1. Research fueled by: MRS Spring Meeting San Francisco April 28th 2011 JAIRO SINOVA Texas A&M University Institute of Physics ASCR Topological thermoelectrics Oleg Tretiakov, Artem Abanov, Suichi Murakami Great job candidate

2. 2 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Topological insulators Topological protected transport through lattice dislocations Thermoelectrics TIs=efficient thermoelectrics Thermoelectric transport via dislocations in TIs Large thermoelectric figure of merit in weak TI with protected 1D states Beyond weak TI: analogy with other systems Summary Topological thermoelectrics

3. Heattronics? Thermomagnotronics? Nanospinheat ? Calefactronics? Fierytronics? Coolspintronics? Thermospintronics? ? What I learned in kinder garden: Fire is cool What I learned in Leiden: Spin+Fire is cooler

4. 4 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Valenzuela et al Nature 06 Inverse SHE Anomalous Hall effect: more than meets the eye Wunderlich, Kaestner, Sinova, Jungwirth PRL 04 Kato et al Science 03 Intrinsic Extrinsic Wunderlich, Irvine, Sinova, Jungwirth, et al, Nature Physics 09 Spin-injection Hall Effect Anomalous Hall Effect I _ FSOFSO FSOFSO _ _ majority minority V Spin Hall Effect I _ FSOFSO FSOFSO _ _ V Topological Insulators Kane and Mele PRL 05 Spin Caloritronics

5. 5 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Discovery of topological insulators HgTe Theory: Bernevig, Hughes and Zhang, Science 314, 1757 (2006), Experiment: Koenig et al, Science 318, 766 (2007), BiSb Theory: Fu and Kane, PRB 76, 045302 (2007), Experiment: Hsieh et al, Nature 452, 907 (2008), Bi 2 Te 3, Sb 2 Te 3, Bi2 S e 3 theory: Zhang et al, Nature Phys. 5, 438 (2009), Experiment Bi 2 Se 3 : Xia et al, Nature Physics 5, 398 (2009), Experiment BieTe 3 : Chen et al Science 325, 178 (2009), and many others …

6. 6 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Topological insulators in 2D Requires spin-orbit interactions. Protected by Time Reversal. Only Z 2 (even-odd) distinction. (Kane-Mele) Time reversal symmetry: two counter-propagating edge modes X X QSHE in HgTe Edge states survive disorder effects. Trivial TINon-trivial TI

7. 7 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Experimental Predictions k  k  x x Courtesy of SC Zhang

8. 8 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Experimental evidence for the QSH state in HgTe

9. 9 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Topological insulators in 3D One obvious route to topological insulator in 3D: –Stack 2D layers of quantum spin Hall insulators. –Defined by the reciprocal vector of the stacking layers. –‘weak’ topological insulators. Less obvious possibility (no quantum Hall analog) –‘strong’ topological insulators in D=3. –Characteristic feature – Surface state: single Dirac node. Fu, Kane & Mele (2006), Moore & Balents (2006), Roy (2006).

10. 10 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Topological protected 1D states in dislocations Ran, Zhang,Vishwanath, Nature Physics (2009) Dislocations have 1D channels which also protected Condition: Easily introduced in tight binding model on diamond lattice: Burgers vector Time reversal invariant momentum vectors

11. 11 Nanoelectronics, spintronics, and materials control by spin-orbit coupling 1D topological protected states in TI Insert a pair of screw dislocations. If Two propagating modes per dislocation: “Helical metal”. Similar to 2D quantum spin Hall edge states

12. 12 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Properties and materials with 1D states in dislocations Stable to disorder: (TR symmetry no backscattering) (non-magnetic) An atomically thin one dimensional wire that does not localize. Similar to 2D quantum spin Hall edge states Materials with nonzero : Bi 1−x Sb x (0.07 < x < 0.22)

13. 13 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Thermoelectric generator

14. 14 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Courtesy of Saskia Fischer

15. 15 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Courtesy of Saskia Fischer

16. 16 Nanoelectronics, spintronics, and materials control by spin-orbit coupling From topological insulators to thermoelectrics Best thermoelectrics Can we obtain high ZT through the topological protected states; are they related to the high ZT of these materials? Vishwanath et al 09 Dislocations have 1D channels which also protected ? ? Seebeck coefficient electrical conductivity electric thermal conductivity phonon thermal conductivity

17. 17 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Bi 1−x Sb x (0.07 < x < 0.22) where the L’s are the linear Onsager dynamic coefficients Localized bulk states Possible large ZT through dislocation engineering Tretiakov, Abanov, Murakami, Sinova APL 2010

18. 18 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Bulk contribution Bulk: Contribution to ZT from the bulk is very small

19. 19 Nanoelectronics, spintronics, and materials control by spin-orbit coupling ZT of one perfectly conducting 1D wire Limiting case: infinite density of dislocations

20. 20 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Possible large ZT through dislocation engineering Remains very speculative but simple theory gives large ZT for reasonable parameters Tretiakov, Abanov, Murakami, Sinova APL 2010

21. 21 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Beyond Bi 1−x Sb x (0.07 < x < 0.22) So far only one material is believed to have protected 1D states on dislocations: how to further exploit TI properties to increase ZT? Analogy to HolEy Silicon Tang et al Nano Letters 2010 Also phononic nanomesh structures (Yu, Mitrovic, et al Nature Nanotechnology 2010)

22. 22 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Extending the idea to the entire class of TI insulators Tretiakov, Abanov, Sinova (in preparation) 2011 The surface of the holes provide the needed anisotropic transport Similar theory analysis as in 1D protected states but not as robust Curvature of the holes can be critical for TI to remain protected (Ostrovsky et al PRL 10, Zhang and Vishwanath PRL 10) d=60 nm R=15 nm

23. 23 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Preliminary results (yesterday) ZT μ

24. 24 Nanoelectronics, spintronics, and materials control by spin-orbit coupling SUMMARY: topological thermoelectrics Qualitative theory was developed on how to increase ZT in topological insulators via line dislocations. The interplay of topologically protected transport through the dislocations and Anderson insulator in the bulk. Estimated ZT ~ 10 at room temperature. Idea can be extended to the entire range of TI