Advanced Quantum Materials 2025

Teaching material for the Advanced Quantum Materials course at Aalto University 2025

Interactive exercise sessions

The folder sessions contains the Jupyter notebooks for the different sessions of the course

• Session 2: Symmetries, reciprocal space and Bloch's theorem
• Session 3: Band structure theory
• Session 4: Topological band structure theory
• Session 5: The quantum Hall effect
• Session 6: Superconductivity and Majorana physics
• Session 7: Magnetism, magnons, quantum magnetism and spinons
• Session 8: Excitations and impurities in quantum materials

Theory lecture pre-recordings

All the pre-recordings can be found here, for the following sessions

• Session 1: Second quantization, mean-field and spontaneous symmetry breaking
• Session 2: Symmetries, reciprocal space, Bloch’s theorem
• Session 3: Band structure theory, tight binding and effective models
• Session 4: Topological band structure theory
• Session 5: Electrons in a magnetic field, quantum Hall effect and Landau levels
• Session 6: Superconductivity, Nambu representation and Majorana physics
• Session 7: Magnetism, magnons, quantum magnetism and spinons
• Session 8: Excitations and defects in quantum materials
• Session 9: Tensor network and neural network many-body wavefunctions
• Session 10: Machine learning for quantum materials

Install

The Jupyter notebooks use pyqula, and can be installed from a terminal with pip as

pip install --upgrade pyqula