PHYM401 Solid State Physics II

2010-2011

Code: PHYM401
Level: M
Title: Solid State Physics II
Instructors: Dr S. Russo
CATS Credit Value: 10
ECTS Credit Value: 5
Pre-requisites: Solid State Physics I (PHY3102)
Co-requisites: N/A
Duration: M1-M11
Availability: unrestricted
Background Assumed: -
Directed Study Time: 22 lectures
Private Study Time: 78 hours
Assessment Tasks Time: -

Aims

The aim of the module is to develop students' understanding of effects which played a key role in the development of the modern solid state physics and provide a general description of its current trends. The module will require students to apply much of the core physics covered in PHY2006, PHY2009, PHY3143 and PHY3102 to novel systems and engage with fundamental electric, magnetic and optical phenomena in metals and dielectrics. The theme linking the different topics covered is the idea that electrons in solids can be treated as quasi-particles interacting with other quasi-particles: electrons, phonons, photons. In addition to electrons, other excitations in solids are considered, e.g. Cooper pairs, plasmons and polaritons. The module illustrates and draws on several research activities at the School: studies of the metal-to-insulator transition, oscillatory effects in strong magnetic fields, optical and magnetic phenomena.

Intended Learning Outcomes

Students should be able to:

Module Specific Skills

• develop the concept of energy bands in the tight-binding approximation and compare the outcome of this methodology with the nearly-free electron model described in PHY3102;
• explain how the conducting properties of metals are affected by disorder and electron-electron interactions, and describe the types of the metal-to-insulator transition;
• explain the significance of complex Fermi surfaces for transport properties of metals and how the shape of the Fermi surface can be mapped using oscillatory effects;
• develop classical and quantum mechanical descriptions of the electron motion in electric and magnetic fields, Hall and magnetoresistive effects;
• explain characteristic features of superconductors and the origin of superconductivity;
• explain how interaction effects modify the properties of quaisi-paricles in solids and descripe the origin of different excitations: plasmon, polariton, polaron, exciton and magnon;
• explain the origin of the fundamental magnetic phenomena and the basic models in their description;

Discipline Specific Skills

• apply core physics to the solution of problems involving unfamiliar systems;

Personal and Key Skills

• use spatial reasoning to derive qualitative solutions to problems;
• manage the own work.

Learning / Teaching Methods

Lectures and problems classes.

Assignments

Students are given a set of problems to be solved during the course of lectures.

Assessment

One 90-minute examination (100%).

Syllabus Plan and Content

1. Electrons in Metals and the Metal-to-Insulator Transition
   1. Calculations of Band Stucture
      1. Tight-binding
      2. Comparison of tight-binding with the nearly-free electron model
      3. Brief introduction to other methods, e.g. LCAO, Pseudo-potentials, LMTO, LAPW
   2. Mott and Anderson types of the metal-to-insulator transition.
   3. Metal-to-insulator transition in three- and two-dimensional metals. Current situation in the field.
   4. Electron-electron interaction in metals: Fermi liquid
2. Fermi Surface and Electron Dynamics in Metals.
   1. Construction of the Fermi surface and Fermi surfaces of some metals.
   2. Semiclassical model of electron dynamics. Electron motion in crossed magnetic and electric fields.
   3. Hall effect and magnetoresistance.
3. Oscillatory Effects in Strong Magnetic Fields
   1. Landau quantisation of the electron spectrum.
   2. Shubnikov-de Haas and de Haas-van Alphen effects, experimental conditions for their observation.
   3. Mapping of the Fermi surface in three-dimensional metals.
4. Superconductivity
   1. Difference between 'ideal' metal and superconductor. Specific features of magnetic, thermal and optical properties of superconductors.
   2. Isotope effect. The concept of the Cooper pair and the outline of the Bardeen-Cooper-Schrieffer (BCS) theory.
   3. Josephson effects. High-temperature superconductivity.
5. Electrons, Phonons and Photons
   1. Dispersion relation for electromagnetic waves in solids and the dielectric function of the electron gas.
   2. Plasma optics and plasmons.
   3. Dielectic function and electrostatic screening. Screened Coulomb potential.
   4. Phonon-photon interaction: polaritons.
   5. Electron-phonon interaction: polarons. Electron-hole interaction: excitons.
6. Quasiparticles in Low-dimensional Solids
   1. Excitons, plasmons, polarons, and polaritons
   2. Graphene
7. Magnetic Properties of Solids
   1. Diamagnetism, paramagnetism and ferromagnetics: general concepts.
   2. Classical model of atomic diamagnetism.
   3. Langevin (classical) theory of paramagnetism and electron paramagnetism in metals.
   4. Ferromagnetism and antiferromagnetism.
   5. Spin waves and magnons.
   6. Giant magneto-resistance.

Core Text

Kittel C. , Introduction to Solid State Physics, Wiley (UL: 530.41 KIT)

Supplementary Text(s)

Ashcroft N.W. and Mermin N.D. (1976), Solid State Physics, Holt-Saunders, ISBN 0-03-083993-9 (UL: 530.41 ASH)
Burns G. (1985), Solid State Physics, Academic Press, ISBN 0-12-146070-3 (UL: 530.41 BUR)
Hook J.R. and Hall H.E. (1991), Solid State Physics (2^nd edition), Wiley, ISBN 0-471-928054 (UL: 530.41 HOO)

Formative Mechanisms

Students monitor their own progress by attempting the problems set which will be discussed in class. Students who need additional guidance are encouraged to discuss the matter with the lecturer.

Evaluation Mechanisms

The module will be evaluated using information gathered via the student representation mechanisms, the staff peer appraisal scheme, and measures of student attainment based on summative assessment.