Incipient Wigner localization in circular quantum dots

We study the development of electron-electron correlations in circular quantum dots as the density is decreased. We consider a wide range of both electron number, N⩽20, and electron gas parameter, r_s≲18, using the diffusion quantum Monte Carlo technique. Features associated with correlation appear to develop very differently in quantum dots than in bulk. The main reason is that translational symmetry is necessarily broken in a dot, leading to density modulation and inhomogeneity. Electron-electron interactions act to enhance this modulation ultimately leading to localization. This process appears to be completely smooth and occurs over a wide range of density. Thus there is a broad regime of “incipient” Wigner crystallization in these quantum dots. Our specific conclusions are (i) the density develops sharp rings while the pair density shows both radial and angular inhomogeneity; (ii) the spin of the ground state is consistent with Hund’s (first) rule throughout our entire range of r_s for all 4⩽N⩽20; (iii) the addition energy curve first becomes smoother as interactions strengthen—the mesoscopic fluctuations are damped by correlation—and then starts to show features characteristic of the classical addition energy; (iv) localization effects are stronger for a smaller number of electrons; (v) finally, the gap to certain spin excitations becomes small at the strong interaction (large r_s) side of our regime.