Quantum materials

In this subject, the student will acquire skills on current concepts in physics of the
condensed matter. The course offers an overview of what is known today
as quantum materials, those whose physical properties are inherently quantum
(beyond the quantum nature of chemical bonding or band theory). The acquisition of
this vision involves understanding the collective states that occur
strongly correlated multielectron systems.

They will be specific competences:

- Understand the concept of quasiparticle and its application to collective states
electronics in solids.

- Understand magnetism as a collective quantum phenomenon.

- Understand the limits of itinerant and localized magnetism.

- Handle the basic concepts of a Hubbard model applied to a metal-to-metal transition.
insulating.

- Know the states of quantum matter and matter with non-trivial topology.

1. Interacting electrons: Systems of many particles and second quantization.
Fermion and boson statistics. Landau's Fermi liquid. Interacting electron gas. Anderson and Mott transition.

2. Quantum magnetism: Heisenberg's model. Hubbard model. ferromagnetic,
antiferromagnetic, metallic and insulating phases.

3. Topological properties of matter: Berry phase. Berry's connection. Berry curvature. Quantum Hall effect. Modern theory of polarization. Dirac equation: Graphene. Topological insulators. Spin quantum Hall effect. Weyl fermions.

Basic bibliography:

-P. Fazekas, “Lecture notes on electron correlation and magnetism”, World Scientific (2003).

- Steven M-Girvin, Kun Yang, "Modern condensed matter physics", Cambridge University Press, (2019).

- Michael El-Batanouny, "Advanced quantum condensed matter physics", Cambridge University Press, (2020).

Further reading:

- Eduardo Fradkin, "Field Theories of consensual matter physics", Cambridge University Press, (2013).

- Henrik Bruus, Karsten Flensberg, "Many body quantum theory in condensed matter physics", Oxford University Press, (2004)

- Piers Coleman, “Introduction to many-body physics”, Cambridge University Press, 2015

- Alexander Altland, Ben Simons, "Condensed matter field theory", Cambridge University Press, 2006.

- M. Sigrist, “Solid State Theory”, downloadable lecture notes from the author's page: http://www.itp.phys.ethz.ch/education/fs13/sst/Lecture-Notes.pdf

- M. P. Marder, “Condensed matter physics”, John Wiley & Sons (2000).

- G. Grosso, G. P. Parravicini, “Solid state physics”, Academic Press (2000). - P. L. Taylor, O. Heinonen, “A quantum approach to condensed matter physics”, Cambridge Press (2002).

- Wolfgang Nolting, "Fundamentals of many body physics", Springer, 2008.

- G. D. Mahan, “Condensed matter in a nutshell”, Princeton University Press (2011).

- A. Auerbach, “Interacting electrons and quantum magnetism”, Springer-Verlag (1994).

- Shun-Qing Shen, Topological Insulators :Dirac Equation in Condensed Matters, Springer-Verlag (2012)

- Bernavig B. Andrei, Topological Insulators and Topological Superconductors, University Princeton Press (2013)

5.5.1.5.1 BASIC AND GENERAL
CG01 - Acquire the ability to carry out research work as a team.
CG02 - Have the capacity for analysis and synthesis.
CG03 - Acquire the ability to write texts, articles or scientific reports in accordance with publication standards.
CG04 - Become familiar with the different modalities used for the dissemination of results and dissemination of knowledge in
scientific meetings.
CG05 - Apply knowledge to solve complex problems.
CB6 - Possess and understand knowledge that provides a basis or opportunity to be original in the development and/or application of
ideas, often in a research context
CB7 - That students know how to apply the knowledge acquired and their ability to solve problems in environments
new or little known within broader (or multidisciplinary) contexts related to your area of study
CB8 - That students are able to integrate knowledge and face the complexity of making judgments based on
information that, being incomplete or limited, includes reflections on the social and ethical responsibilities linked to the
application of their knowledge and judgments
CB9 - That students know how to communicate their conclusions and the ultimate knowledge and reasons that support them to audiences
specialized and non-specialized in a clear and unambiguous way
CB10 - That students have the learning skills that allow them to continue studying in a way that will be
be largely self-directed or autonomous.
5.5.1.5.2 TRANSVERSALS
CT01 - Ability to interpret texts, documentation, reports and academic articles in English, scientific language by
excellence.
CT02 - Develop the capacity to make responsible decisions in complex and/or responsible situations.
5.5.1.5.3 SPECIFIC
CE09 - Master the set of necessary tools so that you can analyze the different states in which the
subject.
CE10 - Understand and assimilate both fundamental and more applied aspects of the Physics of light and radiation

The activities from which the teaching will develop will be of various types: theoretical classes, seminars (both on the blackboard and using the available computer resources) and problem classes. The participation of the student will be essential in the classes of seminars and problems. Likewise, hours of tutorials will be made available to the student for individualized discussion of all doubts that arise about the content of the subjects.

Attendance to class will be mandatory and the evaluation will be continuous through the delivery of exercise bulletins and/or completion of a monographic work on a topic of recent bibliography of interest for the course.

Evaluable activity. Weight in the global note.

Problem delivery. Up to 70%.

Monographic work. up to 30%

Attendance to class will be mandatory with continuous evaluation through exercise bulletins or presentation of monographic works on topics of recent interest for the course.

Evaluable activity. Weight in the global note.

Problem delivery. Up to 70%

Monographic work. Up to 30%

For cases of fraudulent performance of exercises or tests, it will be
of application the one collected in the "Regulation of evaluation of the performance
academic performance of the students and review of qualifications”.

Article 16. Fraudulent performance of exercises or tests.
The fraudulent performance of any exercise or test required in the
evaluation of a subject will imply the qualification of suspense in the
corresponding call, regardless of the process
disciplinary action that may be taken against the offending student. HE
considers fraudulent, among others, the realization of plagiarized works
or obtained from sources accessible to the public without reprocessing or
reinterpretation and without citations to the authors and sources.

It is a subject of 3 ECTS credits. It corresponds to 26 hours of face-to-face classes, 15 expository and 10 interactive, 1 tutorial and 49 hours of personal work.

Review subjects related to it such as Solid State and Quantum Mechanics.