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.


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


Location: BME, FA building, seminar room of the Department of Atomic Physics
Time: Mondays, 10:15-11:45.
First lecture: Feb 19 Monday, 10:15-11:45.
Course language: English
Course website:


  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).


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


Quantum mechanics, basic condensed-matter physics (tight-binding models for electronic bands). We will make reference to the material covered in the lecture "Topological insulators". If you have not completed that course, then we suggest that you read through Chapter 1 of its lecture notes ( before taking "Topological insulators 2".