Maximum-density droplet to lower-density droplet transition in quantum dots

We show that the Landau level mixing in two-dimensional quantum dot wave functions can be taken into account very effectively by multiplying the exact lowest Landau level wave functions by a Jastrow factor which is optimized by variance minimization. The comparison between exact diagonalization and fixed phase diffusion Monte Carlo results suggests that the phase of the many-body wave functions are not affected much by Landau level mixing. We apply these wave functions to study the transition from the maximum density droplet state [incipient integer quantum Hall state with angular momentum $L=N(N-1)∕2$] to lower density droplet states $[L>N(N-1)∕2]$.

Figure 1

The energy as a function of total angular momentum $L$, for (a) $N=4$ at $B=8\mathrm{T}$, (b) $N=7$ at $B=5\mathrm{T}$, obtained by exact diagonalization in LLL approximation (solid line), exact diagonalization including 2LLs (dotted line), and DMC using the full Jastrow term (cross marks). The numbers above the line represent the $C_{-}$ quantum number.

Figure 2

The energy as a function of magnetic field for different many-body states for $N=4$, (a) without the Zeeman term and (b) with the Zeeman term. Lines with symbols represent many-body states which are closely involved in the MDD-LDD transition, and they are identified by their $(L,S)$ values in (a) and by their $(L,S,S_z)$ values in (b). The locations of the maxima in the pair densities are indicated by solid dots, and open dots represent the fixed electrons.

Figure 3

(Color online) The evolution of VMC ground state pair densities as a function of magnetic field for $N=4$, (a) without the Zeeman effect and (b) including the Zeeman effect.

Figure 4

The energy as a function of magnetic field for different many-body states for $N=6$, (a) without the Zeeman term and (b) with the Zeeman term. Lines with symbols represent many-body states which are closely involved in the MDD-LDD transition, and they are identified by their $(L,S)$ values in (a) and by their $(L,S,S_z)$ values in (b).

Figure 5

The evolution of the ground state densities as a functions of magnetic field is increased for $N=6$, obtained by VMC method, (a) without the Zeeman effect and (b) including the Zeeman effect.