Course Syllabus

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Instructor :Jay Sau

Short description: Topology in Condensed Matter Physics - tying quantum knots: A simple and hands-on overview of topological insulators, Majoranas, and other topological phenomena focused on ongoing research activities.

 

Online sign-up (required): There are no specific text-books required for this course - but this is a "flipped-classroom", so it is assumed that you will sign up (free) on the EdX course Topology in Condensed Matter Physics- tying quantum knots.

Online Course Structure:  This is a course in a "flipped-classroom" format where the material (video/assignments/reading
and simulations) will be available through the free EdX course. The in-class section will serve to add discussion and clarification of the material presented. In principle, if you just want to audit (and don't need credits and don't wish to be graded) you can also just sign-up for the online class only and attend lectures as you wish.

Instructor Webpage: http://www2.physics.umd.edu/~jaydsau/

email: jaydsau@umd.edu

Office: Toll Building 2308

Lectures: Toll 1204. Wednesday (2pm - 3:30pm)

Office hours: Toll 2308. Monday (3 pm - 4 pm)

Lecture structure:  As mentioned the lectures will have a "flipped-classroom" structure where we expect the class to be dominated by student participation. Since it will be assumed that class participants have already gone through the weekly material online - the role of the class will be for you to test what you understand and clarify what you missed. Peer-peer discussion is the ideal way to enhance this. To seed the discussion - we will start the class by going through the quizzes in the online class. I hope that this will lead to more questions about the material. Finally, we will discuss the simulation assignment and the reading assignment. Bringing your laptop to class is encouraged (though not necessary) for the simulation assignment.

Weekly online assignments: Weekly assignments consist of 4 to 5 short quiz questions, one simulation assignment and assessment of a recent relevant paper. These are all found and graded online on the EdX course. The online assignments will be graded locally by the instructor in addition to the peer-review. So please email them to jaydsau@umd.edu (until I figure out how to access your online response). While you can get a grade for the simulation assignment even if you submit late (and not online at all), 25% of the grade for a specific problem is allotted to submission online (to encourage online submission).

Class participation grade: The main role of the class is as a forum for discussion of the online material and assignments. The value of the class relies on participation in the discussion. Because of this the entire in-class part of the grade will be based on response in class. To get points for this please prepare a response to as much of the online assignment as possible. The instructor will ask for volunteers for each of the questions ( 4 to 5 quiz questions, 2 to 3 parts in simulation, and each of the 3 papers). Each response will be graded on a three point scale (0 = not responded, 1 = attempt at a response, 2 = a mostly successful attempt). I will record your response after the class. Of course, I do not expect everyone to respond every week, so the best 5 weeks of response will be taken for the final grade.

 

Grade information: Weekly assignments peer graded online - weight (70%) and class participation grade (30%).

You can find a link to the course material here.

Course outline:

After this (i.e. Jan 28 and Feb 4) the class will discuss material + assignments on each week of EdX where the material will appear on the Thursday before the relevant class.

  • Week 1 (starting Feb 5): Preface : Background information
    • About this course
    • Starting questionnaire
  • Week 1 : Topology in toy models
    • Hamiltonians, topology, and symmetry
    • Bulk-edge correspondense in the Kitaev chain
  • Week 2 : Majoranas again
    • From Kitaev chain to a nanowire
    • Majorana signatures: 4π-periodic Josephson effect, Andreev conductance quantization
    • Why Majoranas are cool: braiding and quantum computation
  • Week 3 : More parameters: charge pumping
    • Thouless pumps and winding invariant
    • Laughlin argument: pumping electrons in Landau levels on a cylinder
    • Quantum Hall effect: edge states and quantized Hall conductance
  • Week 4 : Chern insulators
    • Chern number invariant description of Quantum Hall
    • Quantum Hall transition and the Dirac equation
    • Haldane model and Hofstadter butterfly
  • Week 5 : Quantum spin Hall effect
    • Combining quantum Hall effect with time-reversal symmetry
    • Kane-Mele and BHZ models
    • Experiments and materials for QSHE
  • Week 6 : Three-dimensional topological insulators
    • Dirac equation of the surface states, magneto-electric effect
    • BHZ model of 3D TI
    • Materials and experiments
  • Week 7 : Alternative realizations of Majorana fermions
    • Proximity effect in QSHE and 3D TI
    • Atomic chains
    • Review of experimental progress
  • Week 8 : General approach to topological classification
    • 10 symmetry classes and the periodic table of topological insulators
    • Topological defects and Dirac-like equations
    • Alternative approaches to topological invariants
  • Week 9 : Anderson localization and topology
    • Disorder and the scaling theory of localization
    • Flow diagram of topological insulators
  • Week 10 : Extensions of classification I
    • Topology in gapless systems
    • The role crystalline symmetries
    • Mechanical systems
  • Week 11 : Extensions of classification II
    • Floquet topological insulators
    • Quantum Walks
    • Josephson junctions
  • Week 12 : Beyond single-particle physics
    • Topological order and the toric code
    • Fractional quantum Hall effect and topological particles

 

Course Summary:

Date Details Due