research fueled by: mrs spring meeting san francisco april 28th 2011 jairo sinova texas a&m...
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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
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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
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)
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
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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