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Quantum technologies

Dieter Meschede's research group
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Intensive week on topological insulators

Introduction to topological insulators and
their implementations in artificial matter setups

Institut für Angewandte Physik, Universität Bonn,
Wegelerstr. 8, 53115 Bonn
Hörsaal (lecture hall), March 13-17th, 2017

If you are interested, please register for the course on or before March 5th, 2017 by sending an email to This e-mail address is being protected from spambots. You need JavaScript enabled to view it  containing your name, student number (Matrikelnummer), and whether you intend to obtain credit points (4 CP). Please also specify the subject line in the email "Registration: Intensive week on Topological Insulators".

Students who pass a short written examination (30 minutes) on Thursday – consisting of simple conceptual questions – will obtain credit points. Students from Bonn and Cologne should also register themselves in the Basis system to obtain credit points.

Lecturers:

Guest lecturers:

Abstract:

The intensive week consists of lectures introducing graduate students to the very active research field of topological insulators. Participants are required to have good knowledge of basic quantum mechanics and familiarity with basic concepts in condensed matter physics (Bloch theorem, energy bands, etc.). No prior knowledge of topology is assumed.

The main body of the intensive week is a course held by J. K. Asbóth, based on the lecture notes “A Short Course on Topological Insulators”, freely available at https://arxiv.org/abs/1509.02295. Through simple one- and two-dimensional model Hamiltonians, participants will acquire a good physical understanding of the core concepts of topological insulators. Among the questions covered: What is topological in a band insulator? What are edge states? How is their number given by the so-called bulk-boundary correspondence principle? How and against what are edge states protected? This is complemented by A. Alberti, presenting a selection of modern experiments demonstrating topological effects in ultracold atoms and nanophotonics setups. Additionally, guest speakers will give an introduction to “frontier” research topics in this field. The course will be accompanied by laboratory tours, exercise and interactive discussion sessions in the afternoon.

Structure:

  • 5 days, 6 x 45 min lectures each day
  • 16 x 45 min: Introduction to topological insulator materials (J. Asbóth)
  • 2 x 45 min: Presentation of selected experiments with ultracold atoms and optical systems (A. Alberti)
  • Guest lectures
  • Interactive problem solving sessions
  • Laboratory tours (AG Linden, AG Meschede, AG Weitz)

Program:

Please follow this link to visualize the program.

Introductory topics:

  • Simple models of topological insulators in 1D and 2D
  • Physical-mathematical concepts: Berry phase, Chern invariants, bulk polarization
  • Thouless adiabatic pumping mechanism
  • One way (chiral) and two-way (helical) edge states
  • Quantized transverse conductance
  • Cold atom & quantum optical experiments on topological insulators

Examples of ‘frontier’ research topics covered by the external speakers:

  • Topological superconductors,
  • Majoranas,
  • Weyl materials,
  • Scattering theory of topological insulators,
  • Periodically driven systems,
  • Advanced mathematical formulation of topological invariants

Prerequisites for the intensive week course:

  • The course is recommended for graduate students in the Master program
  • Good knowledge of basic quantum mechanics is expected
  • Familiarity with basic concepts in condensed matter physics (Bloch theorem, energy bands, etc.) is recommended
  • No prior knowledge of topology is assumed

FlyerJanos Asboth's book