## Objectives

Why do some materials conduct electricity while other do not? Why do metals shine and dielectric materials are translucent or transparent? A material hosting more electrons, is it always a better conductor? Why do materials composed of the same atoms may have different electric or magnetic properties? Semi-conductors: what is hidden behind this term? How do the electronic devices we use every day work? To address these simple questions, the quantum origin of matter needs to be considered.## Syllabus

- Introduction
- Solid State Physics as a science that addresses properties and phenomena in the condensed matter at all relevant scales. Link to applications.

- Example 1 : electronic data processors. Moor’s « law » of miniaturisation, FET transistors.

- Example 2 : electronic memory devices. HDD, SSD etc.

- History of the solid state physics : A short overview.

- Solid State Physics as a science that addresses properties and phenomena in the condensed matter at all relevant scales. Link to applications.
- Drude model of the electron conduction in metals (classic approach)
- Electric conduction phenomenon: knowledges at the beginning of XXth century, Drude’s hypotheses.

- Drude formula of conductivity. Orders of magnitude of relevant parameters.

- Temperature variation of the electric conductance.

- Specific heat.

- Applications of Drude model.

- High-frequency response of Drude’s electron gas (20 min.): AC-conductivity; local equations, propagation.

- Electric conduction phenomenon: knowledges at the beginning of XXth century, Drude’s hypotheses.
- Hall effect
- Description of the phenomenon. Equation of motion of an electron.

- The Hall constant.

- Applications

- Description of the phenomenon. Equation of motion of an electron.
- Phonons (crystal lattice vibrations), Brillouin zones
- Modelling the crystal potential (Lennard-Jones).

- Harmonic approximation.

- Harmonic vibrations of a 1D atomic chain (one atom per unit cell).

- Harmonic vibrations of a 1D atomic chain (two atoms per unit cell).

- Brillouin zones : Bravais lattice, Vigner-Seitz cell, construction of Brillouin zones of a solid.

- Modelling the crystal potential (Lennard-Jones).
- Quantum model of a non-interaction electron gas (Sommerfeld)
- Limitations and problems with classic Drude model.

- Schrödinger equation. Physical meanning.

- Born von Karman cyclic boundary conditions. Momentum (wave vector) and energy quantization.

- K-space filling. Fermi energy, Fermi sphere.

- Total energy of the system. Density of electronc states (DOS) vs system dimensions.

- TD properties of the Sommerfeld’s electron gas. Specific heat. Strengths and weaknesses of the model.

- Limitations and problems with classic Drude model.
- Quantum near-free electrons model
- Introduction. Historical context.

- A single electron in a periodic potential. Central equation.

- Gap opening (forbidden bands) at the limits of the Brillouin zone. Relation between the gap width and the crystal potential V(r).

- Reduced-zone representation: translation of E(k) branches inside the reduced (1st) Brillouin zone.

- Band occupation. Metals, insulators (semiconductors).

- Introduction. Historical context.
- Tight-binding model. Electronic band dispersion
- Introduction. General ideas.

- Construction of the wave function.

- Energy eigenvalues.

- Dispersion. Group velocity, effective mass.

- Consequence of the existence of the electronic bands on the electronic properties of materials.

- Introduction. General ideas.
- Specific heat of a crystal
- Classical limit : Dulong and Petit law (1812)

- Quantum limit. Phonons.

- Specific heat of a crystal lattice. Einstein model. Debye model.

- Classical limit : Dulong and Petit law (1812)
- Occupation of electronic bands: insulators, semiconductors, metals
- Intrinsic semi-conductors. Fermi level. Effective mass action law. Applications.

- Doped semi-conductors. Microscopic model of a single dopant atom in a solid.

- Examples of applications.

- Intrinsic semi-conductors. Fermi level. Effective mass action law. Applications.
- Introduction to superconductivity
- A bit of history. Discovery of the zero-resistance state.

- Perfect diamagnetism.

- Consequences of the Meissner-Ochsenfeld effect (1933). TD considerations.

- Phase diagram of a superconductor. Vortex.

- Examples of applications

- A bit of history. Discovery of the zero-resistance state.
- Conclusions : recent trends and challenges in the Condensed Matter physics
- Novel quantum materials and nano-structured materials/ Example : low-dimensional semiconducting heterostructures, graphene, topological insulators, surface and interface phenomena). Applications (example: photovoltaics).

- Strongly correlated electron systems (example: cuprates HTSC).

- Mott metal-insulator phase transition materials.

- Novel quantum materials and nano-structured materials/ Example : low-dimensional semiconducting heterostructures, graphene, topological insulators, surface and interface phenomena). Applications (example: photovoltaics).

## Preceptorship

- Vibrations of crystal lattice (phonons 2D).

- Nearly free electrons in a square 2D potential.

- Electronic properties of graphene.

- Doped semiconductors (p-n junctions).

- Upon tutor's choice: Field-Effect transistor; magnetism; Quantum Hall effect; Quantum corral.

**Requirements :**preparatory classes (or L2) + basics of quantum mechanics.

**Evaluation mechanism :**written exam (2 hours).

**Last Modification :**Wednesday 6 September 2017