Research fueled by:

MRS Spring MeetingSan FranciscoApril 28th 2011

JAIRO SINOVATexas A&M University

Institute of Physics ASCR

Topological thermoelectrics

Oleg Tretiakov, Artem Abanov, Suichi Murakami

Great job candidate

2Nanoelectronics, 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 Topological thermoelectrics

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

4Nanoelectronics, 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

IntrinsicExtrinsic

Wunderlich, Irvine, Sinova, Jungwirth, et al, Nature Physics 09

Spin-injection Hall Effect

Anomalous Hall Effect

I

_ FS

OFS

O

_ _majority

minority

V

Spin Hall Effect

I

_ FS

OFS

O

_ _

V

Topological Insulators

Kane and Mele PRL 05

Spin Caloritronics

5Nanoelectronics, spintronics, and materials control by spin-orbit coupling

Discovery of topological insulatorsDiscovery 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),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 …

6Nanoelectronics, spintronics, and materials control by spin-orbit coupling

Topological insulators in 2D

•Requires spin-orbit interactions.•Protected by Time Reversal.•Only Z2 (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

7Nanoelectronics, spintronics, and materials control by spin-orbit coupling

Experimental Predictions

k

ε

k

ε

x

xCourtesy of SC Zhang

8Nanoelectronics, spintronics, and materials control by spin-orbit coupling

Experimental evidence for the QSH state in HgTe

9Nanoelectronics, 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).

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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

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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

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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 :Bi1−xSbx (0.07 < x < 0.22)

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Nanoelectronics, spintronics, and materials control by spin-orbit coupling

Thermoelectric generator

14

Nanoelectronics, spintronics, and materials control by spin-orbit coupling

Courtesy of Saskia Fischer

15

Nanoelectronics, spintronics, and materials control by spin-orbit coupling

Courtesy of Saskia Fischer

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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

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Nanoelectronics, spintronics, and materials control by spin-orbit coupling

Bi1−xSbx (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

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Nanoelectronics, spintronics, and materials control by spin-orbit coupling

Bulk contribution

Bulk:

Contribution to ZT from the bulk is very small

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Nanoelectronics, spintronics, and materials control by spin-orbit coupling

ZT of one perfectly conducting 1D wire

Limiting case:

infinite density of dislocations

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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

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Nanoelectronics, spintronics, and materials control by spin-orbit coupling

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)

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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

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Nanoelectronics, spintronics, and materials control by spin-orbit coupling

Preliminary results (yesterday)

ZT

μ

24Nanoelectronics, spintronics, and materials control by spin-orbit coupling

SUMMARY: topological thermoelectrics

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