MODERN CONDENSED MATTER PHYSICS

This module is part of the Quantum Science and Technology curriculum within the Master's Degree in Engineering Physics. It provides students with advanced knowledge of the fundamental concepts of condensed matter physics, which are crucial for materials science applied to nano and quantum technologies.
The module is connected to ongoing research in the Department and has two main objectives:
1. To prepare students for research in condensed matter physics by introducing models that have shaped our current microscopic understanding of complex electronic properties and phenomena in materials, in particular those used for used for information and quantum technologies.
2. To train students to carry out numerical calculations of the electronic structure of materials for the qualitative prediction of their key properties.
The module will cover Dirac materials, topological systems, (quantum) transport, magnetism, and it will introduce superconductivity. Particular attention will be given to developing problem solving skills, explaining how properties of materials can be practically calculated from models using simple approximations. Furthermore, recent scientific literature will be presented to help students learn how to perform a critical analysis.

1. Knowledge and understanding
• Broad and detailed understanding of the fundamental concepts of condensed matter physics.
• Ability to analyze and explain the physical phenomena emerging in systems used in quantum technologies.

2. Ability to apply knowledge and understanding
• Solve equations related to quantum models to describe some of the main classes of materials studied in modern research.
• Calculate the electronic, conductive, and magnetic properties of materials.
• Participate in research projects in the field of condensed matter theory.

3. Autonomy of judgment
• Identify and correct potential errors through a critical analysis of the applied methods.
• Compare theoretical results with experimental data.
• Understand and critically evaluate the scientific literature in the field of the condensed matter physics.

4. Communication skills
• Clearly and precisely communicate acquired knowledge, using appropriate terminology, both in written and oral forms.

5. Learning skills
• Take notes by selecting and organizing information based on its relevance and priority.
• Achieve a sufficient level of autonomy in gathering relevant data and information from scientific literature.

To enroll in this course, students are required to have knowledge of General Physics, Quantum Mechanics and Mathematical Methods at the level covered in a three-year scientific degree program.
While it is not mandatory to have attended the Solid State Physics course (or another equivalent course) of the three-year scientific degree program, having prior knowledge of some basic solid state physics may be beneficial. In any case, students' pre-existing knowledge will be assessed at the beginning of the course, and the program will be adjusted accordingly.

1. Band theory, focusing on calculations of band structures within the linear combination of atomic orbitals method.
2. Numerical calculations of electronic properties within the linear combination of atomic orbitals method.
3. Graphene.
4. Lattice vibrations and phonons.
5. Boltzmann transport theory.
6. Electrical conduction in metals.
7. Brief introduction to the optical properties of materials.
8. Diamagnetism and paramagnetism.
9. Landau levels.
10. Berry phase.
11. Topological materials.
12. Second quantization.
13. Ferromagnetism and antiferromagnetism. Systems with localized magnetic moments versus itinerant magnetism.
14. Bardeen–Cooper–Schrieffer (BCS) theory of superconductivity.

Efthimios Kaxiras and John D. Joannopoulos, Quantum Theory of Materials (Cambridge University Press, 2019)
Steven M. Girvin and Kun Yang, Modern Condensed Matter Physics (Cambridge University Press, 2019)
Giuseppe Grosso and Giuseppe Pastori Parravicini, Solid State Physics, Second Edition (Academic Press, 2014)
Adrian P. Sutton, Electronic Structure of Materials (Calderon Press, 1994)
Additional materials available online about specific subjects may be suggested during the lectures.

The exam consists of an individual project and an oral exam:
1. Individual Project: This entails solving a series of interconnected exercises on current topics in condensed matter physics. This project will require the use of models and methods that will be covered in detail throughout the course. The exercises may be solved either analytically or numerically, for example using Mathematica or simple Python programs. The results, presented in the form of graphs or tables, should be compiled into a document (in Word or LaTeX) or a PowerPoint presentation and submitted to the teacher at least 24 hours before the oral exam. Otherwise, the student will not be granted access to the oral exam. It is estimated that the project will require one to two weeks of work at home.
2. Oral Exam (30-40 minutes): During the oral exam, the student will present the project results and answer in-depth questions on the fundamental concepts of the course. This session will also serve to verify the student's understanding of the models and techniques applied in the project.

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.

Final Evaluation:
• Excellent (27-30/30): The exam will be considered fully successful if the project contains mostly correct results, and the student can clearly explain their conclusions, respond effectively to most of the teacher’s questions, and demonstrate a comprehensive understanding of the subject.
• Good (22-26/30): An average evaluation will result from a project with at least half of the results correct. During the oral exam, with the assistance of the teacher's questions, the student will demonstrate a good understanding of the key concepts and how to address errors in the project.
• Sufficient (18-21/30): The exam will be considered sufficient if the project contains errors in approximately two-thirds of the results, but the student demonstrates, during the oral exam, an adequate knowledge of the most important concepts covered in the course.

Lectures in presence, homework, and paper reading
The lectures will be carried out using a traditional approach, with all calculations done on a black/whiteboard.
Additionally, students will be given research papers correlated by some questions that will help students learn how to carry out a critical analysis of the literature and how to connect notions learnt during the lectures with real research problems.