Topological Insulators 2 (Topological superconductors)

Course for MSc and PhD students at
Eotvos University Budapest (ELTE), and
Budapest University of Technology and Economics (BME)
2018 Spring semester

If you'd like to join the course officially, then please sign up in Neptun, and contact us at palyi at mail dot bme dot hu. Please send us an email also if you'd like to attend the course unofficially.

Lecturers

János Asbóth, Wigner Research Centre for Physics
László Oroszlány, Eötvös University
András Pályi, Budapest University of Technology and Economics

Details

Lectures

1. Poor man's topological quantum memory based on the Su-Schrieffer-Heeger model
   Lecture notes: pdf.
   Slides of a talk on the same subject: pdf.
2. Superconductors can be described by single-particle Hamiltonians
   Lecture notes: pdf (chapter 1 was covered in the lecture).
3. Kitaev chain as a topological insulator
   Lecture notes: pdf (first two sections were covered in the lecture).
4. Simple quantum information protocols with the Kitaev double dot
   Lecture notes: pdf.
5. Protection of states and braiding-based operations in the Majorana qubit
   Lecture notes: pdf.
6. Protection of states and braiding-based operations in the Majorana qubit, Part 2
   Topological invariants for topological superconductors
   
7. Topological invariants for topological superconductors, Part 2
   
8. Four-pi-periodic Josephson effect
   Lecture notes: pdf.
9. Experimental realization of one-dimensional topological superconductors
   Lecture notes: pdf.
   Slides: pdf.
10. Andreev reflection on s-wave and p-wave superconductors
    Lecture notes: pdf.
    Further reading:
    Slides on superconducting nanostructures, for the BME course Transport in complex nanostructures.
    Section 1.8, "Andreev scattering", in Nazarov & Blanter, "Quantum Transport" (Cambridge University Press, 2009).

Topics

• Topological quantum memories
• Geometry and topology in adiabatic quantum dynamics
• Noise-resistant quantum computing with adiabatic quantum dynamics
• Mean-field theory of topological superconductors
• A toy model for topological superconductivity: the Kitaev wire
• Majorana zero modes in topological superconductors
• Braiding, fusion, and their applications in topological quantum computing
• Hybrid superconductor-semiconductor nanostructures as topological superconductors
• Experimental signatures of topological superconductivity

Further reading

1. Leijnse and Flensberg: Introduction to topological superconductivity and Majorana fermions,
   https://arxiv.org/abs/1206.1736
2. Alicea: New directions in the pursuit of Majorana fermions in solid state systems
   https://arxiv.org/abs/1202.1293
3. Beenakker: Search for Majorana fermions in superconductors
   https://arxiv.org/abs/1112.1950
4. Alicea et al: Non-Abelian statistics and topological quantum information processing in 1D wire networks
   https://arxiv.org/abs/1006.4395
5. Lutchyn et al: Realizing Majorana zero modes in superconductor-semiconductor heterostructures
   https://arxiv.org/abs/1707.04899
6. Zhang et al: Quantized Majorana conductance
   https://arxiv.org/abs/1710.10701
7. Laroche et al: Observation of the 4π-periodic Josephson effect in InAs nanowires
   https://arxiv.org/abs/1712.08459
8. Deacon et al: Josephson radiation from gapless Andreev bound states in HgTe-based topological junctions
   https://arxiv.org/abs/1603.09611
9. He et al: Chiral Majorana edge state in a quantum anomalous Hall insulator-superconductor structure
   https://arxiv.org/abs/1606.05712
10. Mourik et al: Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
    https://arxiv.org/abs/1204.2792

Prerequisites