Topology in condensed matter systems
Main reference: Topological Insulators and Topological Superconductors, by B.A. Bernevig (2013)
Grading: Homework (30%); term report (70%)
Required background: Quantum mechanics, solid state physics
01 Review of Bloch theory
02 Review of Berry Phase
03 Berry curvature of Bloch states
04 Charge polarization and quantum Hall effect
05 1D spin pump
06 2D topological insulator
07 3D topological insulator
08 Effective Hamiltonian of topological insulator
09 Electromagnetic response of surface states
10 More about 4 by 4 Hamiltonian matrix
11 Dimensional reduction
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12 Point degeneracy between energy bands
13 Weyl semi-metal
14 Electromagnetic response of Weyl semi-metal
15 Review of BCS theory
16 1D p-wave superconductor
17 2D p-wave superconductor
18 Superconductor pairing with spin
19 Topological superconductor with time-reversal symmetry
21 Periodic table: Basics
22 Periodic table: Dirac Hamiltonian representative
App. D, E, F
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Topological Insulators, by C. Kane and J.E. Moore, Physics World 24, 32 (2011).
Geometrical Methods of Mathematical Physics, by B.F. Schutz
Topological Insulators: Dirac Equation in Condensed Matters, by S.Q. Shen (2013)
Topological Insulators, Ed M. Franz and L. Molenkamp (2013)
Topological Insulators Fundamentals and Perspectives, by F. Ortman et al (2015)
A Short Course on Topological Insulators, by J. Asboth, L. Oroszlany, and A. Palyi (2016)
Bulk and Boundary Invariants for topological insulators: From K-theory to physics, by E. Prodan and H. Schulz-Baldes (2016)
Berry phase effects on electronic properties, by D. Xiao, M.C. Chang, and Q. Niu, Rev. Mod. Phys. 82, 1959 (2010).
Topological insulators, by M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010).
Topological insulators and superconductors, by X.L. Qi and S.C. Zhang, Rev. Mod. Phys. 83, 1057 (2011).
Topological band theory, by A. Bansil, H. Lin and T. Das, Rev. Mod. Phys. 88, 021004 (2016).
An introduction to topological phases of electrons, by J. Moore at UC Berkeley
Topological insulator (in Japanese), by K. Nomura at Tohoku Univ.
Les Houches: Topological aspects of condensed matter physics 2014
Topological insulators / Topological superconductors (2013)
The Nobel Symposium 156: New forms of matter: topological insulators and superconductors (2015)slides
New J Phys: Focus on
Topological Insulators (2011), Majorana Fermions in Condensed Matter (2014),
Topological Semimetals (2016), Topological Physics (2016)
Topological Band Theory and the Quantum Spin Hall Effect, by C. Kane at KITP, Dec 8, 2008
Topological Insulators and Superconductors, by S.C. Zhang at Stanford, Sep 10, 2009
Physics@FOM Veldhoven, by C. Kane, Jan 2012
Topological Insulators and Superconductors (KITP program, Sep 19 - Dec 16, 2011)
Title: A Short Course on Topological Insulators: Band-structure topology and edge states in one and two dimensions
Authors:János K. Asbóth, László Oroszlány, András Pályi
(Submitted on 8 Sep 2015)
Abstract: This course-based primer provides newcomers to the field with a concise introduction to some of the core topics in the emerging field of topological band insulators in one and two dimensions. The aim is to provide a basic understanding of edge states, bulk topological invariants, and of the bulk--boundary correspondence with as simple mathematical tools as possible. We use noninteracting lattice models of topological insulators, building gradually on these to arrive from the simplest one-dimensional case (the Su-Schrieffer-Heeger model for polyacetylene) to two-dimensional time-reversal invariant topological insulators (the Bernevig-Hughes-Zhang model for HgTe). In each case the model is introduced first and then its properties are discussed and subsequently generalized. The only prerequisite for the reader is a working knowledge in quantum mechanics, the relevant solid state physics background is provided as part of this self-contained text, which is complemented by end-of-chapter problems.
Submission historyFrom: János K. Asbóth [view email]
[v1] Tue, 8 Sep 2015 09:28:54 GMT (15948kb,D)
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