Three-Electron Systems in Quantum Nanostructures: Ground State Transition from a Spin-Doublet State to a Spin-Quartet State

Abstract

The ground state and the lowest excited state of three electrons confined in quantum structures (quantum dots) are calculated. In general, the ground state is a spin-doublet one in a small dot, level crossing occurs as the dot size increases, and the ground state is a spin-quartet state in a large dot. It is found that the spin-quartet ground state is more likely to be realized in a quantum ring (QR) than in a harmonic confinement. In a narrow QR, two-electron exchanges are unlikely to occur because of the large Coulomb barrier while three-electron exchanges are little suppressed, leading to the fully spin-polarized (spin-quartet) ground state. The present calculation conforms to Herring’s theorem that the ground state of three spin-1⁄2 fermions on a one-dimensional ring is a fully spin-polarized one if the repulsive interaction between fermions is sufficiently strong. The extensions of the present result to more complicated cases are also discussed.