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 classes will be in either language on request.
1. Macroscopic measurement, specific heat, bulk modulus, conductivity.
1.1 Low energy states of matter- experimental observations.
1.2 Tools, confined quantum particle, quantum statistics, harmonic oscillator, perturbation theory.
1.3 Free electrons - degeneracy, thermodynamics and transport.
1.4 Lattice vibrations, phonons, Debye theory, structures with a basis, band gaps.
1.5 Crystalography of a cubic lattice, Brillouin zone and crystal momentum.
2. Electrons in solids.
2.1 Energy and electron confinement.
2.2 Bloch’s theorem, electron bands and effective mass.
2.3 Metals and insulators.
2.4 Almost free electrons and modified Fermi surfaces.
2.5 Classification of solids: 1. Elements–metallic, covalent, molecular, Van der Waals.
2. Compounds, ionic, covalent, Hydrogen bonding.
3. Crystal structure.
3.1 Experimental evidence for periodic structures.
3.2 Bravais lattices, classification and unit cells.
3.3 Reciprocal lattices.
3.4 Neutron and X-ray scattering.
4. Interactions and nonlinearity
4.1 Semi classical dynamics – Bloch oscillations -conductivity (a second look).
4.2 Particles and holes in semi-conductors.
4.3 Thermal conductivity and the Wiedemann-Franz law.
4.4 The (classical) hall effect – the end of free electron theory
The Oxford Solid State Basics
Steven H. Simon
Solid State Physics ~N.W. Ashcroft, N.D. Mermin
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)
Prerequisites for the course are – first courses in quantum mechanics, statistical mechanics and thermodynamics.
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!