Academic Year 2022/2023 - Teacher: ELISABETTA PALADINO

Expected Learning Outcomes

Aim of this course is to provide students with advanced knowledge of Physics of superconductivity and superfluidity from fundamental aspects to applications to quantum technologies.

Knowledge and understanding.
Critical understanding of the most advanced developments of Modern Physics, both theoretical and experimental, and their interrelations, also across different subjects.. Adequate knowledge of advanced mathematical and numerical tools, currently used in both basic and applied research. Remarkable acquaintance with the scientific method, understanding of nature, and of the research in Physics. During the course experimental facts, theoretical models, and applications of superconductivity and superfluidity will be presented with reference to modern experiments, applications, and novel theoretical interpretations.

Applying knowledge and understanding
Ability to identify the essential elements of a phenomenon, in terms of orders of magnitude and approximation level, and being able to perform the required approximations. Ability to use analogy as a tool to apply known solutions to new problems (problem solving). In presenting the phenomenology of superconductivity, emphasis will be given to the most important magnitudes, introducing all other magnitudes as successive approximations.

Making judgements

Ability to convey own interpretations of physical phenomena, when discussing within a research team. Developing one's own sense of responsibility, through the choice of optional courses and of the final project. In presenting the different topics, both during the course and during the final exam, links will be given with other courses (mainly, but not only, belonging to the same curriculum), some of which optional, and with possible topics for a research final project, both experimental and theoretical.

Communication skills
Ability to discuss about advanced physical concepts, both in Italian and in English.

Learning skills.
Ability to acquire adequate tools for the continuous update of personal knowledge. Ability to access to specialized literature both in the specific field of one's expertise, and in closely related fields. Ability to exploit databases and bibliographical and scientific resources to extract information and suggestions to better frame and develop one's study and research activity. Ability to acquire, through individual study, knowledge in new scientific fields. We will often make reference to scientific papers, both reviews and
research articles.

Course Structure

Frontal lectures. Should the circumstances require online or blended teaching, appropriate modifications to what is hereby stated may be introduced, in order to achieve the main objectives of the course.

Required Prerequisites

Knowledge of advanced quantum mechanics, solid state physics, e
preferably also of the theory of many-body systems.

Attendance of Lessons

Attendance to the course is normally compulsory (see the Teaching Regulations of the Degree Course)

Detailed Course Content

  • Basic phenomena and phenomenological theories

Vanishing resistance and Meisser effect - Magnetic flux quantization -  Gorter Casimir model -  Electrodynamics of superconductors: London phenomenological theory. Ginzburg Landau theory -  Bose Einstein condensation - Superfluidity.

  • Mircoscopic theory

Cooper instability -  Origin of the attractive interaction and “s-wave pairing” - BCS theory: BCS ground state. Energy bands and superconducting gap, density of states - Finite temperature effects: critical temperature - Penetration depth – Connection with Gizburg Landau theory.

  • Fundamental aspects

Macroscopic quantum coherence - Coherence and Off-Diagonal Long Range Order: laser, superconductivity and superfluidity - Spontaneus simmetry breaking - Phase-number uncertainty relation.

  • Tunneling in metallic heterostructures

Electron and quasiparticles tunneling - Charging effects – Josephson effect –  Proximity effect - Andreev tunneling.

  • Superconducting devices

Classical dynamics of Josephson circuits and Josephson effect in the presence of magnetic field: Superconducting Quantum Interference Devices (SQUID) - Phase quantization - Quantum dynamics of Josephson circuits - Secondary quantum effecs: superconducting devices for quantum computing.

Textbook Information

M. Tinkham, Introduction to Superconductivity, Dover (2004).

Yuli V. Nazarov and J. Danon, Advanced Quantum Mechanics: a practical guide, Cambridge (2013)

James F. Annet, Superconductivity, superfluids and condensates, Oxford University press (2003)

Steven M. Girvin, Kun Yang, Modern Condensed Matter Physics, Cambridge University Press (2019)

A. O. Caldeira, An introduction to Macroscopic Quantum Phenomena and Quantum Dissipation,

Cambridge University Press (2014)

Course Planning

 SubjectsText References
1Characteristic effecs and phenomenological theoriesM. Tinkham, Introduction to Superconductivity, Cap 1 e 2
2Microscopic theoryM. Tinkham, Introduction to Superconductivity Cap 3 and Nazarov, Danon, Advanced Quantum Mechanics Cap 5
3Gizburg Landau TheoryM. Tinkham, Introduction to Superconductivity Cap 4
4Fundamental aspectsJames F. Annet, Superconductivity, superfluids and condensates, Cap 3
5Classical dynamics of Josephson circuitsM. Tinkham, Introduction to Superconductivity, Cap 6
6Quantum dynamics of Josephson systemsA. O. Caldeira, An introduction to Macroscopic Quantum Phenomena and Quantum Dissipation, par. 3.3 and 3.4
7Superconducting devices for quantum informationSteven M. Girvin, Kun Yang, Modern Condensed Matter Physics, par. 19.9


Learning Assessment Procedures

The assessment of learning is entrusted to an oral exam that consists of (a) exposure of a
topic agreed in advance with the teacher; (b) presentation of a topic chosen by the candidate at the
time of the examination between three topics (of different degree of difficoltà) proposed by the teacher. The
passing the exam depends exclusively on the test (a), while the test (b) contributes to
determine the final assessment. At the request of the student, the test (a) may be replaced by a
text that includes an analytical or numerical calculation, which the student will have to develop in a
independent but assisted manner based on the recommended texts and any review articles recommended by the
- The assessment shall take into account:
level of understanding of the exposed contents; accuracy in the exposure of the calculations; ability to
link with other subjects of previous courses and the current course, and to give examples;
language properties and expositive clarity.

- The assesment of learning can also be implemented electronically, if the conditions
should you require.

Examples of frequently asked questions and / or exercises

The following questions do not constitute an exhaustive list but represent only a few examples: Phenomenology of superconducting materials. Theory phenomenological of Ginzburg Landau. Distinction between superconductors of the first and second types. Hypothesis of the BCS model. Structure of the BCS ground state. Excited levels of a superconductor. Josephson effect. Electronic tunnel in superconducting-normal metal junctions and superconducting-superconducting junctions. Spontaneous symmetry breaking.