Properties of spin polarization state of two-electron system on two-dimensional quantum dots with magnetic field

Influence of the magnetic field on the energy of the spin polarization state of a two-electron system in two-dimensional quantum dots (QDs) is studied by using the method of few-body physics. As example, a numerical calculation is performed for a GaAs semiconductor QD to show the variations of the ground-state energy E-0, the spin-singlet energy E-1(A) and spin-triplet energy E-1(S) of the first excited state and the energy difference (i.e. Delta E(A) and Delta E(S)) between the first excited and ground states with the effective radius R-0 of the QD and the magnetic field B. The results show that E-0 increases with increasing B, but decreases with increasing R-0; in the magnetic field, the spin-singlet energy E-1(A) of the first excited state splits into two levels as E1+1(A) and E1-1(A), the spin-triplet energy E-1(S) of the first excited state splits into two sets as E1+1(S) and E1-1(S), and each set consists of three "fine structures" which correspond to M-S=1,0,-1, respectively; each energy level (set, energy difference) decreases with increasing R-0, but there are great differences among the changes of them with B: E1+ 1(A), E-1+1(MS)(S), Delta E1+1(A), and Delta E-1+1(MS) (S) increase significantly with increasing B, but the variations of E1-1(A), E-1-1(MS) (S), Delta E1-1(A), and Delta E-1-1(MS) (S) with B are relatively slow; the splitting degree of each energy level (set, energy difference) is proportional to the first power of the magnetic field B.