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IsraelX: Topological Quantum Matter

The theory and experiments studying topological states of matter including: the quantum Hall effect, topological insulators, superconductors and semimetals, twisted bi-layer graphene and covering advanced theoretical and experimental methods

16 weeks
2–4 hours per week
Instructor-led on a course schedule
This course is archived
Future dates to be announced

About this course

Skip About this course

This advanced course covers the fundamentals of the thriving field of Topological States of Matter. We discuss both theoretical and experimental aspects, and emphasize the physical picture over the technical details. The course is divided to nine units.

The Integer and Fractional Quantm Hall Effects are covered in the first unit, including the concepts of edge states, localization, fractional charges, composite fermions, and non-abelian states.

Topological Superconductivity is covered in the 2nd unit, including the concepts of the Thouless pump, Majorana zero modes, and realizations in one and two dimensions.

Topological Universe on a Graphene Sheet is offered by the 3rd unit, including the concepts of Dirac cones, Klein tunneling and Chern bands, as well as the rich world of twisted bi-layer graphene.

Topological Insulators are covered by the 4th unit, including two- and three- dimensional systems, as well as topological crystalline insulators.

The 5th unit, on Topological Classification , puts all examples of the previous units into a unified framework, introducing the periodic table of gapped topological systems with no topological order.

The 6th unit expands the course into the realm of Gapless Topological Phases , covering Dirac and Weyl semi-metals, both in their bulk and surface.

The 7th unit covers the theoretical tools for Predicting Topological Materials , with an emphasis on Denisty Functional Theory, and the quantities that need to be calculated to probe the topological characteristics of a material.

The 8th unit dives into the abstract world of Topological Order , from the Toric Code all the way to a brief discussion of Topological Quantum Computation.

And finally, the 9th unit describes some Experimental Tools that are of wide use in the study of topological states of matter, and makes connection between measurements and their interpretation.

At a glance

  • Institution: IsraelX
  • Subject: Physics
  • Level: Advanced
  • Prerequisites:

    Students of Physics - Master's degree or higher

  • Language: English
  • Video Transcript: English
  • Associated skills: Hall Effect, Insulator, Localization

What you'll learn

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Fundamental concepts of the field and examples of topological systems

Topological classification of quantum matter

Bulk-Boundary correspondence in topological matter

Responses and anomalies of topological matter

Introduction to common Experimental techniques

Quantum Hall effect and quantum spin Hall effect

Gapped, Gapless and superconducting topological phases

Topological physics of graphene

Topological order and topological quantum computation

1. The quantum Hall effect – Prof. Ady Stern

2. Topological superconductivity – Prof. Yuval Oreg, Dr. Yuval Ronen

3. Topological universe on a graphene sheet – Prof. Raquel Queiroz, Prof.

Shahal Ilani, Prof. Erez Berg

4. Topological insulators – Prof. Haim Beidenkopf, Prof. Binghai Yan,

Prof. Ady Stern

5. Topological classification – Prof. Erez Berg

6. Gapless topological phases – Prof. Roni Ilan, Prof. Haim Beidenkopf

7. Material prediction – Prof. Binghai Yan

8. States of topological Order – Prof. Ady Stern, Prof. Erez Berg, Prof.

Yuval Oreg

9. Experimental tools – Prof. Haim Beidenkopf, Dr. Nurit Avraham, Prof.

Moty Heiblum

Who can take this course?

Unfortunately, learners residing in one or more of the following countries or regions will not be able to register for this course: Iran, Cuba and the Crimea region of Ukraine. While edX has sought licenses from the U.S. Office of Foreign Assets Control (OFAC) to offer our courses to learners in these countries and regions, the licenses we have received are not broad enough to allow us to offer this course in all locations. edX truly regrets that U.S. sanctions prevent us from offering all of our courses to everyone, no matter where they live.

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