Topology in Condensed Matter: Tying Quantum Knots
The complete attributed TU Delft TOPOCMx open course, imported natively into QuantumSpark: from toy-model topology and the Kitaev chain through Majoranas, quantum Hall effects, Chern insulators, symmetry classification, disorder, Floquet phases and topological order. Original lectures, derivations, videos, questions, Python notebook cells and source figures retained. Expanded with original in-page technical chapters, mathematical proofs, independently checked calculation baselines and directly embedded credited original instructor videos where relevant.
Published syllabus
Course Units
Background, topology and toy models
Original TU Delft TOPOCMx lectures: Brief review of band structures; About this course; Hamiltonians, topology, and symmetry; Bulk-edge correspondence in the Kitaev chain; Topics for self-study
Majorana nanowires, experimental signatures and braiding
Original TU Delft TOPOCMx lectures: Why Majoranas are cool: braiding and quantum computation; From Kitaev chain to a nanowire; Majorana signatures: 4π-periodic Josephson effect, Andreev conductance quantization; Topics for self-study
Charge pumping and the quantum Hall effect
Original TU Delft TOPOCMx lectures: Quantum Hall effect: pumping electrons in Landau levels; Thouless pumps and winding invariant; Quantum Hall effect: edge states; Topics for self-study
Chern insulators and the Haldane model
Original TU Delft TOPOCMx lectures: Haldane model, Berry curvature, and Chern number; Quantum Hall Effect on the lattice and Dirac Hamiltonian; Topics for self-study
The quantum spin Hall effect
Original TU Delft TOPOCMx lectures: Time-reversal symmetry and fermion parity pumps; Experimental progress and candidate materials; Topics for self-study
Three-dimensional topological insulators
Original TU Delft TOPOCMx lectures: Experimental progress and candidate materials; Dirac equation of the surface states, 3D Bernevig-Hughes-Zhang model; Topics for self-study
Topological defects and Majorana bound states
Original TU Delft TOPOCMx lectures: Crystalline defects in weak topological insulators; Majoranas in topological insulators and superconductors; Topics for self-study
The periodic table and classification of topological phases
Original TU Delft TOPOCMx lectures: 10 symmetry classes and the periodic table of topological insulators; Different approaches to topological invariants; Topics for self-study
Anderson localization, disorder and topology
Original TU Delft TOPOCMx lectures: Disorder and the scaling theory of localization; Flow diagram of topological insulators; Topics for self-study
Topological semimetals and mechanics
Original TU Delft TOPOCMx lectures: Topology in gapless systems; Topological mechanics; Topics for self-study
Floquet and crystalline topological extensions
Original TU Delft TOPOCMx lectures: Crystalline topological insulators; Floquet topological insulators; Topics for self-study
Fractional quantum Hall, topological order and appendices
Original TU Delft TOPOCMx lectures: Fractional quantum Hall effect and topological particles; Topological order and the toric code; Tight-binding models in a magnetic field: Peierls substitution; Additional notes on computing Chern number; Topics for self-study