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MMath&Phys Mathematics and Physics / Course details
Year of entry: 2024
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Course unit details:
Condensed Matter Physics
|Available as a free choice unit?
Condensed Matter Physics
|Properties of Matter
|Fundamentals of Solid State Physics
To introduce important concepts in condensed matter physics, one of the most active areas of research in modern physics that govern the behaviour of materials in the world around us. This includes a detailed description of periodicity in solids and how it governs electronic properties. Use this quantum mechanical description to understand the emergence of magnetic order and magnetic transition in solids. Generalise the concept of ordering and phase transitions to soft matter. To become familiar with the language of condensed matter physics, enabling the understanding of research papers.
On completion successful students will be able to:
1. construct reciprocal lattices of simple crystal structure, and relate them to x-ray diffraction data.
2. calculate band structures for simple 2D and 3D tight-binding models and construct nearly-free electron approximations.
3. use the nearly-free-electron approximation to calculate equilibrium properties.
4. use the semiclassical dynamics of electrons in solids to interpret magneto-conductance data and its relation with the Fermi surface.
5. describe and make use of the relationship between bonding and electronic structure of semiconductors, metals and insulators.
6. apply Landau and mean-field theories to describe phase transitions in condensed matter.
1. Reciprocal space in crystallography (2 lectures)
• Revision of crystal structure. The reciprocal (Fourier) space and its properties.
• Interpretation of x-ray diffraction data; the structure factor. Brillouin zones.
2. Probing the electronic structure of solids (10 lectures)
• Bloch theorem and Brillouin zones
• Detailed description of the nearly-free electron model of electronic structure; modifications to the band structure and Fermi surface near zone boundaries.
• The Kronig-Penney model and the tight binding method.
• Graphene. Introduction to heterostructures based on 2D materials.
• Semiclassical dynamics of Bloch electrons; magneto-conductance oscillations as a probe of electronic structure. Failure of the semiclassical approximation
• Pauli paramagnetism and Landau diamagnetism in the free electron model.
3. Phase transitions in condensed matter (9 lectures)
• Introduction to phase transition; concept of order parameter and of phase diagram; order of a phase transition; critical exponents and concept of universality.
• Introduction to mean-field theory of phase transitions, mean-field solution of the 1D Ising model; comparison with the exact result.
• Landau theory. Example of a second order transition: magnetism. Ferromagnetic ground-state
• Exchange interaction between magnetic moments; Heisenberg model; magnons.
• Example of a first order transition: van der Waals fluid. Phase diagram. Critical point.
• Revision, connection with further condensed matter units and research.
Feedback will be offered by examples class tutors based on examples sheets, and model answers will be issued.
C. Kittel, Introduction to Solid State Physics 8th edition (Wiley)
P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge)
R. A. L. Jones, Soft Condensed Matter (Oxford)
N. W. Ashcroft and N.D. Mermin, Solid State Physics (Thomson Press)
J.R. Hook and H.E. Hall, Solid State Physics, (Wiley)
|Scheduled activity hours
|Assessment written exam
|Independent study hours