quantum dot

## TL;DR

This paper demonstrates that in double quantum dots, spin polarization decays following a universal power law over time, driven by the interplay of hyperfine interactions and spin blockade, with implications for understanding spin noise.

## Contribution

It reveals a universal $1/t$ decay law for spin polarization in double quantum dots, independent of system parameters, and characterizes the low-frequency divergence of spin noise spectrum.

## Key findings

- Spin polarization decays as 1/t at long times.
- Spin noise spectrum diverges as ln(1/ω) at low frequencies.
- Decay law is universal, regardless of system parameters.

## Abstract

We study the spin dynamics and spin noise in a double quantum dot taking into account the interplay between hopping, exchange interaction and the hyperfine interaction. At short time scales the spin relaxation is governed by the spin dephasing in the random nuclear fields. At long time scales the spin polarization obeys universal power law $1/t$ independent of the relation between all the parameters of the system. This effect is related to the competition between the spin blockade effect and the hyperfine interaction. The spin noise spectrum of the system universally diverges as $\ln(1/\omega)$ at low frequencies.