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PHYS 6810H - Introduction of Topological Band Theory
  
Course last offered 
 :   
Spring 2017/18
Instructor(s)
 :
DAI Xi
No. of credits
 :
1


Teaching Pattern
  • Duration of course: about 14 weeks
  • Lecture hour(s) / tutorial hour(s) / laboratory hour(s) per week: 1 / 0 / 0

 

Content
The course will mainly cover the most recent development in the band theory, which introduces the concept of topology. Topics include Bloch theorem, energy band, Berry’s curvature, Spin Hall effect and quantum spin Hall effect, topological invariance, Chern number and Z2 index, Z2 topological insulator, topological crystalline insulator, topological semimetal and Weyl semimetal.
  • Mathematical preparation: a bit of differential geometry, topology, manifold, connection, fiber bundle
  • Review of band theory: Bloch theorem, energy band, density functional theory and LDA, Berry’s curvature, Wannier function and maximum localized Wannier function
  • TI in one dimensional systems: SSH model, Wannier center, edge states, Kitaev chain and Majarana bound states
  • Spin Hall effect and quantum spin Hall effect: Spin Chern number, QWZ model and Haldane model
  • TI without time reversal symmetry: Chern insulators and quantum anomalous Hall effect, U(1) phase obstruction, Wannier center evolution and Chern number
  • Z2 topological invariance: U(2N) non-Abelian obstruction & U(2N) Wilson loop and Wannier center evolution
  • Graphene, quantum spin Hall systems and 2D topological insulators: electronic structure of Graphene, Symmetry and spin orbital coupling, HgTe quantum Well, band inversion mechanism and BHZ model
  • 3D topological insulators: strong and weak topological insulators, topological insulators with inversion symmetry, Bi/Sb alloy and Bi2Se3 family
  • Dirac type surface states in 3D topological insulators I: spin-momentum locking, pseudo spin and real spin, angle resolved photo emission; Circular dichroism; spin resolved ARPES; surface Landau levels and quantum oscillation; weak localization and surface transport; surface quantum Hall effect
  • Magnetically doped Bi2Se3/Bi2Te3 thin film and quantum anomalous Hall effect: band inversion and Van Vleck mechanism for ferromagnetism; chiral edge states
  • From 3D topological insulators to topological semi metal: Dirac semimetal, Weyl semimetal and node-line semimetal
  • Transport properties in topological semimetal: chiral anomaly, chiral magnetic effect and negative magneto-resistance 
DEPARTMENT OF PHYSICS