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
Location: BME, FA building, seminar room of the Department of Atomic Physics
Time: Mondays, 10:1511:45.
First lecture: Feb 19 Monday, 10:1511:45.
Course language: English
Course website:
http://eik.bme.hu/~palyi/TopologicalInsulators22018Spring/
Lectures
 Poor man's topological quantum memory based on the SuSchriefferHeeger model
Lecture notes: pdf.
Slides of a talk on the same subject: pdf.

Superconductors can be described by singleparticle Hamiltonians
Lecture notes: pdf (chapter 1 was covered in the lecture).

Kitaev chain as a topological insulator
Lecture notes: pdf (first two sections
were covered in the lecture).

Simple quantum information protocols with the Kitaev double dot
Lecture notes: pdf.

Protection of states and braidingbased operations in the Majorana qubit
Lecture notes: pdf.

Protection of states and braidingbased operations in the Majorana qubit, Part 2
Topological invariants for topological superconductors

Topological invariants for topological superconductors, Part 2

Fourpiperiodic Josephson effect
Lecture notes: pdf.

Experimental realization of onedimensional
topological superconductors
Lecture notes: pdf.
Slides: pdf.

Andreev reflection on swave and pwave 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
 Noiseresistant quantum computing with adiabatic quantum dynamics
 Meanfield 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 superconductorsemiconductor nanostructures
as topological superconductors
 Experimental signatures of topological superconductivity
Further reading

Leijnse and Flensberg: Introduction to topological superconductivity and Majorana fermions,
https://arxiv.org/abs/1206.1736

Alicea: New directions in the pursuit of Majorana fermions in solid state systems
https://arxiv.org/abs/1202.1293

Beenakker: Search for Majorana fermions in superconductors
https://arxiv.org/abs/1112.1950

Alicea et al: NonAbelian statistics and topological quantum information processing in 1D wire networks
https://arxiv.org/abs/1006.4395

Lutchyn et al: Realizing Majorana zero modes in superconductorsemiconductor heterostructures
https://arxiv.org/abs/1707.04899

Zhang et al: Quantized Majorana conductance
https://arxiv.org/abs/1710.10701

Laroche et al: Observation of the 4πperiodic Josephson effect in InAs nanowires
https://arxiv.org/abs/1712.08459

Deacon et al: Josephson radiation from gapless Andreev bound states in HgTebased topological junctions
https://arxiv.org/abs/1603.09611

He et al: Chiral Majorana edge state in a quantum anomalous Hall insulatorsuperconductor structure
https://arxiv.org/abs/1606.05712

Mourik et al: Signatures of Majorana fermions in hybrid superconductorsemiconductor nanowire devices
https://arxiv.org/abs/1204.2792
Prerequisites
Quantum mechanics, basic condensedmatter physics
(tightbinding 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
(https://arxiv.org/abs/1509.02295)
before taking "Topological insulators 2".
