Academic Year 2018/2019 - 1° Year - CONDENSED MATTER PHYSICS Curriculum, NUCLEAR AND PARTICLE PHYSICS Curriculum, PHYSICS APPLIED TO CULTURAL HERITAGE, ENVIRONMENT AND MEDICINE Curriculum and THEORETICAL PHYSICS Curriculum

FIS/03 - 6 CFU - 1° Semester

The course aims at providing the student with the fundamentals of the physics of matter in the solid state, with reference to both experiment and theory. Specific interest will be devoted to the crystal structure, the electronic band structure, the lattice dynamics, and the electronic transport and optical properties of solids. A few lectures will focus on selected advanced topics *(in italics, below)* of current interest in experimental and theoretical solid-state physics.

Lectures (taught classes).

**Crystalline solids.** X-ray diffraction. Direct lattices in d ≤ 3 dimensions. Lattices with basis. Wigner-Seitz cell. Reciprocal lattice. Brillouin zones.

*Real crystals: defects.*

*Other correlated phases of matter. Van Hove correlation function. Amorphous solids, liquids, superlattices, quasicrystals.*

**Free electrons.** Free electron gas. Fermi-Dirac statistics, chemical potential, and other thermodynamic potentials (reminder). Sommerfeld expansion. Electronic specific heat. Effective mass. *Heavy-fermion materials.*

**Electrons in crystalline lattices.** *Kronig-Penney model.* Bloch theorem. Quasimomentum and electronic bands. Special points and `spaghetti' plots. **k·p** Hamiltonian.

**Parameter-dependent Hamiltonians.** Hellmann-Feynman and Eppstein theorems. Berry phase and connection. Applications to modern solid-state physics (electrical polarization, AFM: Atomic Force Microscopy, Wannier states and maximally localized states).

**Electron correlation.** Hartree-Fock approximation. From Thomas-Fermi approximation to the Hohenberg-Kohn theorem. Density Functional Theory (DFT).

**Stability of matter.**

**Quasi-free electrons.** Fermi surfaces of metals. Density of states. Electronic topological transitions (van Hove singularities). Band gaps. Metals, semiconductors, insulators. Tight-binding method (LCAO). *Other numerical methods (OPW, APW, KKR).* Effective mass again. 2D examples: square lattice, graphene.

**Mechanical properties of solids.** Cohesion energy. Elastic properties of solids. Lattice dynamics. Phonons in solids. Einstein and Debye models: lattice specific heat. *Anharmonic effects.*

**Transport properties of solids.** Bloch electrons. Electrical conductivity and heat conduction of metals. *Wiedemann-Franz law.* Drude and Sommerfeld models. Hall effect. *de Haas-van Alphen effect. Quantum Hall effect.*

**Optical properties of solids.** Plasmons.

**Electronic phases with broken symmetries.**

*Ferromagnetism. Stoner model. Mean-field approximation. Spin waves.**Antiferromagnetism. Slater model. Spin density waves.**Peierls instability. Charge density waves. Solitons.**Pairing instability: superconductivity. Phenomenology. Ginzburg-Landau theory. Electron-phonon coupling. BCS theory. Josephson effect. Superconducting fluctuations. High-T*_{c}and other `exotic' superconductors: cuprates, MgB_{2}, pnictides, ...

**Topological insulators.**

G. Grosso, G. Pastori Parravicini, *Solid state physics* (Oxford, Academic Press, 2014 : 2nd ed.)

Fuxiang Han, *A modern course in the quantum theory of solids* (Singapore, World Scientific, 2013)

J. Sólyom, *Fundamentals of the physics of solids* (Heidelberg, Springer, 2010) : 3 vols.

N. W. Ashcroft, N. D. Mermin, *Solid state physics* (Saunders, Philadelphia, 1976)

J. M. Ziman, *Principles of the theory of solids* (Cambridge University Press, Cambridge, 1965)

C. Kittel, *Quantum theory of solids* (New York, J. Wiley & Sons, 1963)

W. Jones, N. H. March, *Theoretical solid state physics* (New York, Dover, 1985) : 2 vols.