Content

1. Elastic scattering of radiation and structure. Short and long range order. Diffraction of radiation by crystals. Reciprocal lattice, the Bragg condition, crystal planes and Miller indices. Experimental geometries of diffraction
2. Example of a model in condensed matter: the Drude model and the transport and optical properties of metals.
3. The Sommerfeld model and Fermi-Dirac statistics. Fermi level and Fermi wavevector. Concept of density of states. Density of states in 3D, 2D and 1D. Specific heat and Pauli susceptibility of a gas of electrons.
4. Electrons in a periodic lattice. Bloch's theorem. Concept of Brillouin Zone. Quasi-free electron bands. Degeneracies and opening gaps. Tight -binding models: relationship with LCAO methods. Wannier states and tight-binding parameterization of bands. Examples of bands: bands of aluminum; bands of Si and Ge; bands of grapheme.
5. Semi-classical motion in bands. The insulator of bands (or Wilson). Semi-classical motion in external fields. Electrons, holes and Hall effect.
6. The harmonic lattice; Einstein Model and specific heat. Normal modes, phonons and quantification. Debye model, the phonon density of states and specific heat of the harmonic lattice.

Aims

To know the fundamentals of Solid State Physics, with particular emphasis on the crystalline state. To apply the knowledge of Quantum Mechanics, thermodynamics and Statistical mechanics to the analysis of Solid-State problems. To be aware of the fundamental techniques of material characterization. To understand the metallic state, thermodynamic and transport properties in metals.

It is expected that the students acquire the ability to reproduce some of the basic results of the studied models and to find answers to relatively elementary extensions thereof, demonstrating ability to understand concepts, models and theories of Condensed Matter Physics, by solving problems that mobilize the reasoning, the relationship of concepts and generalizations of the models studied.

Recommended Books

• The Oxford Solid State Basics, Steven H. Simon; Oxford University Press, 2013, ISBN 978–0–19–968076–4.
• Ashcroft Neil W. , Mermin, N. D.; Solid State Physics, Holt- Rinehart and Winston, 1976. ISBN 978-0-521- 87658-2.
• Michael P. Marder; Condensed Matter Physics, Wiley, 2010. ISBN: 0470617985.
• John Ziman; Principles of the Theory of Solids, Cambridge University Press, 1972. ISBN 978-0-521-40670-3.
• John Singleton; Band Theory and Electronic Properties of Solids, Oxford University Press, 2001. ISBN: 978019850644.

Teaching Staff

João Pedro Araújo (responsible)
Teresa Seixas
Joaquim Agostinho Moreira

Hours

42 h (lectures + practicals)

Grading System

Theoretical-practical classes (TP): Presentation of program content using conventional and multimedia methods; specialized topics will be presented in lectures given by invited researcher or professors. Finally, the basic principle of the classes will be based on a discussion between students and teachers.

Evaluation formula:

• Continuous assessment with answers to regular on-line forms (ca. 1 every 2 classes) and class exercise group solving [3/20].
• Oral presentation of a work at the end of the semester [6/20].
• Final exam realization. [11/20]