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

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)

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

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?

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

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

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

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.

IMS, 26 Nov Daily life experience Energy saving materials

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

IMS, 26 Nov Defence Cosy uniform Infrared invisible materials

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

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

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

IMS, 26 Nov Thermal diode/rectifier

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

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

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

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

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

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

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

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

IMS, 26 Nov

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

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

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

IMS, 26 Nov Finite size effect

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

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

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

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

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

IMS, 26 Nov Negative differential thermal resistance /conductance

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

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

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

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

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

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 ….

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.

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

IMS, 26 Nov Thank You!