Topological thermoelectrics

Transcription

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

2 Topological thermoelectrics 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 2

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 Anomalous Hall effect: more than meets the eye Spin Hall Effect Anomalous Hall Effect FSO V Inverse SHE I FSO I minority FSO FSO majority V Wunderlich, Kaestner, Sinova, Jungwirth PRL 04 Extrinsic Intrinsic Topological Insulators Kane and Mele PRL 05 Valenzuela et al Nature 06 Spin Caloritronics Kato et al Science 03 Spin-injection Hall Effect Wunderlich, Irvine, Sinova, Jungwirth, et al, Nature Physics 09 4

5 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, (2007), Experiment: Hsieh et al, Nature 452, 907 (2008), Bi2Te3, Sb2Te3, Bi2Se3 theory: Zhang et al, Nature Phys. 5, 438 (2009), Experiment Bi2Se3: Xia et al, Nature Physics 5, 398 (2009), Experiment BieTe3: Chen et al Science 325, 178 (2009), and many others 5

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

7 Experimental Predictions x Courtesy of SC Zhang x ε ε k k 7

8 Experimental evidence for the QSH state in HgTe 8

9 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. ʻweakʼ topological insulators. Less obvious possibility (no quantum Hall analog) ʻstrongʼ topological insulators in D=3. Characteristic feature Surface state: single Dirac node. Fu, Kane & Mele (2006), Moore & Balents (2006), Roy (2006). 9

10 Topological protected 1D states in dislocations Dislocations have 1D channels which also protected Condition: Ran, Zhang,Vishwanath, Nature Physics (2009) Burgers vector Time reversal invariant momentum vectors Easily introduced in tight binding model on diamond lattice: 10

11 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 11

12 Properties and materials with 1D states in dislocations Stable to disorder: (TR symmetry no backscattering) An atomically thin one dimensional wire that does not localize. Similar to 2D quantum spin Hall edge states (non-magnetic) Materials with nonzero : Bi1 xsbx (0.07 < x < 0.22) 12

13 Thermoelectric generator 13

14 Courtesy of Saskia Fischer 14

15 Courtesy of Saskia Fischer 15

16 From topological insulators to thermoelectrics electrical conductivity ZT = electric thermal conductivity σs2 T κ e + κ l Seebeck coefficient S = πk2 β T 3e ln σ(e) E E F phonon thermal conductivity Best thermoelectrics Dislocations have 1D channels which also protected κ l σ S? Vishwanath et al 09 Can we obtain high ZT through the topological protected states; are they related to the high ZT of these materials?? 16

17 Possible large ZT through dislocation engineering where the L s are the linear Onsager dynamic coefficients Bi1 xsbx (0.07 < x < 0.22) Localized bulk states Tretiakov, Abanov, Murakami, Sinova APL

18 Bulk contribution Bulk: Contribution to ZT from the bulk is very small 18

19 ZT of one perfectly conducting 1D wire Limiting case: infinite density of dislocations 19

20 Possible large ZT through dislocation engineering Remains very speculative but simple theory gives large ZT for reasonable parameters Tretiakov, Abanov, Murakami, Sinova APL

21 Beyond Bi1 xsbx (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) 21

22 Extending the idea to the entire class of TI insulators 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) R=15 nm d=60 nm Tretiakov, Abanov, Sinova (in preparation)

23 Preliminary results (yesterday) ZT µ 23

24 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 24