This document discusses topological insulators, beginning with an overview of the integer quantum Hall effect and how topology relates to boundary states. It then covers how spin-orbit coupling allows for topological insulator phases even with time-reversal symmetry. Several key papers on topological insulators are referenced, including the discovery of the quantum spin Hall effect and theoretical descriptions of topological phases in two and three dimensions. Experimental observations of topological insulator materials via angle-resolved photoemission spectroscopy are also summarized.

1. PHYS701 Special Topics in Condensed Matter Physics : Topological Insulators
Paper Review
Dongwook Go (POSTECH)
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2. PHYS701 Special Topics in Condensed Matter Physics : Topological Insulators
Integer Quantum Hall Effect
@ Interface
The difference of the two Chern
numbers decides the number of 1D
interface states
→ Bulk-boundary correspondence
, Chern number
Ref : Hasan and Kane (2010)
,
Ref : Moore (2010)
The effect can happen in the T-symmetry
broken system : Haldane (1988)
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3. PHYS701 Special Topics in Condensed Matter Physics : Topological Insulators
Topological Insulator without
T-symmetry Breaking : Spin-Orbit Coupling
T-symmetry is unbroken, but
spin-orbit coupling allows for
a different topological class.
Intrinsic spin-orbit coupling
From the T-symmetry,
But,
Ref : Kane (2010)
Quantum Spin Hall Effect !
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4. PHYS701 Special Topics in Condensed Matter Physics : Topological Insulators
Ref: Hasan and Kane (2010)
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
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5. PHYS701 Special Topics in Condensed Matter Physics : Topological Insulators
Question : What is the measure of the band inversion ?
Same question :
Answer :
where
and
Ref : Kane and Mele (2005)
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6. PHYS701 Special Topics in Condensed Matter Physics : Topological Insulators
Topological Phase Transition
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7. PHYS701 Special Topics in Condensed Matter Physics : Topological Insulators
Berry-Phase-Protected Edge State
Ref : Xiao-Liang Qi and Shou-Cheng Zhang (2010)
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8. PHYS701 Special Topics in Condensed Matter Physics : Topological Insulators
3D Topological Insulator
Ref : Kane (2010)
Ref : Kane and Hasan (2010)
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9. PHYS701 Special Topics in Condensed Matter Physics : Topological Insulators
3D Topological Insulator
Ref : Kane (2010)
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10. PHYS701 Special Topics in Condensed Matter Physics : Topological Insulators
Ref : Teo et al. (2010)
Ref : Kane and Hasan (2010)
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11. PHYS701 Special Topics in Condensed Matter Physics : Topological Insulators
Angle-Resolved Photoemission
Spectroscopy (ARPES)
(
assumed )
Experimentally determined parameter
approximately -10 eV for bismuth
Ref : Moore (2010)
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12. 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)
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13. 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.
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14. 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 Insulator
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15. PHYS701 Special Topics in Condensed Matter Physics : Topological Insulators
Thank You !
Questions ?
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/talks
C. L. Kane, Windsor Summer School lectures on Topological Insulators and Superconductors (2010)
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http://www.physics.upenn.edu/~kane/

16. PHYS701 Special Topics in Condensed Matter Physics : Topological Insulators
Supp. #1
Resistivity Measurement
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17. PHYS701 Special Topics in Condensed Matter Physics : Topological Insulators
Supp. #2
Spin-orbit Coupling Effect on the Band
Structure of Bismuth near L-point
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