Introduction to Condensed Matter Physics
SCQF Level 10
Academic year(s): 2019-2020
SCOTCAT credits : 15
ECTS credits : 7
Level : SCQF Level 10
Availability restrictions: Not automatically available to General Degree students
This module explores how the various thermal and electrical properties of solids are related to the nature and arrangement of their constituent atoms. For simplicity, emphasis is given to crystalline solids. The module covers: the quantum-mechanical description of electron motion in crystals; the origin of band gaps and insulating behaviour; the reciprocal lattice and the Brillouin zone, and their relationships to X-ray scattering measurements; the band structures and Fermi surfaces of simple tight-binding models; the Einstein and Debye models of phonons, and their thermodynamic properties; low-temperature transport properties of insulators and metals, including the Drude model; the physics of semiconductors, including doping and gating; the effect of electron-electron interactions, including a qualitative account of Mott insulators; examples of the fundamental theory applied to typical solids.
Pre-requisite(s): Before taking this module you must pass PH3081 or pass PH3082 or ( pass MT2506 and pass MT2507 ) and ( pass PH3061 or pass CH3712 )
Co-requisite(s): You must also take PH3061 or take PH3082 or take PH3081
Weekly contact: 3 lectures or tutorials
Scheduled learning hours: 34
Guided independent study hours: 116
As used by St Andrews: 2-hour Written Examination = 80%, Coursework = 20%
As defined by QAA
Written examinations : 80%
Practical examinations : 0%
Re-assessment: Oral Re-assessment, capped at grade 7
Module coordinator: Dr C A Hooley
Module teaching staff: Dr C Hooley
To set up a quantum-mechanical theory of the propagation of electrons and lattice vibrations in solids, and to link this theory to various observable properties (specific heat capacity, magnetic susceptibility, X-ray diffraction, electrical resistivity). To understand, using this theory, the following models and properties of solids:
By the end of this course, students should:
Introductory material (3 lectures):
The quantum mechanics you'll need; the thermal and statistical physics you'll need; a survey of the properties of solids.
The Sommerfeld model – neutral fermions in a box (3 lectures):
Momentum space and the Fermi sphere; the density of states and the Fermi energy; the specific heat capacity and magnetic susceptibility of the Fermi gas.
The tight-binding model – neutral fermions hopping on a lattice (4 lectures):
Exact solution of the one-dimensional case; the interpretation of the phase ; the Brillouin zone; the group velocity; Bloch oscillations; how a two-site basis leads to two energy bands.
The nearly-free-electron model – neutral fermions in a weak periodic potential (3 lectures):
The Fourier transform of a periodic potential; resonant scattering, standing waves, and band gaps; the Brillouin zone (again); multiple bands, and the comparison to the tight-binding model.
The reciprocal lattice (4 lectures):
The reciprocal lattice as the Fourier transform of a periodic potential; Laue diffraction; square vs. triangular Laue patterns; Fermi surfaces for tight-binding models with different lattice geometries.
Phonons – quantised vibrations of the crystal lattice (3 lectures):
An exact solution of a one-dimensional model of phonons; acoustic and optical phonons; the specific heat capacity of phonons; the Debye temperature.
Electrical transport in solids (3 lectures):
The Drude model; the temperature-dependence of the electrical resistivity of metals; insulators, metals, and semiconductors.
The physics of semiconductors (2 lectures):
Direct and indirect band gaps; doping and gating semiconductors.
Electron-electron interactions (2 lectures):
Screening of the Coulomb interaction in metals; the Mott metal-insulator transition.
Additional information on continuous assessment etc.
The continuous assessment for the module consists of four tutorial sheets, each of which is worth 5 per cent of the credit for the module. Hand-out dates and hand-in deadlines for these may be found on the PH4039 Moodle page. Students taking this module will be divided into tutorial groups, each of which will meet four times during the semester.
This module may not contain material that is part of the IOP “Core of Physics”, but does contribute to the wider and deeper learning expected in an accredited degree programme. The skills developed in this module, and others, contribute towards the requirements of the IOP “Graduate Skill Base”.
Please view University online record: http://resourcelists.st-andrews.ac.uk/modules/ph4039.html
Please also read the general information in the School's honours handbook that is available via st-andrews.ac.uk/physics/staff_students/timetables.php.