Course11510800249 lectures
Topological Phases of Matter
Prof. Tanmoy Das · IISc Bangalore
About
Topological phases of matter are a recently discovered class of quantum phases in condensed matter physics. Their underlying principles originate in abstract branches of mathematics, yet they manifest concretely in the electronic structure and many-body physics of real materials. In recent years, numerous experimental realizations have been achieved, and several databases of topological materials are now available. Owing to the relative newness of the field, courses on this subject are not yet part of the mainstream curriculum at most institutes. Despite its seemingly intimidating name and concepts, the subject can be made accessible to fourth-year undergraduates and master’s students when taught with appropriate physical intuition.
Intended audience: UG (dual degree), PG, and PhD
Prerequisites: Quantum Mechanics – II Mathematical Methods for Physics Condensed Matter - I
Lectures
Week 1 Mathematical Foundation of Geometry and Topology
- Introduction to the course
- Algebraic structures and Topological space
- Homotopy Group-I
- Homotopy Group-II
Week 2 Mathematical Foundation (Continued) and Geometric Phases
- Manifold and Calculus on Manifold
- Fibre bundles and Covariant derivative
- Parallel Transport
- Geometric phases
week 3 Integer Quantum Hall Effect
- Integer Quantum Hall Effect
- Landau levels and the Laughlin argument
- QHE in lattice-I
- QHE in lattice-II
Week 4 Berry Phase and Topological Invarinat
Week 5 Model Hamiltonian
Week 6 Topological Semi-metals and Superconductors
- Weyl & Nodal-line Semi-metals
- Graphene & Spin–Orbit Coupling
- Haldane Model
- BCS Theory & p-wave Superconductor
- Kitaev Model & Majorana Fermions
Week 7 Symmetry-I
- Classification of Symmetries
- First quantization representation
- Parity & Time-Reversal Symmetry
- Symmetry in Second quantization-I
week 8 Symmetry-II and Topological Classification
- Symmetry in Second quantization-II
- Symmetry in Second quantization-III
- Symmetry Classification - I
- Symmetry Classification - II
- Symmetry Classification - III
Week 9 Time-reversal symmetric Topollogical Insulators
- Kramers Degeneracy and the BHZ Model
- The Z2 Topological Invariant - I
- The Z2 Topological Invariant - II (Sewing Matrices and Pfaffians)
- Strong and Weak Topological Insulators
- 3D Topological Insulators and Axions
Week 10 Quantum Geometry
- The Quantum Geometric Tensor
- Quantum Distance and Fidelity
- Metric Inequalities and the Wannier Obstruction
- Optical Responses and Topological Bounds
Week 11 Edge State and Bulk-Boundary Correspondence
- Quantum Hall state and Charge pumping
- Polarization, edge states and k.p model
- Kitaev model and 2D Chern insulators
- Time reversal invariant topological insulators
Week 12 Experimental Signatures
Syllabus and materials
At NPTEL, as the course publishes them.
Credits and licence
- Institution
- IISc Bangalore
- Department
- Physics
- Teacher
- Prof. Tanmoy Das
- Level
- Undergraduate
- Language
- English
- Subjects
- Physics
- Source
- NPTEL
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
- Who can watch
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