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This course highlighted applications of topology in the condensed matter based on bulk-edge correspondence, extensions of topology to further areas of condensed matter, such as photonic and mechanical systems, topology in fractionalized systems, driven or dissipative systems. Students can learn the variety of subtopics in topological materials, their relation to each other and to the general principles and acquire skills required to engage in research.

Assessment

This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.

Certification

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Course Credit: TU Delft

Course Curriculum

Module: 1
Topology and symmetry 00:05:00
Conclusion: Hamiltonians, topology, and symmetry 00:02:00
Kitaev chain and bulk-edge correspondence 00:05:00
Three approaches to analysing topological systems 00:06:00
From Kitaev model to an experiment 00:05:00
Outlook: From Kitaev chain to a nanowire 00:05:00
Module: 2
How to detect Majoranas 00:07:00
Summary: Majorana signatures: 4π-periodic Josephson effect, Andreev conductance quantization 00:05:00
Braiding of Majoranas 00:05:00
Summary: Why Majoranas are cool: braiding and quantum computation 00:05:00
Thouless pumps 00:06:00
Quantized charge and scattering invariant 00:02:00
Module: 3
Introduction to Quantum Hall effect: pumping electrons in Landau levels 00:08:00
Conclusion: Quantum Hall effect: pumping electrons in Landau levels 00:03:00
Important things to know about edge states 00:08:00
Introduction: stacking wires 00:07:00
Conclusion: Quantum Hall Effect on the lattice and Dirac Hamiltonian 00:04:00
Module: 4
Introduction to Haldane model, Berry curvature, and Chern number 00:08:00
Summary: extending the model to spinful electrons and photons 00:03:00
Introduction to Time-reversal symmetry and fermion parity pumps 00:06:00
Summary: Time-reversal symmetry and fermion parity pumps 00:08:00
Introduction to Experimental progress and candidate materials 00:07:00
Module: 5
Summary: Experimental progress and candidate materials 00:02:00
Introduction to Dirac equation of the surface states, 3D Bernevig-Hughes-Zhang model 00:05:00
Conclusion: integers, half-integers, and two types of electromagnetic response 00:05:00
Introduction: searching the periodic table for topological materials 00:12:00
Outlook: from basic science to potential applications 00:03:00
Introduction to Majoranas in topological insulators and superconductors 00:09:00
Module: 6
Conclusions: Majoranas in topological insulators and superconductors 00:03:00
Introduction: weak topological phases 00:14:00
Conclusions: Crystalline defects in weak topological insulators 00:04:00
Introduction to 10 symmetry classes and the periodic table of topological insulators 00:07:00
Conclusions: 10 symmetry classes and the periodic table of topological insulators 00:05:00
Module: 7
Introduction to Different approaches to topological invariants 00:05:00
Conclusions: Different approaches to topological invariants 00:02:00
Introduction to Disorder and the scaling theory of localization 00:08:00
Conclusions: Disorder and the scaling theory of localization 00:06:00
Introduction to Flow diagram of topological insulators 00:06:00
Module: 8
Conclusions: Flow diagram of topological insulators 00:03:00
Introduction to Topology in gapless systems 00:05:00
Introduction to Topological mechanics 00:08:00
Conclusions: Topological mechanics 00:06:00
Introduction to Floquet topological insulators 00:05:00
Module: 9
Conclusions: Floquet topological insulators 00:05:00
Introduction to Crystalline topological insulators 00:03:00
Introduction to Fractional quantum Hall effect and topological particles 00:06:00
Conclusion: Fractional quantum Hall effect and topological particles 00:05:00
Introduction to Topological order and the toric code 00:04:00
Assessment
Submit Your Assignment 00:00:00
Certification 00:00:00

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