Paper Review Dongwook Go (POSTECH) PHYS701 Special Topics in Condensed Matter Physics : Topological Insulators 1
Jul 18, 2015
Paper Review
Dongwook Go (POSTECH)
PHYS701 Special Topics in Condensed Matter Physics : Topological Insulators
1
PHYS701 Special Topics in Condensed Matter Physics : Topological Insulators
Integer Quantum Hall Effect
, Chern number
,
Ref : Hasan and Kane (2010)
@ InterfaceThe difference of the two Chernnumbers decides the number of 1D interface states→ Bulk-boundary correspondence
Ref : Moore (2010)
The effect can happen in the T-symmetry broken system : Haldane (1988)
2
PHYS701 Special Topics in Condensed Matter Physics : Topological Insulators
Topological Insulator without T-symmetry Breaking : Spin-Orbit Coupling
T-symmetry is unbroken, butspin-orbit coupling allows fora different topological class.
Intrinsic spin-orbit coupling
From the T-symmetry,
But,
Ref : Kane (2010)
Quantum Spin Hall Effect !
3
PHYS701 Special Topics in Condensed Matter Physics : Topological Insulators
Kramer’s degeneracy @ TRIM (Time Reversal Invariant Momenta)
Even # of crossings→ band-gap may be opened (not topological)Odd # of crossings → Topologically protected metallic boundary state
Ref: Hasan and Kane (2010)
4
PHYS701 Special Topics in Condensed Matter Physics : Topological Insulators
Question : What is the measure of the band inversion ?
Answer :
Same question :
where
andRef : Kane and Mele (2005)
5
PHYS701 Special Topics in Condensed Matter Physics : Topological Insulators
Topological Phase Transition
6
PHYS701 Special Topics in Condensed Matter Physics : Topological Insulators
Berry-Phase-Protected Edge State
Ref : Xiao-Liang Qi and Shou-Cheng Zhang (2010)
7
PHYS701 Special Topics in Condensed Matter Physics : Topological Insulators
3D Topological Insulator
Ref : Kane (2010)
Ref : Kane and Hasan (2010) 8
PHYS701 Special Topics in Condensed Matter Physics : Topological Insulators
3D Topological Insulator
Ref : Kane (2010)
9
PHYS701 Special Topics in Condensed Matter Physics : Topological Insulators
Ref : Teo et al. (2010)
Ref : Kane and Hasan (2010)10
PHYS701 Special Topics in Condensed Matter Physics : Topological Insulators
Angle-Resolved Photoemission Spectroscopy (ARPES)
Ref : Moore (2010)
( assumed )
Experimentally determined parameterapproximately -10 eV for bismuth
11
PHYS701 Special Topics in Condensed Matter Physics : Topological Insulators
ARPES Intensity Map near the L-point
Consistent with pure bismuth tight-binding calculation : Liu and Allen (1995)
12
PHYS701 Special Topics in Condensed Matter Physics : Topological Insulators
Separating the Surface State from the Bulk
Surface states do not disperse along a direction perpendicular to the surface whereas the bulk state do.
13
PHYS701 Special Topics in Condensed Matter Physics : Topological Insulators
Nontrivial Topology of the Fermi Surface
Odd # of crossings along the line joining two TRIM points
→ Topological Insulator14
PHYS701 Special Topics in Condensed Matter Physics : Topological Insulators
Thank You !
Questions ?
15
References
D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Nature 452, 06843 (2008).M. Z. Hasan and C. L. Kane, Rev. Mod. Phys, 82, 3045 (2010).F. D. M. Haldane, Phys. Rev. Lett. 61, 2015 (1988).C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 226801 (2005).C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 146802 (2005).Xiao-Liang Qi and Shou-Cheng Zhang, arXiv:1001.1602v1 (2010).Jeffrey C.Y. Teo, Liang Fu and C.L. Kane, Phys. Rev. B 78, 045426 (2008).
J. Moore, Tutorial on topological insulators, APS March meeting (2011).https://sites.google.com/site/xlqistanford/home/talksC. L. Kane, Windsor Summer School lectures on Topological Insulators and Superconductors (2010)http://www.physics.upenn.edu/~kane/
PHYS701 Special Topics in Condensed Matter Physics : Topological Insulators
Supp. #1Resistivity Measurement
16
PHYS701 Special Topics in Condensed Matter Physics : Topological Insulators
Supp. #2Spin-orbit Coupling Effect on the Band Structure of Bismuth near L-point
17