Spin Polarization of Two-Dimensional Electron System in a Finite Domain

We analyze the ground state of the two-dimensional quantum system of electrons confined in a parabolic potential with the system size around 100. We map the system onto a classical system on the basis of the classical-map hypernetted-chain (CHNC) method which has been proven to work in the integral-equation-based analyses of uniform unbounded systems and then apply classical numerical simulations. We find that the confined system undergoes the transition to the spin polarized state with the decrease of the average density and the corresponding critical value is as low as rs ∼ 0.3 in terms of the usual rs parameter estimated for the average density. As the ground state for given value of the rs parameter, our data give the critical value for the transition around 20 which is consistent with the known possibility. The advantage of our method is a direct applicability to geometrically complex systems which are difficult to analyze by integral equations. The application to the structure like quantum dots reported here is the first example of such applications.