# Condensed Matter Physics I

## Presentation

Programme (detailed contents):

Angular momenta (orbitals, spin) and their addition. Stationary perturbation theory (non-degenerate and degenerate case) and applications. Time dependent perturbation theory (two-states systems, absorption, stimulated and spontaneous emission, selection rules). Identical particles (Pauli’s principle, multi-electron atom, periodic table).

Electric conductivity: Drude and Sommmerfeld Model. Basic Crystallography. Band structure theory. Band structure and resulting properties of graphene & carbon nanotubes. Transport properties, effective carrier mass, and carrier statistics.

Organisation:

The student will be given supports for lectures, tutorials and labwork. The lectures focus on the new concepts, their illustration and the demonstrations of some mathematical expressions related to the physical phenomena. The tutorials, with the help of computational calculations, directly relate to the lectures through practical examples extracted from modern nano/micro-technology.

Main difficulties for students:

The main difficulties for students relate only to the use of the mathematical tools used in matrix-based calculations. However, thanks to the use of Maxima, a symbolic calculation software, the student is capable to overcome these difficulties.

## Objectives

At the end of this module, the student will have understood and be able to explain several concepts of quantum mechanics and electronic structure of solids, associated to band structure engineering in modern devices.

He should be able to apply the following concepts: the quantized angular moments and their addition, stationary perturbation theory and time dependent perturbation theory, and to treat the identical particles system’s, to solve simple examples such as radiative recombination, multiple electrons atom, two-level systems and magnetism model. The student will be able to calculate energy spectra from model-hamiltonians and discuss their interpretation.

The student should be capable to relate the working principle of diodes to the specific electronic structure of the material used. For example, the student will be able to present and interpret the band structure of semiconductors, its relationship with the Brillouin Zone concepts, effective mass, electron-hole formalism, and deduce the physical properties.

## Needed prerequisite

Nanophysics I and II (S5 I3AIPH20, S6 I3AIPH30)

Quantum physics  (S6 I3MAPH30)

Solid State Physics (S6 I3MAPH10, I3MAPH50)

Mathematical tools: complex number, vector field, differential and matrix calculus.

## Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...