MPhys Physics

Year of entry: 2024

Course unit details:Condensed Matter Physics

Unit code PHYS30051 10 Level 3 Semester 1 No

Overview

Condensed Matter Physics

Pre/co-requisites

Unit title Unit code Requirement type Description
Properties of Matter PHYS10352 Pre-Requisite Compulsory
Fundamentals of Solid State Physics PHYS20252 Pre-Requisite Compulsory

Aims

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.

Learning outcomes

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.

Syllabus

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.

Assessment methods

Method Weight
Written exam 100%

Feedback methods

Feedback will be offered by examples class tutors based on examples sheets, and model answers will be issued.

Recommended texts

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)

Useful references

N. W. Ashcroft and N.D. Mermin, Solid State Physics (Thomson Press)

J.R. Hook and H.E. Hall, Solid State Physics, (Wiley)

Study hours

Scheduled activity hours
Assessment written exam 1.5
Lectures 22
Independent study hours
Independent study 76.5

Teaching staff

Staff member Role
Alessandro Principi Unit coordinator