SUPERCONDUCTIVITY

Aim of this course is to provide students with advanced knowledge of Physics of superconducting materials and of graphene and on their potential applications in nano- and 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 we will present both experimental facts, theoretical models, and applications concerning the phenomenology of superconductivity, with reference to modern experiments, applications, and novel theoretical interpretations.

Applying knowledge and understanding

Ability to identify the essential elements in 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 one's 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.

Frontal lectures.

• 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.

• Mircoscopic Bardeen-Cooper-Schrieffer (BCS) theory

Cooper pairs. Origin of the attractive interaction and “s-wave pairing” - BCS ground state. Energy bands and superconducting gap, density of states - Finite temperature effects: critical temperature - Penetration depth – Electron tunneling and Cooper-pair tunneling – Josephson effect – Josephson effect in the presence of magnetic field: Superconducting Quantum Interference Devices (SQUID).

• Grafene

Band structure: tight binding model. Weyl Dirac fermions. Landau levels. Klein tunneling, Landuer Buettiker formalism. Graphene Josephson junctions (SNS).

• Special topics

Josephson effect in mesoscopic junctions – Superconducting artificial atoms - Introduction to high-temperature superconductivity - The Lawrence Doniach model. Superconductivity in graphene, hydrodynamic transport in graphene.

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

M. I. Katsnelson, Graphene: carbon in two dimensions, Cambridge University Press (2009).