# Topological Phases of Matter - Institution: IISc Bangalore - Department: Physics - Teacher: Prof. Tanmoy Das - Level: Undergraduate - Language: English - Subjects: Physics - Source: [NPTEL](https://nptel.ac.in/courses/115108002) - Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.) - Syllabus: [at the source](https://nptel.ac.in/courses/115108002) - Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words) 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 1. [Introduction to the course](https://invisiblenetwork.ai/learn/nptel/115108002/7eac467eb03b) (YouTube) 2. [Algebraic structures and Topological space](https://invisiblenetwork.ai/learn/nptel/115108002/92b256aa3c9a) (YouTube) 3. [Homotopy Group-I](https://invisiblenetwork.ai/learn/nptel/115108002/83d082fa390a) (YouTube) 4. [Homotopy Group-II](https://invisiblenetwork.ai/learn/nptel/115108002/5ecb4fa47927) (YouTube) 5. [Manifold and Calculus on Manifold](https://invisiblenetwork.ai/learn/nptel/115108002/98d68b46d2da) (YouTube) 6. [Fibre bundles and Covariant derivative](https://invisiblenetwork.ai/learn/nptel/115108002/91862a6cfc49) (YouTube) 7. [Parallel Transport](https://invisiblenetwork.ai/learn/nptel/115108002/3f66868e2a75) (YouTube) 8. [Geometric phases](https://invisiblenetwork.ai/learn/nptel/115108002/a9adef5c2bea) (YouTube) 9. [Integer Quantum Hall Effect](https://invisiblenetwork.ai/learn/nptel/115108002/91a913b119e6) (YouTube) 10. [Landau levels and the Laughlin argument](https://invisiblenetwork.ai/learn/nptel/115108002/6bb088ce978e) (YouTube) 11. [QHE in lattice-I](https://invisiblenetwork.ai/learn/nptel/115108002/609cddf8d9d4) (YouTube) 12. [QHE in lattice-II](https://invisiblenetwork.ai/learn/nptel/115108002/d119778a2890) (YouTube) 13. [Adiabatic Evolution](https://invisiblenetwork.ai/learn/nptel/115108002/917b09593d0a) (YouTube) 14. [Berry phase and topological obstruction](https://invisiblenetwork.ai/learn/nptel/115108002/1ba06518cd22) (YouTube) 15. [Topological Invariants](https://invisiblenetwork.ai/learn/nptel/115108002/85fca89e2b6c) (YouTube) 16. [SSH Model in 1D](https://invisiblenetwork.ai/learn/nptel/115108002/645637f9ac2d) (YouTube) 17. [Chern Insulator & 2D Dirac Model](https://invisiblenetwork.ai/learn/nptel/115108002/b1d28c4b4042) (YouTube) 18. [2D Rice–Mele Model](https://invisiblenetwork.ai/learn/nptel/115108002/03e85624cacc) (YouTube) 19. [Weyl & Nodal-line Semi-metals](https://invisiblenetwork.ai/learn/nptel/115108002/c1efabc57692) (YouTube) 20. [Graphene & Spin–Orbit Coupling](https://invisiblenetwork.ai/learn/nptel/115108002/55bd603a8c37) (YouTube) 21. [Haldane Model](https://invisiblenetwork.ai/learn/nptel/115108002/161d9b9230e1) (YouTube) 22. [BCS Theory & p-wave Superconductor](https://invisiblenetwork.ai/learn/nptel/115108002/efa8c5374357) (YouTube) 23. [Kitaev Model & Majorana Fermions](https://invisiblenetwork.ai/learn/nptel/115108002/b052f228dffa) (YouTube) 24. [Classification of Symmetries](https://invisiblenetwork.ai/learn/nptel/115108002/4a7608296643) (YouTube) 25. [First quantization representation](https://invisiblenetwork.ai/learn/nptel/115108002/d989e93b6466) (YouTube) 26. [Parity & Time-Reversal Symmetry](https://invisiblenetwork.ai/learn/nptel/115108002/fc998b68fd1a) (YouTube) 27. [Symmetry in Second quantization-I](https://invisiblenetwork.ai/learn/nptel/115108002/d5a488d76fbe) (YouTube) 28. [Symmetry in Second quantization-II](https://invisiblenetwork.ai/learn/nptel/115108002/536307531406) (YouTube) 29. [Symmetry in Second quantization-III](https://invisiblenetwork.ai/learn/nptel/115108002/c52379db8e79) (YouTube) 30. [Symmetry Classification - I](https://invisiblenetwork.ai/learn/nptel/115108002/6d2a4d852355) (YouTube) 31. [Symmetry Classification - II](https://invisiblenetwork.ai/learn/nptel/115108002/0c853ee91932) (YouTube) 32. [Symmetry Classification - III](https://invisiblenetwork.ai/learn/nptel/115108002/e255c46f23a6) (YouTube) 33. [Kramers Degeneracy and the BHZ Model](https://invisiblenetwork.ai/learn/nptel/115108002/d6130cf6e48f) (YouTube) 34. [The Z2 Topological Invariant - I](https://invisiblenetwork.ai/learn/nptel/115108002/885f8b6c2cf8) (YouTube) 35. [The Z2 Topological Invariant - II (Sewing Matrices and Pfaffians)](https://invisiblenetwork.ai/learn/nptel/115108002/5549228c08ae) (YouTube) 36. [Strong and Weak Topological Insulators](https://invisiblenetwork.ai/learn/nptel/115108002/793b95430979) (YouTube) 37. [3D Topological Insulators and Axions](https://invisiblenetwork.ai/learn/nptel/115108002/453a4698f10e) (YouTube) 38. [The Quantum Geometric Tensor](https://invisiblenetwork.ai/learn/nptel/115108002/5dae1b7b8a11) (YouTube) 39. [Quantum Distance and Fidelity](https://invisiblenetwork.ai/learn/nptel/115108002/21fb6efc2047) (YouTube) 40. [Metric Inequalities and the Wannier Obstruction](https://invisiblenetwork.ai/learn/nptel/115108002/97c179f71937) (YouTube) 41. [Optical Responses and Topological Bounds](https://invisiblenetwork.ai/learn/nptel/115108002/4af16a9f917b) (YouTube) 42. [Quantum Hall state and Charge pumping](https://invisiblenetwork.ai/learn/nptel/115108002/de1dbc1ed8c1) (YouTube) 43. [Polarization, edge states and k.p model](https://invisiblenetwork.ai/learn/nptel/115108002/85346a73e3d3) (YouTube) 44. [Kitaev model and 2D Chern insulators](https://invisiblenetwork.ai/learn/nptel/115108002/c8db11602cde) (YouTube) 45. [Time reversal invariant topological insulators](https://invisiblenetwork.ai/learn/nptel/115108002/483eabf8ed49) (YouTube) 46. [Topological protection and Dissipationless transport](https://invisiblenetwork.ai/learn/nptel/115108002/9029a5925e5b) (YouTube) 47. [Negative Magneto resistance](https://invisiblenetwork.ai/learn/nptel/115108002/a775db6c5ae6) (YouTube) 48. [Transport signatures of topology](https://invisiblenetwork.ai/learn/nptel/115108002/2af87a013158) (YouTube) 49. [Non-linear Hall effect](https://invisiblenetwork.ai/learn/nptel/115108002/cf599b38f987) (YouTube)