SUPERCONDUCTIVITY AND QUANTUM MATERIALS SCIENCE

The course "Superconductivity and Quantum Materials Science" is part of the Quantum Science and Technology curriculum of the Master's Degree in Engineering Physics. This module enables students to acquire knowledge and understanding of the fundamental and applied concepts of quantum materials science and superconductivity.

Students will be offered an overview of several classes of quantum materials, which possess unconventional properties that are already having a significant impact on our daily lives. For example, quantum materials are present in common technologies such as hospital MRI machines, which use superconductors, and hard disk drives, which employ giant magnetoresistance sensors. These unconventional properties are direct manifestations of quantum mechanical effects on a macroscopic scale, without which it is impossible to even form an approximate image of these materials.

Among the unconventional properties, particular emphasis will be placed on superconductivity. This property of matter holds enormous potential: by taking full control of that, the ambitious goal is to lead in the near future to unprecedented innovative solutions for sustainability, which is one of the primary missions of the Department of Molecular Sciences and Nanosystems. For example, superconductivity allows for the transport of electricity without energy losses, enhancing the efficiency of power distribution systems. Additionally, it has significant applications in transportation, such as magnetic levitation trains, which promise faster and cleaner transportation. The search for superconducting materials with critical temperatures closer to room temperature is one of the most promising frontiers for revolutionizing technology and reducing environmental impact.

Therefore, the course addresses cutting-edge topics in ongoing research not only within the Department but also in the broader contemporary scientific community, particularly in condensed matter physics, both basic and applied. Through this course, students will develop theoretical skills to understand quantum materials and analyze the fundamental models and properties of superconductors. Additionally, the course will include the study of some modern experimental techniques commonly used for the characterization and analysis of these materials.

By the end of the course, students will be able to develop critical thinking about contemporary scientific literature and will be prepared to actively contribute to technological and scientific innovation in the field of quantum materials.

1. Knowledge and Understanding
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, characteristics, and phase diagrams of different classes of quantum materials.
More generally, understand the importance of scientific culture in the innovation processes of modern technologies.

2. Ability to Apply Knowledge and Understanding
Apply London equations to superconductors to explain their electromagnetic properties.
Use Ginzburg-Landau theory to describe various characteristic lengths of superconductors, such as penetration depth and coherence length, and explain the differences between type I and type II superconductors.

3. Autonomy of Judgment
Evaluate the logical consistency of results, both in theoretical contexts and in the case of experimental data.
Recognize possible errors through a critical analysis of the applied method.

4. Communication Skills
Communicate the acquired knowledge using appropriate terminology, both orally and in writing.
Interact respectfully and constructively with the instructor and fellow students, especially during group work.

5. Learning Skills
Take effective notes, selecting and gathering information according to its importance and priority.
Be sufficiently autonomous in collecting data and information relevant to the investigated issue.

The course has no formal prerequisites; however, the material covered in the lectures refers to concepts discussed in the undergraduate courses of Quantum Mechanics, and Solid State Physics.

The course can be taken independently or concurrently with “Modern Condensed Matter Theory”.

The topics covered, many of which are of considerable complexity and at the frontiers of contemporary research, will be presented with an emphasis on their physical significance, ensuring that the mathematical formalism does not overshadow the fundamental understanding. Although this course focuses on the theoretical foundations of superconductivity and quantum materials, concepts will occasionally be illustrated by reference to experimental techniques used in the field of condensed matter.

The three main areas, which will often be interconnected, that the course will cover are as follows:

SUPERCONDUCTIVITY
- Phenomenology: transport, susceptibility, thermodynamics.
- London equations, electromagnetic properties, penetration depth.
- Ginzburg-Landau theory: coherence length, type I and type II superconductors.
- BCS theory: Cooper-pairing, energy gap.
- Cooper pair tunneling, Josephson effect.
- Superconducting devices: SNS and SIS junctions, SQUIDs, superconducting photon detectors.
- Overview of applications.
- Cuprate High-Tc superconductors: structure, order parameter, phase diagram (strange metal, charge density wave, pseudogap).


QUANTUM MATERIALS
- Dirac materials: graphene, topological insulators, Weyl semimetals.
- Unconventional superconductors: iron-based superconductors, infinite-layer nickelates, magic-angle graphene.

EXPERIMENTAL TECHNIQUES
- Synthesis techniques for quantum materials: selected examples of deposition processes.
- Synchrotron radiation-based techniques for understanding quantum materials and building their phase diagram: selected examples of X-ray spectroscopy.
- Elastic and inelastic scattering of neutrons and x-rays for probing charge and magnetic excitations.

- J.R. Waldram: Superconductivity of Metals and Cuprates
- J. F. Annett: Superconductivity, Superfluids and Condensates

The achievement of the course objectives is assessed through participation in activities (quizzes) during the course and a final oral exam.

The exam consists of two parts held during a single interview, in English.
1) A seminar of 20-25 minutes on a subject pre-assigned by the teacher (suggestions from the student are welcome). The student must present the general concepts of the topic in a correct and comprehensive manner, providing examples at the level of the lectures and the textbook. The student is also encouraged to look for original examples, applications, and interconnections with other subjects to demonstrate a higher level of understanding. A PowerPoint presentation is best suited for the seminar, but the blackboard option is also possible.
2) Two/three questions on the core of the course as presented in the lectures. The student is required to answer (if needed, with the support of the blackboard) to show their understanding of the basic concepts and notions of the course. Theoretical and experimental aspects will be equally valued.

A fully successful exam (27-30/30) will be deemed when a solid and broad mastery of the concepts discussed during the classes is demonstrated. An average grade (22-26/30) will be the result of fairly complete understanding of individual themes but with limited interconnection among subjects. A pass level (18-21/30) will correspond to a minimum knowledge of individual notions.

Students attending the lectures can accumulate additional points by participating in quizzes proposed in class. The bonus will be added to the final oral exam grade and/or result in a reduction in the number of questions on the core of the course.

The teaching methods are organized as follows:
- Lectures, during which the teacher uses either the blackboard or PowerPoint presentations.
- Group work activities and exercises/quizzes assigned in class.

Through the university's "Moodle" platform, the following will be made available:
- The teaching materials presented during the lectures;
- Supplementary materials for in-depth study of specific topics covered in class.

English

The syllabus is still provisional and may be subject to changes.

oral

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