The first aim of the course is to illustrate the electronic ad optical properties developed by low-dimensional systems, where phenomena such as the symmetry reduction, the lower coordintion number, the quantum confinement may induce novel and exotic properties with respect to those that can be observed inside the bulk of a solid. The physical mechanisms acting inside the bulk or at the surface of a solid will be compared in order to highlight their role in defining how the electronic and optical properties of solid matter are influenced by symmetry reduction. During the course the students will be also introduced to the physics of many-body systems beyond the single particle approximation.

The second aim of the course is to discuss the experimental methods suited fot the study of fundamental structural, morphologic and electronic properties of surfaces and interfaces of crystalline solids, which represent examples of low-dimensional systems. Surface sensitive techniques are therefore needed to study the physical mechanisms acting at the low dimensional scales: some of the most widely employed methods will be presented in details.

-Knowledge and understanding (DD1)
The student will be able to implement concepts and theories learned in basic Physics courses (fundamental classical physics, basic quantum mechanics and basic solid state physics) to derive and discuss theories describing the physical properties of low dimensional systems.
The student will learn how to describe complex systems, corresponding to real-world examples, by introducing appropriate models and approximations.
The student will learn what are the relevant phenomena that intervene to determine optical and electric properties in low dimensional systems.
The student will understand how low dimensional systems could be engineered to induce artificial properties.
The student will know the basic component of ultrahigh vacuum systems used to host surface sensitive experimental apparatuses.

-Applying knowledge and understanding (DD2)
The student will be able to learn the reference performances of state-of-the-art instrumentation suitable for the study of low dimensional systems.
The student will be able to analyze and discuss the results of experimental measurements related to the discussed techniques.
The student will be able to learn the reference performances of state-of-the-art instrumentation suitable for the study of low dimensional systems.

-Making judgements (DD3)
The student will be able to identify the surface sensitive technique best suited to investigate the structural, morphologic and electronic properties of low dimensional solid systems.

-Learning skills (DD5)
The student will be able to access the state-of-the-art scientific literature of the reference topics, in terms of understanding the employed experimental methodologies and the related scientific results.
The student will be able to analyze and discuss the results of experimental measurements related to the discussed techniques.

- Surface energetics.
- Surface relaxation and reconstructions.
- Growth of ultrathin films.
- Morphology of surfaces and nanostructures.
- Preparation of surfaces, interfaces and thin films in controlled vacuum conditions.

- Band structure.
- Examples of simple metals, 3d metals and insulators. Nearly free electron model and tight binding approximation.
- Density of states: examples in 1, 2 and 3 dimensions.
- Surface electronic states: projected bands structure, Shockley states, Tamm states.
- Transport properties: seclassical electron dynamics, Boltzmann equation.
- Beyond the single particle approximation: Hartree and Hartree-Fock equations. Fermi-Thomas screening.
- Selected examples: graphene, topological insulators, …

- Diffraction of electrons at surfaces.
- Electron spectroscopies at different energy scales and with different probes.

- Optical properties.
- Kramers-Kronig relations. Direct and indirect transitions. Joint density of states in 1, 2 and 3 dimensions.
- Excitons and plasmons. Surface plasmons and plasmonics.
- Experimental techniques.

- Classical Electromagnetism
- Thermodynamics
- Principles of Quantum Mechanics
- Principles of Solid State Physics

Oral evaluation aimed to probe the student preparation with respect to the pedagocical objectives outlined above.