Physics of bulk-edge correspondence by Y. Hatsugai
Hiroshima Univ. June 27-29 (2012) ( hosted by Prof. Akio Kimura )
Plan
- [1] Classical order
- Symmetry breaking and low energy excitations
- Ref. Talk PDF
- [2] Topological order
- Quantum liquids, topological order & edge states
- Ref. Talk PDF
- [3]Various edge states and their physical realization
- Ref. Talk PDF
- [4]Z2 quantization & topological order parameter
- Z2 Berry phases as a singlet order parameter
- Ref. paper
- Ref. Talk PDF Talk at KITP 2008
- [5]Gauge transformation & topological term
- Ref. Lorentz force: Analytical mechanics: Univ. of Tsukuba, lecture note (2007) in Japanese
- Ref. Path integral & gauge transformation : Univ. Tokyo, lecture note (2004) in Japanese
- [6]Local U(1) for continuum & lattice
- Peierls substitution
- Harper equation
- Ref. 2007 Grad. Course at U. Tsukuba
- Topological origin of the Hall conductance : Note taken by Ms. JiYoung Kang
- [7]The first Chern number as the quantized Hall conductance
- Quantization of the first Chern number
- Gauge freedom of the Berry connection
- Ambiguity of the Berry phase
- Gauge invariant form of the Chern numbers
- Ref. paper1
- Ref. paper2
- Ref. paper3
- [8]Dirac monopole & degeneracy
- Gauge fixing & Dirac strings
- The first Chern number & the Berry phase
- Ref. paper1
- Ref. paper2
- Ref. [Y. Hatsugai in Focus issue in topological insulators :NJP][direct link to the paper]
- [9]Bulk-edge correspondence
- Laughlin argument & quantization
- Winding numbers of the edge states
- Ref. papers with comments
- Ref. Talk PDF
- Ref. KOTAIBUTSURI in Japanese
- [10]Chiral symmetry & fermion doubling:*
- Topological stability of the the massless Dirac cones
- Landau levels of the massless Dirac fermions
- Ref. article : KOTAI BUTSURI in Japanese
- Ref. paper
- Ref. 2010 Grad. Course at U. Tsukuba
- Graphene and Berry connection : Note taken by Mr. R. Hidekata
- [11]Time reversal invariance
- Kramers degeneracy & Quaternions
- Ref. Talk PDF
- Yang monopole & degeneracy with the TR invariance
- Ref. [Y. Hatsugai in Focus issue in topological insulators :NJP][direct link to the paper]
- TR invariant edge states & Z2
- Ref. Talk PDF
*:skipped due to time limitation