MPhys Physics with Study in Europe

This units introduces frontier topics of Condensed Matter physics, in particular the physics of superconductors, low-dimensional quantum materials, and nanoscale systems and techniques to probe them.  

This unit aims to provide an overview of advanced topics in Condensed Matter Physics, in particular superconductivity, low-dimensional quantum systems, and nanoscale physics. The unit develops the basic frameworks required to understand topological phases of matter and other emergent phenomena in Condensed Matter systems and at the nanoscale/atomic-scale and related modern techniques to probe such phenomena and physical properties. The unit also presents experimental developments in the field that have occurred in the last few years, giving students a flavour of modern research work in academia or industry. 

ILO 1

Explain and analyse the fundamental physical principles governing superconductivity, topological phases, and nanoscale phenomena and related measurement approaches.  

ILO 2

Apply theoretical models and quantitative methods to derive, estimate, and interpret key physical quantities and phenomena in superconductors, quantum materials, and nanoscale systems.  

ILO 3

Analyse, evaluate and interpret experimental data, models, and physical behaviours in advanced quantum and nanoscale systems using modern scientific methods.

ILO 4

Demonstrate how standard and modern experimental techniques can be used to study quantum and nanoscale systems.  

Syllabus (S1, 33 lectures)

Superconductors (11 Lectures)  

1. Properties of superconductors and their microscopic and macroscopic description  

- Persistent current and Meissner effect, evidence for energy gap (1 lecture)

- Elements of BCS theory, excitations (1 lecture)

- Thermodynamics and critical field (1 lectures)

2. London and Ginzburg-Landau phenomenological theories

- London electrodynamics and penetration depth, macroscopic wavefunction and flux  quantization. (2 lectures)

- Ginzburg-Landau theory and coherence length (2 lecture)

3. Vortex state and Josephson effect, applications

- Type I and type II superconductors, vortex state, flux pinning and applications. (2 lectures)

- Weakly coupled superconductors, Josephson effect, DC SQUID and applications. (1 lectures)

4. Revision (1 lecture)  

Low-dimensional systems and quantum phenomena (11 Lectures)  

1. Topological phases of matter (3 lectures):  

- integer, fractional and anomalous Hall effects,  

- topological insulators, edge physics

2. Quantum materials (3 lectures):  

-  2D materials, moiré heterostructures,  

-  twistronics  

3. Emergent phenomena in quantum materials (4 lectures)  

-  magnetism, spintronics, ferroelectricity.

4. Revision (1 lecture)  

Nanoscale physics (11 Lectures)  

1. Large-scale measurement techniques and associated physical quantities (3 lectures)

- electric measurements (resistivity, impedance, magnetotransport, electrochemical)

- far-field optical microscopies (bright-field, fluorescent, confocal)

2.  Atomic-scale measurement techniques and associated physical quantities (4 lectures)

-  Electron microscopy  

- Scanning Tunnelling Microscopy, Atomic Force Microscopy and Scanning Near-Field Optical Microscopy  

- Advanced electrical, magnetic and in-liquid microscopy techniques.  

3. Examples of application on nanoscale systems (3 lectures):

- case study: 2D materials.  

- case study: 2D liquids.  

4. Revision (1 lecture) 

Synchronous learning:

33 lectures

3 revision sessions / example classes

Asynchronous learning:

Material available online prior to teaching sessions:

Lecture slides  

Bernevig, B. A., & Hughes, T. L. (2013). Topological Insulators and Topological Superconductors. Princeton, NJ: Princeton University Press.

Hasan, M. Z., & Kane, C. L. (2010). Colloquium: Topological insulators. Reviews of Modern Physics, 82(4), 3045–3067.

Prange, R. E., & Girvin, S. M. (Eds.). (1990). The Quantum Hall Effect (2nd ed.). New York, NY: Springer-Verlag.

Aoki, H. (Ed.), & Dresselhaus, M. S. (Ed.). The Physics of Graphene (2nd ed.). Cambridge, UK: Cambridge University Press.

Avouris, P., Heinz, T. F., & Low, T. (Eds.). (2017). 2D Materials: Properties and Devices. Cambridge, UK: Cambridge University Press.

Intermolecular and Surface Forces, Jacob N. Israelachvili, Academic Press - Third Edition (2011)

Tilley, D.R. & Tilley, J. Superfluidity and Superconductivity, (Bristol: Hilger 1990);

Annett, J.F. Superconductivity, Superfluids and Condensates (Oxford 2004);

Schmidt, V.V. The Physics of Superconductors:  Introduction to Fundamentals and Applications, (Springer 1997);