Quantum Materials

Code:

FIS4043

Acronym:

FIS4043

Level:

400

Keywords
Classification	Keyword
OFICIAL	Physics

Instance: 2025/2026 - 2S

Active?	Yes
Responsible unit:	Department of Physics and Astronomy
Course/CS Responsible:	Master in Physics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
M:F	28	Official Study Plan	1	-	6	42	162

Teaching language

English

Objectives

To introduce and promote dexterity in a range of physical principles, models and theoretical methods that underpin our understanding of electrical, optical, magnetic, and transport properties of quantum materials, with emphasis on two-dimensional materials and quantum condensed materials (condensates and superconductors).

To empower students for independent and critical assessment of the current literature in this field, and to provide tools for subsequent research and/or technological development activities in the physics and applications of quantum materials.

Learning outcomes and competences

Upon completion of this course unit, students will:

• Be acquainted with key physical properties, phenomena and representative materials that underpin the current and envisaged implementation of quantum technologies.

• Have a good perspective of the unique features of 2D materials and of many-body condensed states, with an eye on the opportunities they provide for exploring novel and intrinsically quantum-mechanical phenomena.

• Understand fundamental models and concepts of the theoretical description of these materials, and acquire skills to independently apply or extend such models.

• Understand the relations between the physics that underlines the properties of a material and the technologies and devices it enables.

• Have know-how and skills to engage effectively and in depth with the current research literature on these materials, the underlying phenomena, and their applications.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

A good knowledge of quantum theory, statistical physics and solid-state physics.

Program

1. Two-dimensional materials — Representative systems and their distinctive feaures. Electronic structure based on tight-binding and effective low-energy models. Electronic structure of monolayers, bilayers and multilayers. Applications.

2. Quantum magnetism — Exchange interactions and the origin of magnetism. Spontaneous symmetry breaking, ferro- and anti-ferromagnetism. Magnetic ground states and excitations. 

3. Condensed materials I: Bose-Einstein condensates — Condensed state of weakly interacting bosons, broken gauge symmetry, order parameter and superfluity. Ohase of the order parameter and condensate motion. Vorticity quantization.

4. Condensed materials II: superconductors — Broken gauge symmetry of charged particles and the Higgs-Anderson mechanism. Cooper instability and BCS theory, ground state and excitations. Ginzburg-Landau theory. Meissner effect. Superconductors of type I and type II. Josephson’s effect.

Mandatory literature

Steven M. Girvin; Modern condensed matter physics. ISBN: 978-1-107-13739-4
Mikhail I. Katsnelson; The physics of graphene. ISBN: 978-1-108-61756-7 e-book
C. J. Pethick; Bose-Einstein condensation in dilute gases. ISBN: 978-0521-84651-6
C. Kittel; Quantum theory of solids
Michael Tinkham; Introduction to superconductivity. ISBN: 0-07-064877-8 ((2nd edition))
James F. Annett; Superconductivity, superfluids, and condensates. ISBN: 0-19-850756-9

Complementary Bibliography

Neil W. Ashcroft; Solid state physics. ISBN: 0-03-083993-9 US College Edition
Phaedon Avouris; 2D materials. ISBN: 978-1-316-68161-9 e-book
Various authors; Research and review articles and other readings to be distributed during the course.

Teaching methods and learning activities

The contact hours blend lecturing, discussion of previously assigned readings and work with practical examples.

keywords

Technological sciences > Technology > Quantum technology
Physical sciences > Physics > Condensed matter properties

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	70,00
Trabalho escrito	30,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	120,00
Frequência das aulas	42,00
Total:	162,00

Eligibility for exams

Cannot be absent to more than 25% of the scheduled lectures.

Calculation formula of final grade

The assessment comprises the submission of homework assignments (30%) and a final exam (70%). Each assignment will be announced in due time and may take different forms, such as: solve a problem, expand a calculation or provide further details on a selected topic, critically review a published research paper.

Classification improvement

Allowed for the "Exam" component, as prescribed in Article 12 of the Regulation for the Evaluation of Students at FCUP.

Observations

Juri of the course unit:

- Vitor M. Pereira
- J. Agostinho Moreira.