PHYS701 paper review : D. Hsieh et al., Nature, 458, 970-974 (2008) - A topological Dirac Insulator...

Paper Review

Dongwook Go (POSTECH)

PHYS701 Special Topics in Condensed Matter Physics : Topological Insulators

1


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


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


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


Question : What is the measure of the band inversion ?

Answer :

Same question :

where

andRef : Kane and Mele (2005)

5


Topological Phase Transition

6


Berry-Phase-Protected Edge State

Ref : Xiao-Liang Qi and Shou-Cheng Zhang (2010)

7


3D Topological Insulator

Ref : Kane (2010)

Ref : Kane and Hasan (2010) 8


3D Topological Insulator

Ref : Kane (2010)

9


Ref : Teo et al. (2010)

Ref : Kane and Hasan (2010)10


Angle-Resolved Photoemission Spectroscopy (ARPES)

Ref : Moore (2010)

( assumed )

Experimentally determined parameterapproximately -10 eV for bismuth

11


ARPES Intensity Map near the L-point

Consistent with pure bismuth tight-binding calculation : Liu and Allen (1995)

12


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


Nontrivial Topology of the Fermi Surface

Odd # of crossings along the line joining two TRIM points

→ Topological Insulator14


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/

https://sites.google.com/site/xlqistanford/home/talks

https://sites.google.com/site/xlqistanford/home/talks

http://www.physics.upenn.edu/~kane/


Supp. #1Resistivity Measurement

16


Supp. #2Spin-orbit Coupling Effect on the Band Structure of Bismuth near L-point

17

Date post:	18-Jul-2015
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PHYS701 paper review : D. Hsieh et al., Nature, 458, 970-974 (2008) - A topological Dirac Insulator...

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