Third stable branch and tristability of nuclear spin polarizations in a single quantum dot system

Semiconductor quantum dots provide a spin-coupled system of an electron and nuclei via enhanced hyperfine interaction. We showed that the nuclear spin polarization in single quantum dots can have three stable branches under a longitudinal magnetic field. The states were accompanied by hysteresis loops around the boundaries of each branch with a change in the excitation condition. To explain these findings, we incorporated the electron spin relaxation caused by the nuclear spin fluctuation into the previously studied dynamic nuclear spin polarization mechanism. The model reproduces the features of nuclear spin polarization and the associated strong reduction in the observed electron spin polarization, and can refer to the tristability of nuclear spin polarization.