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IMS, 26 Nov Models for Thermal & Thermal : Pave the way for heat control Baowen Li ( 李保文 ) Nonlinear and Complex Systems Lab Department of Physics

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IMS, 26 Nov Acknowledgement Collaborators: Lei Wang (Temasek Lab, NUS) Giulio Casati (Como, Italy and NUS) Financial Support: NUS Faculty Research Grant Temasek Young Investigator Award (DSTA - Defense Science and Technology Agency, Singapore)

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IMS, 26 Nov Introduction Motivations and objective 2Thermal diode: Rectification of heat flux 3Thermal Transistor Pave the way for heat control 4 Summary BL, LWang, G Casati, PRL 93, (2004) (27 Oct.) (Diode) BL, LWang, G Casati, PRL 94, xx(2005), cond-mat/ (Transistor) Outline

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IMS, 26 Nov Transistor was probably the most important invention in the 20 th century! What is the most important invention in the 20 th century?

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IMS, 26 Nov YearCPUNo.of Trans *2, *3, , , , , ,200, Pentium3,100, Pentium Pro5,500, Pentium II7,500, Pentium IV42,000, Pentium IV55,000,000

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IMS, 26 Nov Brief History of (Electric) Transistor Dec (J. Barden and W. Brattain) June 1948 (Made public Annoucement) July 1951 FET (W Shockley - a Theorist) Sept (Transistor Symposium to comm. Licence for 25,000US$) 1953 (Mass production by RAYTHEON) Texas Instrument Bell Lab

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IMS, 26 Nov J. Bardeen and Brattain J. Bardeen and Brattain Phys. Rev. 74, 230 (1948) (Letters to the editor)

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IMS, 26 Nov How about heat? Can we invent similar device to control heat? Heat is more important than electricity for human being and other forms of life.

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IMS, 26 Nov Daily life experience Energy saving materials

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IMS, 26 Nov Efficient thermal remover/taker for electronic chips Electronic Industry THE STRAITS TIMES : Tuesday, May 18, 2004

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IMS, 26 Nov Defence Cosy uniform Infrared invisible materials

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IMS, 26 Nov Diode: one way street 2. Diode: one way street

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IMS, 26 Nov Thermal diode/Rectifier 2. Thermal diode/Rectifier

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IMS, 26 Nov Question: Can we control heat flow in solid state device? If T L > T R, heat flows from left to right. If T L < T R, heat flow is inhibited from right to left. TLTL TRTR 2. Thermal diode/rectifier

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IMS, 26 Nov Thermal diode/rectifier

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IMS, 26 Nov Terraneo, Peyrard, and Casati Terraneo, Peyrard, and Casati PRL 99, (2002) |J + /J - |~ 1.7

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IMS, 26 Nov New configuration? T+ T+ T- T- T- T- T+ T+

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IMS, 26 Nov Configuration of the diode model from two coupled nonlinear oscillator chains

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IMS, 26 Nov Heat conduction properties of the Frenkel- Kontorova model (BH,BLi,HZ, PRE 57, 2992 (1998).

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IMS, 26 Nov Heat conduction properties of the Frenkel- Kontorova model (BH,BLi,HZ, PRE 57, 2992 (1998).

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IMS, 26 Nov Heat conduction properties of the Frenkel- Kontorova model (BH,BLi,HZ, PRE 57, 2992 (1998). Temperature profile For N=100,200, 300 dT/dx ~ 1/N

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IMS, 26 Nov Heat conduction properties of the Frenkel- Kontorova model ( BH,BLi,HZ, PRE 57, 2992 (1998) ). Thermal Conductivity: Heat current J~ 1/N

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IMS, 26 Nov Phonon band of the Frenkel-Kontorova model Low temperature limit: High temperature limit: Maximal rectifying efficiency:

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IMS, 26 Nov

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IMS, 26 Nov I-V curve ( Li and Wang and Casati, PRL 93, (2004 ) T+ T+ T+ T+ T -

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IMS, 26 Nov (a) Heat current vs coupling constant (b) Temperature profile

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IMS, 26 Nov Heat current versus the ratio of two lattice constants

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IMS, 26 Nov Finite size effect

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IMS, 26 Nov Transistor: witching and Amplification 1. Bipolar Transistor (Barden and Brattain)

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IMS, 26 Nov G(Gate) D(Drain) S(Source) V D (+) V S (-) ISIS IDID IGIG MOSFET I G ≈ 0, I D ≈ I S VGVG

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IMS, 26 Nov TDTD TGTG JDJD How to build a thermal transistor ? Differentil thermal resistance: TSTS ToTo JGJG J JSJS TDTD T 0 ~T G TSTS JDJD

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IMS, 26 Nov How to build a thermal transistor? The thermal transistor never works !!! Current amplification:

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IMS, 26 Nov How to build a thermal transistor? Think something differently!!! How about if one of the thermal resistance is negative? JSJS JDJD T 0 ~T G

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IMS, 26 Nov Negative differential thermal resistance /conductance

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IMS, 26 Nov III Negative Differential Thermal Resistance/Conductance ( BLi et al. cond-mat/ )

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IMS, 26 Nov III. Negative differential thermal resistance/conductance: The physical mechanism ( BLi et al. cond-mat/ )

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IMS, 26 Nov IV. Thermal transistor: configuration ( BLi et al. cond-mat/ )

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IMS, 26 Nov IV. Thermal transistor: A switch ( BLi et al. cond-mat/ ) At the three points T G =.04,.09,.14 J G =0 J D =2.4e-6, 1.1e-4, 2.3e-4 2.3e-4/2.4e-6~100

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IMS, 26 Nov IV Thermal Transistor: Modulator/Amplifier ( BLi et al. cond-mat/ )

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IMS, 26 Nov IV. Possible nanoscale experiment Temperature (simulation): T ~ (0.1 ~ 1) Real temperature T r ~ (10 ~ 100K) System size: Simulation: Simulation: N ~ ( ) Lattice sites Real size: Real size: (10-100nm) Possible nanomaterials Possible nanomaterials: Nanotubes, Nanowires, Thin film ….

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IMS, 26 Nov III Summary Rectifying effect is very generic in nonlinear lattices. A thermal diode model is proposed. A thermal diode model is proposed. A thermal transistor model is built based on theA thermal transistor model is built based on the negative differential thermal resistance. negative differential thermal resistance. Physical mechanism for the thermal diode/transistor are fully understoodPhysical mechanism for the thermal diode/transistor are fully understood.

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IMS, 26 Nov B Li, L Wang, and G Casati, Phys. Rev. Lett. 94 (2005) (in press) cond-mat/ (transistor) 2B Li, L Wang, and G Casati, Phys. Rev. Lett. 93, (2004) (diode) 3B Li, G Casati, J Wang, and T Prosen, Phys. Rev. Lett. 92, (2004) 4J.-S Wang and B. Li, Phys. Rev. Lett. 92, (2004) 5B Li and J Wang, Phys. Rev. Lett 92, (2004) 6B Li and J Wang, Phys. Rev. Lett 91, (2003) 7B Li, L Wang, and B Hu Phys. Rev. Lett 88, (2002) 8B Li, H Zhao, and B Hu Phys. Rev. Lett 87, (2001) 9B Li, H Zhao, and B Hu Phys. Rev. Lett. 86, 63 (2001) 1B Li, J Wang, L Wang, and G Zhang, CHAOS (FPU’s 50 th focus issue, 2005 March), cond-mat/ G Zhang and B Li, Phys. Rev. B. cond-mat/ G Zhang and B Li, Phys. Rev. E. cond-mat/ J.-S Wang and B Li, Phys. Rev. E 70, (2004) 5B Li, G Casati, and J Wang, Phys. Rev. E 67, (2003) 6B Hu, B Li and H Zhao, Phys. Rev. E 61, 3828 (2000) 7B Hu, B Li, and H Zhao, Phys. Rev. E 57, 2992 (1998) Heat conduction Related Publications

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IMS, 26 Nov Thank You!

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