The course aims at presenting a detailed quanto-mechanical description of the behavior of electrons and phonons in nanoscale materials and devices. The occurrence of peculiar quantum phenomena is demonstrated by means of analytical models focusing on confinement effects and their correspondent characteristic length scales (to answer the question: ‘why does it happen and under which conditions?’). The discussion of the effects arising from electron and phonon confinement in low dimensional structures (2-D, 1-D and 0-D) is accompanied by seminal examples of real nanostructures, experimental techniques and possible applications in novel devices taken form the recent literature (to answer the question: ‘how to observe it and/or how to use it?’). The physical models used to describe the properties are critically discussed to outline the premises, the underlying assumptions and the related limitations (to answer the question: ‘to what extent is it valid?’).

At the end of the course the student

• Knows the behaviour of electrons and phonons in nanostructures and confined systems and the how they can be experimentally measured
• Knows how to use the tools of quantum mechanics to properly describe the change in the electronic and phononic properties by model systems and understands the limits of the adopted physical models.
• Is able to apply analytical models to critically discuss the exploitation of quantum behavior in novel devices and the related length scales
• Is able to apply the models presented in the course to critically discuss the electronic and vibrational properties of carbon nanostructures outlining the differences with respect to conventional materials.

• Introduction and preliminary concepts: Effective mass approximation and the envelope function
• Electrons in nanostructures: Electron states and DOS of semiconductor heterostructures, wires, dots and artificial structures. STM and STS to measure electronic properties in nanostructures.
• Transport in nanostructures:  Fundamental length scales. Transport regimes, parallel and vertical transport. Coulomb Blockade. Ballistic transport in nanowires. Quantum Interefrence Transistor (QUIT), Single electron transistor (SET), Resonant Tunneling diode (RTD).
• Phonons in nanostructures: Surface phonons and localized vibrations in confined systems. Acoustic waves in low dimensional structures and phonon density of states (PDOS). Raman spectroscopy in solids: from crystals to nanostructures. 
• Carbon nanostructures: fabrication and properteis of graphene, derivation of graphene bandstructure, Dirac’s cones and massless Dirac fermions; electrons and phonons in single wall nanotubes (the zone folding approximation), derivation of the metallicity condition and size dependent gap in semiconducting tubes; Raman of carbon: from graphite to graphene and nanotubes. 2-D materials beyond graphene. Carbon atomic wires.

Laboratory visits: laboratory visits are aimed at showing STM and Raman measurements of nanostructures including semiconductors, oxides and carbon-based systems (graphene, nanotubes, cluster-assembled carbon). 

To attend the course the students are expected to know the fundamentals of quantum mechanics (e.g. given in introductory courses in quantum/modern physics, atomic/molecular physics, nanoscience and nanotechnology, condensed matter or structure of matter). Having attended a course in solid state physics is not strictly required but is recommended (at least the concept of reciprocal space and band structure in solids, electron effective mass and phonons).

The examination will consist in an oral discussion (about 30-45 minutes) of the topics presented in the course. The examination will verify that the student:

- knows the topics with the related hypotheses, the critical points, the mathematical approach and the physical constrains and consequences. Understanding the physics underlying the mathematical approach is considered a fundamental aspect.

- knows the value or order of magnitude of the main important quantities used to describe nanostructures (universal constants, fundamental length scales, typical size and energy values).

- is able to apply the tools of quantum mechanics to describe and critically discuss the electron and phonon states in confined systems and particularly in carbon nanostructures

- is able to use analytical models to describe the working of a quantum device

Additional material is available in the course website on the BeeP portal

Additional material is available in the course website on the BeeP portal

Additional material is available in the course website on the BeeP portal