Studying at York
Condensed Matter Physics: Electrons in Solids - PHY00073H
- Department: Physics
- Credit value: 20 credits
- Credit level: H
- Academic year of delivery: 2024-25
Module summary
To understand the rich physical properties of materials such as electrical conductivity, magnetism or optical reflectivity and absorption, it is necessary to study the electronic structure and transport properties of the electrons in solids. Starting with the classical free electron gas approximation, we will develop the concepts of the Fermi gas and nearly free electron theory making use of the quantum mechanical description of electrons in a periodic potential. This leads to the band structure model, which will allow us to describe material systems such as semiconductors and metals. These concepts will then be used to obtain insights into the origin of magnetism, superconductivity and the optical properties of materials. State of the art techniques, that allow the various electronic structures in materials to be measured, will be highlighted and discussed. Finally, the role of surfaces and interfaces in modifying the electronic properties of solids will be visited.
Related modules
Pre-requisites: Quantum Mechanics, Statistical and Solid State, stage 2, or equivalent
Module will run
| Occurrence | Teaching period |
|---|---|
| A | Semester 2 2024-25 |
Module aims
Starting with the classical free electron gas approximation, we will develop the concepts of the Fermi gas and nearly free electron theory making use of the quantum mechanical description of electrons in a periodic potential. This leads to the band structure model, which will allow us to describe material systems such as semiconductors and metals. These concepts will then be used to obtain insights into the origin of magnetism, superconductivity and the optical properties of materials. State of the art techniques, that allow the various electronic structures in materials to be measured, will be highlighted and discussed. Finally, the role of surfaces and interfaces in modifying the electronic properties of solids will be visited.
Module learning outcomes
Understand the different models involved in describing the various electronic interactions and the underlying physical principles.
Mathematically describe and apply the free and nearly free electron approximations in solids and evaluate these systems in environments with constant electric and magnetic fields
Understand how the electronic structure affects the optical properties of solids.
Distinguish the different types of magnetic and dielectric properties in solids.
Understand the principles and characteristics of superconductivity
Explain how the surface modifies the electronic properties of solids.
Understand the various transport phenomena in materials and their applications.
Detail the various experimental techniques used to probe the electronic structure and excitations of electrons in solids including the benefits and limitations of each.
Module content
Solid State Physics: Electrons in Solids
Free electron gas approximation: (Drude – d.c. and a.c. response)
Free electron gas approximation - Sommerfeld Model: Fermi-Dirac statistics, Fermi-sphere, Fermi-distribution, density of electronic states, Energy dispersion
Electrical conductivity of the Fermi-gas: Interactions with electric & magnetic fields.
Nearly Free electron model: Electrons in a periodic potential, Reduced Zone scheme, Extended Zone scheme.
Tight Binding Model: 1D chain, simple cubic and body centred cubic.
Band structure and band gap, Effective electron mass approximation
The Fermi surface: Measuring the Fermi surface, de-Haas van Alphen effect
Boltzmann transport equation
Failures of the Band-theory of Metals and Insulators
Optical processes in metals and semiconductors
Dielectrics and Ferroelectrics: Properties of dielectrics, Polarizability, Clausius-Mossotti relation, Ferroelectrics
Origin and properties associated with diamagnetism and paramagnetism (both localised and of conduction electrons).
Ordered magnetism: ferromagnetism, antiferromagnetism and ferrimagnetism. Curie-Weiss and Neel Laws, Weiss Molecular field, direct and indirect exchange interactions, band ferromagnetism. Ising and Hubbard model of Ferromagnetism including Stoner Criteria.
Spin waves and spin wave dispersion.
Superconductivity: London equations, Meissner effect and BCS theory
Surface Physics: Crystal surfaces, surface electronic structure, work function, surface states, Thermionic emission. Role of surfaces in heterogeneous interface formation
The role of solid state physics in technology
Motivation for studying surfaces and interfaces. Relationship to technology - “the interface is the device”
2DEGs: Quantum Hall effect, High electron mobility transistor
Spintronics: semi-classical free electron theory, classical magnetoresistance:
Spin-dependent transport: Giant Magnetoresistance, Tunnelling Magnetoresistance, Spin Transfer torque
Characterization of the solid state
Overview of limitations and advantages of different probes for solid state analysis: atoms, ions, photons, and electrons
Interaction and detection of scattered electrons / photons from solids: elastic and inelastic mean free path, attenuation length, elastic scattering cross section, stopping power.
Spectroscopic techniques to measure band structure and electronic excitations: electron spectroscopy, loss spectroscopy, Auger electron spectroscopy, X-ray photoelectron spectroscopy, ARPES, inelastic neutron scattering, STS and SP-STM, VSM.
Indicative assessment
| Task | % of module mark |
|---|---|
| Closed/in-person Exam (Centrally scheduled) | 80 |
| Essay/coursework | 20 |
Special assessment rules
None
Indicative reassessment
| Task | % of module mark |
|---|---|
| Closed/in-person Exam (Centrally scheduled) | 80 |
Module feedback
'Feedback’ at a university level can be understood as any part of the learning process which is designed to guide your progress through your degree programme. We aim to help you reflect on your own learning and help you feel more clear about your progress through clarifying what is expected of you in both formative and summative assessments.
A comprehensive guide to feedback and to forms of feedback is available in the Guide to Assessment Standards, Marking and Feedback. This can be found at:
https://www.york.ac.uk/students/studying/assessment-and-examination/guide-to-assessment/
The School of Physics, Engineering & Technology aims to provide some form of feedback on all formative and summative assessments that are carried out during the degree programme. In general, feedback on any written work/assignments undertaken will be sufficient so as to indicate the nature of the changes needed in order to improve the work. Students are provided with their examination results within 25 working days of the end of any given examination period. The School will also endeavour to return all coursework feedback within 25 working days of the submission deadline. The School would normally expect to adhere to the times given, however, it is possible that exceptional circumstances may delay feedback. The School will endeavour to keep such delays to a minimum. Please note that any marks released are subject to ratification by the Board of Examiners and Senate. Meetings at the start/end of each semester provide you with an opportunity to discuss and reflect with your supervisor on your overall performance to date.
Our policy on how you receive feedback for formative and summative purposes is contained in our Physics at York Taught Student Handbook.
Indicative reading
Introduction to Solid State Physics: Kittel
Solid State Physics: Ashcroft and Mermin