Introductory description

N/A.

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

1. Overview of the quantum many body problem of the interacting electrons and nuclei in materials
   a) introduction to 2nd quantisation and 1- and 2-electron Green functions
   b) excitation spectra, quasiparticles and spectroscopy measurements
   c) Fermi surface, electron momentum density
2. Recap of electron Density Functional Theory - relationship of Kohn-Sham electronic structure to spectroscopy measurements. Starting point for many body Green function descriptions.
3. Description of transport properties ab-initio
   a) Sommerfeld theory
   b) Beyond the relaxation time approximation
4. Linear response and collective electron effects
   a) dielectric response
   b) spin susceptibility and spin waves
   c) X-ray and neutron scattering experiments
   d) DFT-based calculations
5. DFT and finite temperatures
   a) time scale separation of electronic and nuclear motion, phonons, electron-phonon effects.
   b) atom-atom interchange parameters from DFT for Bragg-Williams models of alloys, CALPHAD database
   c) identification of 'local moment' degrees of freedom in magnetic materials and spin model construction
   d) atom and spin correlation functions - tested against X-ray and neutron scattering data
   e) modelling alloy and magnetic phase diagrams ab-initio and T-dependent electronic
   structure
6. 1. Strong electron correlation effects
      a) Self-interaction correlation, DFT+U and brief overview of Dynamical Mean Field Theory
      b) Examples
      c) Outstanding challenges.

Learning outcomes

By the end of the module, students should be able to:

• It is expected that by the end of this module students will be able to understand the basis to quantum many body theory and the context for Density Functional Theory.
• It is expected that by the end of this module students will be able to appreciate what in principle needs to be calculated to test theory with and interpret spectroscopy, scattering and transport measurements.
• It is expected that by the end of this module students will be able to understand some collective electron effects and how they are explored experimentally and modelled computationally.
• It is expected that by the end of this module students will be able to appreciate how temperature dependent materials properties can be described by the identification and calculation of ab-initio parameters and used in appropriate models; examples of alloy and magnetic phase diagrams.
• It is expected that by the end of this module students will be able to engage with cutting-edge topics in the study of strongly correlated electron materials.

Indicative reading list

‘Electronic Structure’ by Richard Martin (C.U.P)
‘Principles of Condensed Matter Physics’ by P.M. Chaikin and T.C. Lubensky

Subject specific skills

understand the basis to quantum many body theory and the context for Density Functional Theory.
appreciate what in principle needs to be calculated to test theory with and interpret spectroscopy, scattering and transport measurements
understand some collective electron effects and how they are explored experimentally and modelled computationally
appreciate how temperature dependent materials properties can be described by the identification and calculation of ab-initio parameters and used in appropriate models; examples of alloy and magnetic phase diagrams
engage with cutting-edge topics in the study of strongly correlated electron materials

Transferable skills

Mathematical Model-building, comparison to experiment, mathematics, programming and scripting.