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, 10:15-11:45.
First lecture: Feb 19 Monday, 10:15-11:45.
Course language: English
Course website:
http://eik.bme.hu/~palyi/TopologicalInsulators2-2018Spring/
Lectures
- 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.
-
Superconductors can be described by single-particle 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 braiding-based operations in the Majorana qubit
Lecture notes: pdf.
-
Protection of states and braiding-based operations in the Majorana qubit, Part 2
Topological invariants for topological superconductors
-
Topological invariants for topological superconductors, Part 2
-
Four-pi-periodic Josephson effect
Lecture notes: pdf.
-
Experimental realization of one-dimensional
topological superconductors
Lecture notes: pdf.
Slides: pdf.
-
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
-
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: Non-Abelian statistics and topological quantum information processing in 1D wire networks
https://arxiv.org/abs/1006.4395
-
Lutchyn et al: Realizing Majorana zero modes in superconductor-semiconductor 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 4π-periodic Josephson effect in InAs nanowires
https://arxiv.org/abs/1712.08459
-
Deacon et al: Josephson radiation from gapless Andreev bound states in HgTe-based topological junctions
https://arxiv.org/abs/1603.09611
-
He et al: Chiral Majorana edge state in a quantum anomalous Hall insulator-superconductor structure
https://arxiv.org/abs/1606.05712
-
Mourik et al: Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
https://arxiv.org/abs/1204.2792
Prerequisites
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
(https://arxiv.org/abs/1509.02295)
before taking "Topological insulators 2".
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