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**

Edukite courses are free to study. To successfully complete a course you must submit all the assignment of the course as part of the assessment. Upon successful completion of a course, you can choose to make your achievement formal by obtaining your Certificate at a cost of £49.

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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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