During the last decade semiconductor technology has made an impressive advance
toward miniaturization. Progress in lithography and epitaxial growth have made
it possible to fabricate structures in which carriers or excitons are confined
in one, two or three dimensions.
Quantum dots are nanometer-sized regions of semiconductor which confine
electrons in all three dimensions. They are also known as "artificial
atoms"[1]; like atoms they have a discrete spectrum which, in addition, can be
artificially tailored by changing the size, the shape and the composition of
the single quantum dot.
Moreover, quantum dots have much more interesting properties than atoms due to
the prominent role of many-body effects. Thus, to fully exploit their properties, one
should completely understand their electronic structure [2].
We investigate the electronic structure of etched quantum dots done with
modulation-doped AlGaAs-GaAs heterostructures, which confine electron {\em
via} an effective two-dimensional parabolic potential (they are also known as
parabolic quantum dots). We present an extensive study of ground-state
spin-densities and pair distribution functions over a broad range of
electronic coupling constant and electron number [3].
The ground state spin-densities are obtained using spin-density-functional
theory and are compared with Diffusion Monte Carlo data. The accurate
knowledge of the one-body properties is used to devise and test a local
approximation for the electron-pair correlations; with this approximation we
provide a detailed picture of two-body correlations in a coupling-strength
regime preceding the formation of Wigner-like electron ordering.
Finally, we obtain the momentum distribution of the interacting electrons [4]
using an optimized Jastrow-type wave function in which the Slater determinant
part is calculated using density-functional theory. The momentum distribution,
which can be measured via Compton scattering, can be used as a further tool to
study the role of interaction in these nano-structures.
References
[1] M.~A Kastner, Phys. Today 46, 24 .
[2] S.~M. Reimann, and M. Manninen, Rev. Mod. Phys. 74, 1283.
[3] M. Gattobigio, et al., Phys. Rev. B 72, 045360 (2005).
[4] M. Gattobigio, and P. Capuzzi, Phys. Rev. B 73, 235312 (2006). |