Power-law dependence of the angular momentum transition fields in few-electron quantum dots

Abstract

We show that the critical magnetic fields at which a few-electron quantum dot undergoes transitions between successive values of its angular momentum (M ), for large M values follow a very simple power-law dependence on the effective inter-electron interaction strength. We obtain this power law analytically from a quasi-classical treatment and demonstrate its nearly-universal validity by comparison with the results of exact diagonalization.

Quasiclassical theory of quantum dots

“…This figure pertains to the simplest two-electron quantum dot. Similar figures have been obtained for three-and four-electron quantum dots as well [42]. The dependence (18) is very simple indeed; its validity made us realize that the considered phenomenon of structure formation must be essentially classical.…”

Metastable configurations of Wigner crystals in a circular trap

“…Here one finds in total five stable configurations. At high temperatures the most probable is not the ground state (1,6,12,17) but the second one (1,7,12,16). The third lowest state is (1,6,13,16) and at high temperatures also becomes more probable than the ground state.…”

“…Thus, is it handy to identify configurations by enumerating the numbers of particles in each shell starting with the innermost one. For example, the ground state configuration of 21-particle system is (1, 7, 13), while the arrangement of particles in two metastable states is (2,7,12) and (2,8,11). We note, however, that when the number of particles exceeds 30 it is not always possible to discern the shell structure in some configurations.…”

“…Evidently, the metastable state (2,7,12) is at the bottom of a substantially larger basin of attraction, therefore, its probability becomes the largest.…”

“…The trajectories of microparticles can be recorded with the aid of ordinary CCD cameras, and typical periods of their normal-mode oscillations are on the order of seconds [11]. The behaviour of these crystals can be analysed within a completely classical or quasiclassical approach [12].…”