Matière condensée / Condensed Matter

Etablissement
École Normale Supérieure de Lyon
Discipline
Physique
Niveau
M1+M2
Semestre
1e semestre
Crédits ECTS
6.00
Volume Horaire Cours
24
Volume Horaire TD
24
Présentation

When many body systems are allowed to relax their energy, they are observed to form hadrons on the GeV scale, plasmas of electrons and nuclei on the MeV scale, neutral atoms and molecules on the eV scale and finally dense, condensed matter phases on the Kelvin scale – this end game, which is a subtle trade off between electrostatic interactions and quantum phenomena, is the subject of this course. 

Condensed phases of matter show a stunning variation of physical phenomena and geometrical structures. For example, without talking of superconductors or engineered metamaterials, the room temperature resistivity of materials varies over 25 orders of magnitude between good metals and good insulators – how can that be? It’s a direct consequence of the difference between discrete and continuous translational symmetry, I hear you say !?! This will be discussed in detail in the course.

Despite their complexity, a good quantitative picture of low temperature behaviour can emerge in terms of “quasi-particle” excitations – composite objects that look like fundamental particles in a vacuum. Examples are phonons, Landau or Dirac electronic quasi-particles or even exotic objects like Higgs Bosons or magnetic monopoles. Sadly, the latter will probably be outside the range of this course but they give notice to the fact that modern research often uses condensed matter hosts as testing grounds for the most fundamental physics and mathematics. 

A vital element in condensed matter research, either fundamental or applied, is the synthesis of new materials and solid state chemistry is probably the most important element in this vibrant research domain. The search for new, quantum materials is on and the stakes are high! Quantum computers, new devices, ever more resistant materials, testing grounds for fundamental ideas – the motivation is diverse and the opportunities are there. 

The lecture course will be given in English with interventions in French and problem classed will be in either language on request.

Plan du cours

1. Macroscopic measurment, specific heat, bulk modulus, conductivity. -Low energy states of matter. -Free electrons - degeneracy, thermodynamics and transport. -Lattice vibrations, phonons, Debye theory, structures with a basis, band gaps. -Crystalography of a cubic lattice, Brilloin zone and Bloch waves.

2. Electrons in solids. -Energy and electron confinement. -Bloch’s theorem, electron bands and effective mass. -Almost free electrons and modified Fermi surfaces. -Metals and insulators. -Classification of solids, ionic, covalent, Van der Waals, Hydrogen bonding.

3. Crystal structure. -Experimental evidence for periodic structures. -Bravais lattices, classification and unit cells. -Reciprocal lattices. -Neutron and X-ray scattering.

4. Interactions and nonlinearity -Electronic conductivity – a second look. -Thermal conductivity and the Wiedemann-Franz law. -Hole conductivity in semi-conductors. -Electron-electron interaction and why one can often ignore it.

5. Some modern themes* -Quantum fluids -Emergent phenomena -Topology

*Time permitting

Bibliographie

The Oxford Solid State Basics
Steven H. Simon

Solid State Physics ~N.W. Ashcroft, N.D. Mermin
Thomson Learning
Hardcover - May 1976

La physique des solides
de Neil-W Ashcroft, N-David Mermin

Introduction to Solid State Physics ~Charles Kittel
John Wiley and Sons (WIE)  Hardcover - October 1995

Principles of the Theory of Solids ~J. M. Ziman
Cambridge University Press
Paperback - November 29, 1979

Principles of Condensed Matter Physics ~Paul Chaikin
Cambridge University Press; 
Revised ed. edition (28 Sept. 2000)

 

Pré-requis

Un premier cours de mécanique statistique et de mécanique quantique, niveau L3

Modalités d'examen

There will be a 3 hour written exam at the end of the course with text in English and in French and replies in either language. The exam will be open book, that is all hand-written notes, hand-outs and problems can be take into the exam, but no books or internet connections are allowed!