1. Topological Insulators
Jason Lambert
University of Tennessee
Department of Physics

2. Outline Topological Invariants and State of matter
The Quantum Hall Effect ( QHE )
The Quantum Spin Hall Effect ( QHSE )
Experimental Realization QHSE
Exotic Physics

3. Prediction
I predict that some worker in this field will win the big prize!!!

4. Topological States of Matter
M. Z. Hasan and C. L. Kane, arXiv(Febuary 2010)

5. Topological States of Matter
Chiral
Symmetry
Particle
Hole
Symmetry
Topological
classification
Dimensionality
Time
Reversal
Symmetry
QHE
QHSE

6. The Quantum Hall Effect
Discovered in 1980 by Klaus von Klitzing.
Nobel Prize awarded in 1985.
Extremely accurate resistance is now used as a NIST standard
K. v. Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. 45, 494 (Aug. 1980)

7. Quantum Hall Effect The resistance in the y direction quantized.
Resistance in the xy direction goes to zero

8. Topological Invariant of QHE
Topological invariant referred as the TKNN invariant.
Determined from the integral of the Brillouin zone.
The topology of the manifold of occupied states distinguishes the quantum hall state and conventional insulator
M. Z. Hasan and C. L. Kane, arXiv(Febuary 2010)

9. Quantum Spin Hall effect
The QSHE effect has quantized conduction bands due to surface states.
The electrons are spin polarized depending upon direction of flow.
C. Day, Physics Today 61, 19 (2008)

10. Quantum Spin Hall Effect
Requires a linearly dispersing edge state
also known as a dirac cone
Bulk Valence and conduction bands are connected by the surface conducting states
C. Day, Physics Today 61, 19 (2008)

11. QSHE
The surface states of the quantum spin hall effect are protected by time reversal symmetry
There must be an odd number of dirac cones in the Brillouin zone.

12. Is this a strong topological insulator?
In three dimensional systems you can have both strong and weak topological insulators
We want strong topological insulators.
Determining the nature of the topological insulator is not trivial
Easiest method works when material has inversion symmetry.

13. Is this a strong topological insulator?
L. Fu and C. L. Kane, Phys. Rev. B 76, (Jul. 2007)
H. Zhang, C.-X. Liu, X.-L. Qi, X. Dai, Z. Fang, and S.-C. Zhang, Nat Phys 5, 438 (Jun. 2009)

14. Experimental Realization
Looking for materials that have a bulk insulating gap with strong spin orbit coupling.
The spin orbit coupling should be strong enough to invert the highest valence band and lowest conduction band.
Need to look toward heavy elements on periodic table spin orbit coupling is strong

15. CdHgTe Quantum wells First topological insulator HgTe quantum wells.
M. König et al., Science 318, 766 (2007).

16. Second Generation Topological insulators
H. Zhang et al., Nat. Phys. 5, 438 (2009).
Y. Xia et al., Nat. Phys. 5, 398 (2009); D. Hsieh et al., Science 323,
919 (2009).

17. Potential Applications
Spintronics
Room temperature dissipation-less conduction Because of the perfectly conducting edge state
Possible applications topological quantum computing
Table Top testing of the Standard Model

18. Physics Exotic Majorana Fermions Image Magnetic Monopoles
Unobserved in nature
Nuetrinos?
Predicted to exist in s-wave superconductor TI boundary
Image Magnetic Monopoles
Because of unique EM field theory that describes TI
An image magnetic monopole is expected to exist in response to a
S.-C. Z. Xiao-Liang Qi, Physics Today 63, 33 (2010)
F. Wilczek, Nature 458, 129 (2009); Nat. Phys. 5, 614 (2009).

19. Conclusions
Topological States of matter including the topological insulator have become a very Hot topic.
The “second generation” materials have a lot of promise.
Some topological insulator properties are very applicable
Testing ground exotic physics and the standard model