Massimo Rontani

Full configuration interaction approach to the few-electron problem in artificial atoms

We present a new high performance configuration interaction code optimally designed for the calculation of the lowest-energy eigenstates of a few electrons in semiconductor quantum dots (also called artificial atoms) in the strong interaction regime. The implementation relies on a single-particle representation, but it is independent of the choice of the single-particle basis and, therefore, of the details of the device and configuration of external fields. Assuming no truncation of the Fock space of Slater determinants generated from the chosen single-particle basis, the code may tackle regimes where Coulomb interaction very effectively mixes many determinants. Typical strongly correlated systems lead to very large diagonalization problems; in our implementation, the secular equation is reduced to its minimal rank by exploiting the symmetry of the effective-mass interacting Hamiltonian, including square total spin. The resulting Hamiltonian is diagonalized via parallel implementation of the Lanczos algorithm. The code gives access to both wave functions and energies of first excited states. Excellent code scalability in a parallel environment is demonstrated; accuracy is tested for the case of up to eight electrons confined in a two-dimensional harmonic trap as the density is progressively diluted up to the Wigner regime, where correlations become dominant. Comparison with previous quantum Monte Carlo simulations in the Wigner regime demonstrates power and flexibility of the method.

COULOMB CORRELATION EFFECTS IN SEMICONDUCTOR QUANTUM DOTS : THE ROLE OF DIMENSIONALITY

We study the energy spectra of small three-dimensional (3D) and two-dimensional (2D) semiconductor quantum dots through different theoretical approaches (single-site Hubbard and Hartree-Fock Hamiltonians); in the smallest dots we also compare with exact results. We find that purely 2D models often lead to an inadequate description of the Coulomb interaction existing in realistic structures, as a consequence of the overestimated carrier localization. We show that the dimensionality of the dots has a crucial impact on (i) the accuracy of the predicted addition spectra, and (ii) the range of validity of approximate theoretical schemes. When applied to realistic 3D geometries, the latter are found to be much more accurate than in the corresponding 2D cases for a large class of quantum dots; the single-site Hubbard Hamiltonian is shown to provide a very effective and accurate scheme to describe quantum dot spectra, leading to good agreement with experiments.

Quantum phases in artificial molecules

The few-particle state of carriers confined in a quantum dot is controlled by the balance between their kinetic energy and their Coulomb correlation. In coupled quantum dots, both can be tuned by varying the inter-dot tunneling and interactions. Using a theoretical approach based on the diagonalization of the exact Hamiltonian, we show that the transitions between different quantum phases can be induced through the inter-dot coupling both for a system of few electrons (or holes) and for aggregates of electrons and holes. We discuss their manifestations, in addition energy spectra (accessible through capacitance or transport experiments) and optical spectra.

Evidence of Correlation in Spin Excitations of Few-Electron Quantum Dots

We report inelastic light scattering measurements of spin and charge excitations in nanofabricated AlGaAs/GaAs quantum dots with few electrons. A narrow spin excitation peak is observed and assigned to the intershell triplet-to-singlet monopole mode of dots with four electrons. Configuration-interaction theory provides precise quantitative interpretations that uncover large correlation effects that are comparable to exchange Coulomb interactions.

Multiple quantum phases in artificial double-dot molecules

We study coupled semiconductor quantum dots theoretically through a generalized Hubbard approach, where intra- and inter-dot Coulomb correlation, as well as tunneling effects are described on the basis of realistic electron wavefunctions. We find that the ground-state configuration of vertically coupled double dots undergoes non-trivial quantum transitions as a function of the inter-dot distance d; at intermediate values of d we predict a new phase that should be observable in the addition spectra and in the magnetization changes.

Correlated Electrons in Optically Tunable Quantum Dots: Building an Electron Dimer Molecule

We observe the low-lying excitations of a molecular dimer formed by two electrons in a GaAs semiconductor quantum dot in which the number of confined electrons is tuned by optical illumination. By employing inelastic light scattering we identify the intershell excitations in the one-electron regime and the distinct spin and charge modes in the interacting few-body configuration. In the case of two electrons, a comparison with configuration-interaction calculations allows us to link the observed excitations with the breathing mode of the molecular dimer and to determine the singlet-triplet energy splitting.

Imaging quasiparticle wave functions in quantum dots via tunneling spectroscopy

We show that in quantum dots the physical quantities probed by local tunneling spectroscopies\char22{}namely, the quasiparticle wave functions of interacting electrons\char22{}can considerably deviate from their single-particle counterparts as an effect of Coulomb correlation. From the exact solution of the few-particle Hamiltonian for prototype dots, we find that such deviations are crucial to predict wave function images at low electron densities or high magnetic fields.

Raman signatures of classical and quantum phases in coupled dots: A theoretical prediction

We study electron molecules in realistic vertically coupled quantum dots in a strong magnetic field. Computing the energy spectrum, pair correlation functions, and dynamical form factor as a function of inter-dot coupling via diagonalization of the many-body Hamiltonian, we identify structural transitions between different phases, some of which do not have a classical counterpart. The calculated Raman cross-section shows how such phases can be experimentally singled out.

Addition energies in semiconductor quantum dots: Role of electron–electron interaction

We show that the addition spectra of semiconductor quantum dots in the presence of magnetic field can be studied through a theoretical scheme that allows an accurate and practical treatment of the single-particle states and electron–electron interaction up to large numbers of electrons. The calculated addition spectra exhibit the typical structures of Hund-like shell filling, and account for recent experimental findings. A full three-dimensional description of Coulomb interaction is found to be essential for predicting the conductance characteristics of few-electron semiconductor structures.

Correlation effects in wave function mapping of molecular beam epitaxy grown quantum dots.

We investigate correlation effects in the regime of a few electrons in uncapped InAs quantum dots by tunneling spectroscopy and wave function (WF) mapping at high tunneling currents where electron-electron interactions become relevant. Four clearly resolved states are found, whose approximate symmetries are roughly s and p, in order of increasing energy. Because the major axes of the p-like states coincide, the WF sequence is inconsistent with the imaging of independent-electron orbitals. The results are explained in terms of many-body tunneling theory, by comparing measured maps with those calculated by taking correlation effects into account.