Quantum Monte Carlo study of composite fermions in quantum dots: The effect of Landau-level mixing

Composite fermion wave functions projected onto the lowest Landau level, provide an accurate description of two-dimensional quantum dots in the limit of strong magnetic fields. We show that the range of validity of these wave functions can be extended to smaller magnetic fields by incorporating Landau level mixing effects with the variational and diffusion Monte Carlo methods. We apply our method to 14 and 15 electron systems to study ground state properties in the fractional quantum Hall regime. Landau level mixing is found to be important for a quantitative understanding of experimental addition spectra.

Figure 1

Total energy as a function of total angular momentum for $N=15$, $B=8\mathrm{T}$, obtained from lowest LL composite fermions (CF-LLL) and diffusion Monte Carlo $(\mathrm{CF}+\mathrm{DMC})$ calculations.

Figure 2

Ground state total angular momentum as a function of magnetic field for $N=15$, obtained from lowest LL composite fermions (CF-LLL) and diffusion Monte Carlo $(\mathrm{CF}+\mathrm{DMC})$ calculations.

Figure 3

Addition energy $\mu \left(N\right)$ (dashed line) and its slope $-d\mu ∕dB$ (solid line) obtained from diffusion Monte Carlo calculations. Downward arrows correspond to transitions to the $\nu =1∕3$ state.

Figure 4

Dot area as a function of total angular momentum for $N=15$, $B=8\mathrm{T}$, obtained from the lowest LL composite fermions (CF-LLL) and diffusion Monte Carlo $(\mathrm{CF}+\mathrm{DMC})$ calculations.

Figure 5

Ground state dot area as a function of the magnetic field for $N=15$, obtained from diffusion Monte Carlo calculations. MDD refers to the maximum density droplet.