Electron-electron interaction effect on the singlet-triplet transitions in one-dimensional quantum dots

We have studied singlet-triplet transitions (STTs) in a system of two interacting electrons in a one-dimensional quantum dot in the presence of the spin-orbit interaction (SOI) and a magnetic field. The STTs are shown to occur owing only to a combined action of the SOI and magnetic field. The energy gap at the STT point depends on the relative direction of the external magnetic field and an effective magnetic field of the SOI. An interesting effect is produced by the electron-electron interaction that can be controlled by nearby gates. The increase of the interaction strength results in the significant reduction of the critical magnetic field, under which the STT occurs, and lowering of the energy gap.