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Corso per il dottorato- 2012-13 Nanostrutture e sistemi di bassa dimensionalita'

Corso per il dottorato- 2012-13 Nanostrutture e sistemi di bassa dimensionalita' (Michele Cini).

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Corso per il dottorato- 2012-13 Nanostrutture e sistemi di bassa dimensionalita'

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  1. Corso per il dottorato- 2012-13 Nanostrutture e sistemi di bassa dimensionalita' (Michele Cini) 1-Introduzione: Nanoparticelle metalliche e Mie scattering -Fullereni-Punti quantici-Pozzi quantici- Embedding-Stati a 1 elettrone nel Grafene e nei Nanotubi di Carbonio -Catene di Heisenberg- Bethe Ansatz-Magnoni. 2-Trasporto quantistico: correnti balistiche- caratteristiche corrente-tensione- Effetti magnetici nei circuiti nanoscopici-Pumping. 3-Ordine e dimensionalita': teoria di Ginzburg Landau delle transizioni di fase- Ferromagnetismo di Weiss - modello di Ising in 1d- Assenza di transizioni in 1d- Approccio del gruppo di rinormalizzazione per la percolazione e per il modello di Ising - modello di Ising in 2d: transfer matrix. Fermionizzazione della transfer matrix- Soluzione di Onsager e transizione di fase- Caso a infinite dimensioni. Magnetismo in 2d nel modello di Hubbard- Teoremi di Lieb  -Ferromagnetismo di Nagaoka 4-Effetti di correlazione in 1d: andamenti a legge di potenza nei nanotubi di carbonio: liquido di Luttinger-Tecnica della Bosonizzazione-Separazione di spin e carica- Applicazioni. 5-Effetti di correlazione in 2d: Gas di Fermi in campo magnetico ed effetto Hall quantistico intero e frazionario. http://people.roma2.infn.it/~cini/

  2. 2d, 1d, 0d nano-objects: molecular size in 1, 2 or 3 dimensions Small is different: all properties of nanostructures are size dependent Rich phenomenology, many applications Models of reduced dimensionality are endorsened by quantum mechanics at low temperatures: gaps develop and degrees of freedom are frozen! Exact solutions:Bethe ansatz,Ising model,Nagaoka ferromagnetism…. But strong correlation (not only in models, but in reality): exotic behavior, troubles in standard treatments Phase transitions strongly depend on dimensionality! Special Methods:Topology plays an important role, bosonization, Bethe Ansatz New concepts and specific phenomena: anyons, charge fractionalization,spin-charge separation, QHE

  3. Stained Glass Gothic window of Notre Dame de Paris (XIV century) The colors were achieved by a colloid dispersion of gold nano-particles in glass.

  4. Transverse electromagnetic wave in homogeneous isotropic medium Putting together the inhomogeneus equations, Consider the plane wave going upwards 4

  5. Assuming a transverse elecromagnetic wave in homogeneous local medium

  6. Drude’s bold theory of electromagnetic waves in metals

  7. Drude dielectric function

  8. Simple metals have propagating waves have From Blaber et al., J.Chem.Phys (2009) experimental, with g=1/t absorption should be in the UV, width 1/d. unexplained!

  9. At surfaces, Surface plasmon polaritons! vacuum wave metal z e=1 X e(w) They are plasmon-photon modes localized at an interface. Consider vacuum for z>0 with e=1 and metal with e(w) for z<0, wave propagating along x.

  10. vacuum wave metal z e=1 X e(w) Next, we find the electric field, which is also localized: 12

  11. Continuity condition at z=0  dispersion law the other sign is not acceptable because it gives

  12. photon-like polariton This is not yet suitable for the nanoclusters.

  13. Scattering of light by a spherical metal particle: Rayleigh approximation Rayleigh scattering describes the elastic scattering of light by spheres which are much smaller than the wavelength of light. The intensity of the scattered radiation is given by Blue is scattered much more than red.

  14. Mie scattering Mie in 1908 solved Maxwell’s equations for the scattering of a plane-wave in a medium on a sphere with refractive index n. Absorption coefficient In Freiburg, during the Nazi dictatorship, Mie was member of the university opposition of the so-called "Freiburger Kreis" (Freiburg circle) and one of the participants of the original "Freiburger Konzil".

  15. Quantum size effects See kawabata and Kubo J. Phys. Soc. Japan (1966) ; M.Cini and P.Ascarelli J. Phys. C (1974): the dielectric constant of small Ag particles is semiconductor-like For d<<l the dipole plasmon dominates. With increasing d the quadrupole term acquires importance, and it leads to a higher resonance frequency; then higher multipoles enter. For a large sphere one gets the plane response. Important Complications nonspherical shapes size distributions, distance distributions, interparticle multipolar interactions matrix interactions

  16. U. kreibig, Journal de Physique Colloque C2 (1977)

  17. Quantum Dots and wires Quantum dots are semiconductor “nanoparticles” (e.g. CdSe , ZnS) Sizes range from 2 to 10 nanometers in diameter (about the width of 50 atoms) They are produced by molecular beam epitaxy or by lithographic techniques (lithography is based on covering a plate with chemicals such that the image is produced by a chemical reaction) Optical and electrical properties that are different in character to those of the corresponding bulk material.

  18. smaller dots larger dots By the size one can control the band gap and so the color. Larger dots give a redder fluorescence spectrum.

  19. The energy spectrum of a quantum dot can be engineered by controlling size and shape. One can also tailor the strength of the confinement potential. Also, one can connect quantum dots by tunnel barriers to conducting leads. One can also order arrays of quantum dots by electrochemical techniques SET= single electron tunneling Applications to electronics (single-electron transistor, showing the Coulomb blockade effect) and qbits for quantum computers are also envisaged. Also photovoltaic devices, LED, photodetectors have been built.

  20. Type I Quantum wells Type II Quantum wells electrons and holes are confined electrons are confined, lowest hole energy in host Quantum wells produced by MBE: several monolayers of semiconductor over a host crfystal by molecular beams

  21. 1-body Density of states per spin in QW Modulation doping By adding donors in semiconductors one introduces conduction electrons (wanted) and scattering centres (unwanted). Modulation doping: donors added to host, outside the QW give electrons to QW but with very little scattering.

  22. Confined excitons get distorted and have a position-dependent binding energy. Type I Quantum wells Type II Quantum wells electrons and holes are confined electrons are confined, lowest hole energy in host Although band gaps are known, determining the conduction and valence band offsets theoretically and experimentally is not easy. Confinenment is a particle-in-a box problem but walls are finite and masses are different: say, m inside and m outside. Matching conditions: A more microscopic approach is based on embedding techniques

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