Teaching plan for the course unit



Close imatge de maquetació




General information


Course unit name: Quantum Materials

Course unit code: 574654

Academic year: 2021-2022

Coordinator: Bruno Julia Diaz

Department: Department of Quantum Physics and Astrophysics

Credits: 3

Single program: S



Estimated learning time

Total number of hours 75


Face-to-face and/or online activities



-  Lecture

Face-to-face and online




-  Lecture with practical component

Face-to-face and online



Supervised project


Independent learning






Students are advised to have completed or be enrolled in the subjects advanced quantum mechanics and condensed matter physics.



Competences to be gained during study


  1. Knowledge about main classes of quantum materials (Dirac matter and topological materials, van der Waals heterostructures, magnetic systems) in terms of their structural, electronic, spintronic and optical responses. Basic theoretical concepts such as Berry´s phase and Berry curvature will be derived and connected to symmetry breaking operations, anomalous quantum transport properties as well as spin dynamics. Presentation of Haldane model for Chern insulators, Kane-Mele for topological insulators will be studied in details. Efficient numerical methods to study transport phenomena in model systems of quantum materials will be introduced. Understanding of main experimental challenges in terms of materials and device fabrication, and applications to the field of quantum transport, photonics and spintronics.





Learning objectives


Referring to knowledge

  1. To acquire a theoretical minimum background of main aspects of electronic properties of quantum materials

  2. To become familiar with the basic concepts and theoretical tools of topological physics and their connection to quantum transport phenomena (Berry curvature, topological invariant, quantum spin Hall effect, photonic Floquet topological insulators, etc). 

  3. To grasp the fundamental and “big questions” concerning spintronics, photonics and exotic superconductivity in topological materials such as twisted layered quantum materials. 



Teaching blocks


1. Basics


  1. Introduction to Quantum Materials & course objectives 

  2. Reminder on advanced quantum mechanics; concepts & methods (Schrödinger and Dirac equations, spin and spin-orbit coupling, wavefunction collapse and entanglement (EPR, Bell´s inequality); quantum transport (Green functions and transport theory Kubo-Streda) 

  3. Fundamentals of quantum transport in Quantum Materials (Symmetries and Topology, Berry phase and anomalous velocity, massless Dirac fermions, Klein tunneling and weak antilocalization) 

  4. Topological transport physics (Berry curvature, Chern number) and quantum Hall effects (quantum spin/valley Hall effects, quantum anomalous Hall effect) 

  5. Strong spin-orbit coupling two-dimensional materials & optoelectronics and photonics (transition metal dichalcogenides (TMDs), massive Dirac Fermions, valley-spin locking/valleytronics) 

  6. Engineering Van der Waals Heterostructures: Moiré effects in layered materials (multilayer graphene, graphene/hBN, TMDs, etc..) proximity effects: Graphene/TMD, magnetic topological insulators, giant spin transport anisotropy, spin Hall Effect, topological photonics and plasmonics 

2. Theoretical & Experimental aspects and challenges of quantum materials-based devices and applications


  1. Quantum simulation for topological materials 

  2. Quantum Nano-Optoelectronics 

  3. Spintronics in Quantum Materials 

  4. Superconducting & strongly correlated physics:

Some introduction of related topics will be given through zoom presentations, while supervised projects will be related to the presented topics 

2.1. Exercices

2.2. Exercices



Teaching methods and general organization


  1. Lectures where theoretical contents of the subject are presented. 

  2. Practical exercise classes in which students may participate. 

  3. Activities related to the subject suggested by the teaching staff. 



Official assessment of learning outcomes


  1. One written examination and one oral presentation. Each examination is worth 2 points, carried out during a session and announced previously. 

  2. A final written examination on the entire course content worth 6 points. 

  3. Members of the teaching staff may also consider students’ participation in class and in the optional tasks they suggest. Evaluation of competences



Reading and study resources

Consulteu la disponibilitat a CERCABIB


Introduction to graphene-based nanomaterials: from electronic structure to quantum transport; L.E.F. Torres, S. Roche, J.C. Charlier (Cambridge University Press 2020)

Advanced Quantum Condensed Matter Physics, M. El-Batanouny (Cambridge University Press 2020)

Topological Insulators: Fundamentals and Perspectives (Wiley CH, 2015)

Web page

The 2020 Quantum Materials Roadmap

F. Giustino et al. Journal of Physics: Materials (in press 2020- OPEN ACCESS)



Online resources- some materials and code information will be provided on www.lsquant.org  EnllaƧ