SUPERCONDUCTIVITY AND QUANTUM MATERIALS SCIENCE

The course Superconductivity and Quantum Materials Science is part of the Quantum Science and Technology curriculum within the Master’s Degree Programme in Engineering Physics. It provides students with the conceptual and methodological tools needed to understand the fundamental principles of quantum materials science and superconductivity, with attention to both basic aspects and technological applications.

The course offers an overview of several classes of quantum materials, namely materials whose unconventional properties arise directly from quantum-mechanical effects manifested on a macroscopic scale. These materials already underpin widely used technologies, such as superconducting magnets in magnetic resonance imaging and giant magnetoresistance sensors employed in magnetic storage devices.

Among the emergent properties of quantum materials, particular emphasis will be placed on superconductivity, owing to both its scientific relevance and its technological potential. The possibility of transporting electrical current without energy dissipation makes superconducting materials especially promising in the context of technological innovation and sustainability. Their applications range from advanced power-distribution systems to magnetic-levitation transport, as well as to important technologies in medicine, research, and quantum electronics. In this context, the search for superconducting materials with increasingly higher critical temperatures represents one of the most active and promising frontiers in contemporary condensed matter physics.

The course therefore addresses topics at the forefront of current international research in condensed matter physics, in line with the scientific interests and development of the Department of Molecular Sciences and Nanosystems. Students will acquire the theoretical tools required to describe and analyse the main physical models underlying the behaviour of quantum materials and superconductors. The course will also introduce a selection of modern experimental techniques commonly used for their characterization and investigation.

By the end of the course, students will have developed a critical understanding of the main themes in the contemporary scientific literature on quantum materials and superconductivity, and will have acquired competencies that are valuable for research activities and technological innovation in this field.

1. Knowledge and understanding
By the end of the course, students will be able to:
- know and understand the fundamental properties of low- and high-critical-temperature superconductors;
- understand the key concepts of BCS theory, such as Cooper pairs and the energy gap;
- know the main physical properties, characteristic features, and phase diagrams of different classes of quantum materials;
- understand, more broadly, the role of scientific culture in the innovation processes of modern technologies.

2. Applying knowledge and understanding
By the end of the course, students will be able to:
- apply the London equations to describe and interpret the electromagnetic properties of superconductors;
- use Ginzburg–Landau theory to describe the main characteristic lengths of superconductors, such as penetration depth and coherence length;
- distinguish and explain, on the basis of the theoretical models studied, the differences between type-I and type-II superconductors.

3. Making judgements
By the end of the course, students will be able to:
- assess the logical consistency of results, both in theoretical contexts and in the analysis of experimental data;
- identify possible errors or inconsistencies through a critical analysis of the methods applied.

4. Communication skills
By the end of the course, students will be able to:
- communicate the acquired knowledge clearly and effectively, using appropriate scientific terminology, both orally and in writing;
- interact with the instructor and with fellow students in a respectful, constructive, and relevant way, especially during discussion and group-work activities.

5. Learning skills
By the end of the course, students will be able to:
- take, organize, and process notes and information effectively, distinguishing contents according to their relevance;
- develop an adequate degree of autonomy in collecting and selecting data and information relevant to the topics under investigation.

The course has no formal prerequisites. However, the topics covered rely on basic knowledge typically acquired in undergraduate courses, in particular Physics I, Physics II (especially electromagnetism), Quantum Mechanics, and Solid State Physics.

The course can be attended either independently or concurrently with Modern Condensed Matter Theory.

The topics covered in the course, many of which are highly complex and in some cases lie at the frontier of contemporary research, will be presented with particular emphasis on their physical meaning, so that mathematical formalism does not obscure conceptual understanding. Although the course is primarily focused on the theoretical foundations of superconductivity and quantum materials, selected topics will also be illustrated through references to experimental techniques currently used in condensed matter physics.

The course is organized into three main and closely interconnected areas.

SUPERCONDUCTIVITY
- phenomenology of superconductivity: transport, magnetic susceptibility, and thermodynamic properties;
- London equations, electromagnetic properties, and penetration depth;
- Ginzburg–Landau theory: coherence length, type-I and type-II superconductors;
- BCS theory: Cooper pairs and energy gap;
- Cooper-pair tunnelling and the Josephson effect;
- superconducting devices: SNS and SIS junctions, SQUIDs, and superconducting photon detectors;
- overview of the main applications of superconductivity;
- high-Tc cuprate superconductors: crystal structure, order parameter, and phase diagram, with particular attention to the strange-metal phase, pseudogap, and charge-density waves.

QUANTUM MATERIALS
- Dirac materials: graphene, topological insulators, and Weyl semimetals;
- other unconventional superconductors: iron-based superconductors, infinite-layer nickelates, and magic-angle twisted bilayer graphene.

EXPERIMENTAL TECHNIQUES
- synthesis techniques for quantum materials: selected examples of deposition processes;
- synchrotron-radiation-based techniques for the study of quantum materials and the reconstruction of their phase diagrams: selected examples of X-ray spectroscopy;
- elastic and inelastic neutron and X-ray scattering for the investigation of charge and magnetic excitations.

- J.R. Waldram: Superconductivity of Metals and Cuprates

Achievement of the course learning objectives is assessed through participation in the activities proposed during the course, including quizzes, and through a final oral examination.

The final examination is held in English and consists of a single oral session divided into two parts:

1. Individual seminar
Students are required to give a 20–25 minute seminar on a topic assigned in advance by the instructor; suggestions from the student are welcome. During the presentation, the student is expected to discuss the general concepts related to the assigned topic in a correct, clear, and comprehensive way, including examples consistent with the level of the lectures and the reference textbook. Original examples, applications, and connections with other course topics will be positively considered, as they reflect a more mature and critical understanding of the subject. A PowerPoint presentation is the recommended format for the seminar, although a blackboard presentation is also possible.

2. Oral discussion on the core topics of the course
The second part of the examination consists of two or three questions on the core contents of the course as presented in the lectures. Students are expected to answer them in a way that demonstrates a solid understanding of the fundamental concepts; when appropriate, they may also use the blackboard. In the assessment, theoretical and experimental aspects will be given equal weight.

Students who regularly attend the course may earn an additional bonus through participation in the quizzes proposed during the lectures. This bonus will be added to the oral examination grade and/or may result in a reduction in the number of questions on the core topics of the course.

oral

The lecturer has a duty to ensure that the rules regarding the authenticity and originality of exam tests and papers are respected. Therefore, if there is suspicion of irregular conduct, an additional assessment may be conducted, which could differ from the original exam description.

An excellent performance (27–30/30) corresponds to an examination in which the student demonstrates a solid, broad, and well-structured command of the concepts covered during the course, together with the ability to establish critical connections among the different topics discussed.

An intermediate grade (22–26/30) corresponds to an overall good preparation, with a fairly complete understanding of the individual topics, but with a limited ability to connect the different themes of the course.

A pass grade (18–21/30) corresponds to the achievement of the minimum learning requirements, with an essential knowledge of the fundamental contents of the course.

The award of honours (lode) is reserved for outstanding performances characterized not only by full mastery of the contents, but also by clarity of presentation, independent judgement, and critical insight.

The course is delivered through:
- lectures, during which the instructor uses the blackboard and/or PowerPoint presentations;
- group-work activities;
- exercises and quizzes carried out in class.

Through the University Moodle platform, the following materials will be made available:
- the teaching materials presented during the lectures;
- supplementary materials for the further study of specific topics covered in the course;
- recordings of the lectures.

The course programme is provisional and may be subject to changes during the academic year.

This subject deals with topics related to the macro-area "Climate change and energy" and contributes to the achievement of one or more goals of U. N. Agenda for Sustainable Development