Teaching
I will give a 20h graduate lectures on "Mesoscopic superconductivity" in April-May 2017.
The exploration of superconductivity at mesoscopic scales has known a continuous progress over the last thirty years. It has enabled the study of many fundamental issues, such as the minimal size for a material to become superconducting, how superconducting properties can be induced in a non-superconducting metal with the help of the proximity effect, or which new properties may result from the competition between the induced superconductivity and a magnetic order that would be a priori incompatible. These advances have also been useful to build superconducting quantum circuits, based on the Josephson effect. Hybrid superconducting systems are also promising for realizing Majorana bound states that are possible candidates to realize topologically protected quantum computation.
The aim of the lecture is to provide an introduction to the main concepts in this field. The course is addressed to anyone interested and having some basic knowledge in quantum mechanics, statistical physics, or condensed matter physics.
Lectures on Tuesdays April 4, 11, 25, and May 2 (9am-12am) and May 9, 16, 23, and 30 (9am-11am) in GreenEr - Polygone scientifique - Salle 2 D 006
Outline (with slides on related experiments):
- 1) Superconducting grains (BCS theory, fluctuations, parity effect)
- 2) Quasiparticle current in N/I/S junctions (cooling, charge imbalance, Coulomb blockade)
- 3) Andreev reflection (doubling of the noise, crossed AR, MAR)
- 4) Andreev bound states (quantum dots: Shiba state, Kondo effect vs superconductivity, SIS junction)
- 5) Classical Josephson effect (Meissner, SQUIDs, Fraunhoffer, Josephson radiation, Shapiro)
- 6) Quantum Josephson effects (Cooper pair box, Superconducting qubit)
- 7) Josephson chains and arrays (phase slips, BKT, superconductor/insulator transition)
- 8) Guest lecture on experimental aspects [Part 1] [Part 2], by Timothy Duty, University of New South Wales, Australia
- 9) Superconducting hybrids and proximity effect (N/S and F/S hybrids)
- 10) Topological superconductivity (Kitaev model, Majorana fermions, signatures)
Handwritten notes of the lecture given in 2015 can be found here.
Handwritten notes (in French) of a 3h lecture on "hybrid systems" given in 2012 in Cargese
can be found here.
Lecture notes on "applications of symmetries in superconductivity" can be found here.
Useful textbooks on superconductivity:
- Introduction to superconductivity, M. Tinkham.
- Superconductivity of metals and alloys, P.G. De Gennes.
- Fundamentals of the theory of metals, A.A. Abrikosov.
Recent textbooks including a discussion of some aspects of mesoscopic superconductivity:
- Theory of fluctuations in superconductors, A. Larkin and A. Varlamov.
- Quantum transport, Yu. Nazarov and Ya. Blanter.
- The physics of nanoelectronics, T. T. Heikilla.
Pedagogical reviews on aspects of the proximity effect in mesoscopic superconductivity:
-
Random-matrix theory of quantum transport, C.W. Beenakker, Rev. Mod. Phys. 69, 731 (2007).
- Quasiclassical Green's function approach to mesoscopic superconductivity, W. Belzig et al., Superlattices and Microstructures, 25, 1251 (1999).
- Scattering Theory of Mesoscopic Superconductivity, S. Datta, P. F. Bagwell and M. P. Anantram, Physics of Low Dimensional Structures, 3, 1 (1996).
Pedagogical reviews on topological superconductivity and Majorana fermions:
-
Colloquium: topological insulators, M. Z. Hasan and C.L. Kane, Rev. Mod. Phys. 82, 3045 (2010).
-
New directions in the pursuit of Majorana fermions in solid state systems, J. Alicea, Rep. Progr. Phys. 75, 076501 (2012).
-
Random-matrix theory of Majorana fermions and topological superconductors, C.W.J. Beenakker, Rev. Mod. Phys. 87, 1037 (2015).