Lectures: 20 h - Preceptorship: 10 h

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

1. 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.
   
   
2. 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.
   
   
3. Hall effect
   
   
   • Description of the phenomenon. Equation of motion of an electron.
     
   • The Hall constant.
     
   • Applications
   
   
4. 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.
   
   
5. 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.
   
   
6. 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).
   
   
7. 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.
   
   
8. 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.
   
   
9. 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.
   
   
10. 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
    
    
11. 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.

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