Pairing in the Hubbard model: the Cu_{5}O_{4} Cluster versus the Cu-O plane

We study the Cu_{5}O_{4} cluster by exact diagonalization of a three-band Hubbard model and show that bound electron or hole pairs are obtained at appropriate fillings, and produce superconducting flux quantisation. The results extend earlier cluster studies and illustrate a canonical transformation approach to pairing that we have developed recently for the full plane. The quasiparticles that in the many-body problem behave like Cooper pairs are W=0 pairs, that is, two-hole eigenstates of the Hubbard Hamiltonian with vanishing on-site repulsion. The cluster allows W=0 pairs of d symmetry, due to a spin fluctuation, and s symmetry, due to a charge fluctuation. Flux quantisation is shown to be a manifestation of symmetry properties that hold for clusters of arbitrary size.Comment: 13 pages, 3 figures, a few intermediate steps added for clarit

Ordering of Ge quantum dots on silicon surfaces via bottom-up and top-down approaches

The nanoscale ordering of inorganic semiconductor quantum dots (QDs) is crucial to obtain reliable structures for novel nanotechnological applications such as nanomemories, nanolasers and nanoelectronic devices. We have directly grown Ge QDs by physical vapour deposition (PVD) on Si(111), Si(100) and some of its vicinal surfaces and studied innovative bottom up techniques to order such nanostructures. Specifically, we harnessed naturally occurring instabilities due to reconstruction and intrinsic anisotropic diffusion in Si bare surfaces, such as step bunching and natural steps occurring in silicon vicinal surfaces, to order the QDs both in one dimension and in the plane. We have also shown the use of controlled quantities of surfactants, like Sb, dramatically improves the desired ordering. Moreover, we have assisted these self-assembling processes using top-down approaches like Focused Ion Beam (FIB) milling and STM nanoindentation to control the nucleation sites and the density of the Ge QDs. Real-time study of growth and self-assembly has been accomplished using Scanning Tunneling Microscopy imaging in UHV. An explanation of the occurring processes is given, and a software routine is used to quantify the ordering of the QDs both in pre-patterned and bare surfaces. Applications, mainly in the field of Nanocrystal Nonvolatile Memories, are discussed

A study of the pair distribution function of self-organized Ge quantum dots

We explore the use of the pair distribution function to study the self-organization process of Gequantum dots on both nanopatterned and nonpatterned oxidized Si(001) surfaces.Dots formation and ordering upon annealing of a Ge thin film are analyzed. The method we use is not limited to this case study. We show how it can be applied to determine short and long range self-ordering of nanostructures. We support our results by applying a software routine to simulate patterns of dots to finally spot the relevant physical aspects of Ge islands self-assembly

W=0 pairing in Hubbard and related models of low-dimensional superconductors

Lattice Hamiltonians with on-site interaction $W$ have W=0 solutions, that is, many-body {\em singlet} eigenstates without double occupation. In particular, W=0 pairs give a clue to understand the pairing force in repulsive Hubbard models. These eigenstates are found in systems with high enough symmetry, like the square, hexagonal or triangular lattices. By a general theorem, we propose a systematic way to construct all the W=0 pairs of a given Hamiltonian. We also introduce a canonical transformation to calculate the effective interaction between the particles of such pairs. In geometries appropriate for the CuO$_{2}$ planes of cuprate superconductors, armchair Carbon nanotubes or Cobalt Oxides planes, the dressed pair becomes a bound state in a physically relevant range of parameters. We also show that W=0 pairs quantize the magnetic flux like superconducting pairs do. The pairing mechanism breaks down in the presence of strong distortions. The W=0 pairs are also the building blocks for the antiferromagnetic ground state of the half-filled Hubbard model at weak coupling. Our analytical results for the $4\times 4$ Hubbard square lattice, compared to available numerical data, demonstrate that the method, besides providing intuitive grasp on pairing, also has quantitative predictive power. We also consider including phonon effects in this scenario. Preliminary calculations with small clusters indicate that vector phonons hinder pairing while half-breathing modes are synergic with the W=0 pairing mechanism both at weak coupling and in the polaronic regime.Comment: 42 pages, Topical Review to appear in Journal of Physics C: Condensed Matte

Quantum dots: substrate nanopatterning as a path towards the applications

Nanotechnology aims at exploiting the remarkable size effects that arise when materials are reduced to nanoscale dimensions. Exploiting such effects will lead to new applications in different areas of human endeavour. The self assembly of three-dimensional islands is one of the most promising paths towards the fabrication of artificial atoms, or quantum dots (QDs) devoted to nanoelectronic and nanophotonic applications. In order to exploit the unique electronic properties of semiconductor quantum dots in novel quantum effect devices, lateral dimensions of these structures have to be reduced to the order of tens of nm’s, the range of De Broglie wavelength of electrons inside these materials. Moreover, millions of quantum dots should be orderly packed in dense arrays to achieve the necessary active volume. So far, the most promising quantum structures have been fabricated using techniques based on self assembling, but their ordering is possible only by appropriate substrate nanopatterning. In this paper we will explore different ways of patterning a substrate and how they affect the growth and ordering of the quantum dots