Triplet-singlet transition in a quantum dot with disorder

Random potentials for disorder are included in a two-dimensional parabolic quantum dot. In this theoretical study, exact diagonalization is used in order to find ground-state energy, which depends upon seven parameters: (1) number of electrons, (2) strength of confining potential, (3) magnetic field, (4) Zeeman $g$-factor, (5) factor in front of Coulomb matrix elements (combination of effective mass and dielectric constant), (6) width of random potential fluctuation, and (7) mean value of random potential strength. The phase diagram of the ground state shows spin triplet-singlet transition. This triplet-singlet degeneracy on the transition point is discussed as a key ingredient for the integer Kondo effect.

Figure 1

The spin characters of ground states are shown in the reduced parameter space of $\hslash {\omega }_c$ and $U$ for different values of $p$ for $N_e=2$: (a) $p=0.0$, (b) $p=0.5$, (c) $p=1.0$. As mentioned in the text, three parameters among seven are fixed as $\hslash {\omega }_0=1.0$, $g=0.0$, $V∕\sqrt{\hslash \omega }=1.19$.

Figure 2

The same as Fig. 1, except for $N_e=4$.

Figure 3

The same as Fig. 1, except for $N_e=6$.