ABOUT DONRODRIGO

A configuration-interaction suite of codes for electronic correlations in confined systems
Semiconductor quantum dots (QDs) are nanometer sized regions where free carriers are confined by electrostatic fields. Different techniques lead to QDs with different shapes and strengths of the confinement, and it is possible to control a remarkable variety of parameters in the laboratory. Almost all QD-based applications rely on electronic correlation effects which are prominent in these systems. The treatment of correlation in QDs is a non-trivial task, and requires a numerical accuracy which is usually beyond the possibilities of standard mean-field approaches like Density Functional Theory and Hartree-Fock. For this reason we have develeped, entirely within the INFM-CNR National Research Center S3, a suite of parallel Full Configuration Interaction computer codes named DONRODRIGO.

The package solves the problem of N interacting electrons in a QD-device with arbitrary numerical accuracy, and provides full access to both energies and wave functions of ground and excited states. The correlated wave function is written as a superposition of many Slater determinants, obtained by filling in with N electrons a truncated set of single-particle orbitals in all possible ways (full configuration interaction). The implementation is independent of the orbital basis and, therefore, of the details of the device. The large eigenvalue problem is reduced to its minimal size by exploiting the symmetry of the effective-mass interacting Hamiltonian, including total spin. The resulting Hamiltonian matrix, which represents the Coulomb interaction in the Slater-determinant basis, is diagonalized via a parallel version of the Lanczos algorithm. The maximum size of eigenproblems manageable depends on N and on the orbital-basis dimension. While the accuracy is comparable to quantum Monte Carlo, DONRODRIGO uniquely provides the excitation spectrum and allows for easy post-processing of eigenstates, including calculation of various static and dynamic correlation functions or propagators.

The figure shows one of the several physical observables DONRODRIGO may calculate. The conditional probability for the six-electron quantum dot ground state is shown as the density is varied, going from the high- (left) to the low-density (right) regime. The contour plots provide the probability of measuring one electron in the xy quantum dot plane, given that the position of another one has been fixed (black dot). Lengths are in units of the characteristic dot radius (= radius mean square root for the lowest-energy single-particle eigenfunction of a two-dimensional harmonic trap).
Left: Liquid-like charge distribution at high density. Middle: Hexagonal molecule, corresponding to a classicaly metastable state, for intermediate values of the density. Right: Cristallyzed "Wigner" molecule corresponding to the stable classical configuration made of five electrons at the vertices of a regular pentagon plus an electron at the center, in the low-density regime.