Bhaskaran Muralidharan

Transcription

1 Molecular thermoelectric heat engines and coolers Ĥ,, in Q out Q P V app Bhaskaran Muralidharan Department of lectrical ngineering, II Bombay RI Allahabad

2 Outline Prelude: Fundamentals Brief timeline: Macro to nano ingle Molecules as eat ngines pilogue: Future outlook Ĥ,, in Q out Q P V app B Muralidharan and M Grifoni, PRB, 0 B Muralidharan and M Grifoni, PRB, 03 A Agarwal and B Muralidharan, APL, 04 A ingha, D Mahanti and B Muralidharan, AIP Adv 05

3 PRLIMIARI: Molecular onduction-an perspective harge transport: lectrochemical potential gradients. Ĥ L R LUMO L R OMO, in Q Ĥ out Q, hermoelectric transport in the presence of electrochemical potential and temperature gradients. RGY OVRIO

4 PRLUD: What drives currents at an atomic level? 4

5 ano-devices hannel 0 e- e- ontacts/leads ource/drain electrodes 5

6 anoscale Devices + Landauer insight γ /, D qv, I I f f dξ D ransport Function Driving Force V qv D D 6

7 PRLIMIARI: Molecular onduction-an perspective harge transport: lectrochemical potential gradients. Ĥ L R LUMO in Q Ĥ out Q L R OMO,,

8 World of Quantum transport 0. mm 0 m m 0. m 0 nm nm 0. nm Macroscopic dimensions <--- L --> Atomic dimensions 8

9 hermoelectric energy conversion POWR GRAIO: UIG BK FF RFRIGRAIO: UIG PLIR FF Discovered in early 800s eebeck and Peltier heory by Onsager-allen -930s Practical energy conversion ideas after 950s Ioffe anoscale energy conversion after 000s

10 Metric for material Performance technology Power generation Refrigeration eebeck effect Peltier effect fficiency of heat pump Or cooling increasing Function of z fz z σ k

11 Ideas to improve z z z σ κ + κ el ph lectron engineering Phonon engineering DO engineering Other exotic ideas anostructuring ngineering barriers, Anharmoicity etx., Quantum Dots Molecular Devices

12 lectron ngineering: Landauer viewpoint Macroscopic eebeck effect Microscopic eebeck effect _ V D _ f Peltier effect Peltier effect I Asymmetry in DO results in a better material Barriers create better cooling systems

13 What nano-structuing does? Distorting the DO uperlattices lectron filtering

14 anoscale Devices-he energy picture hannel ource Drain,, Δ Δ + 4

15 anoscale Devices/eat ngines? Δ tot ΔF 0 Δ Δ 0 I Δ 0 V + 0 pv + + M F n F n Δ n Q V app Δ Onsager-allen theory s M I Δ > 0 V app V V 5

16 in Q P η η η P V app P V app app V V,, 0 V Δ Molecular converters V q P Q Q L R R Q L Q R R Q L L Q R R L L Δ Δ

17 ransport theories: a hannel limit k,γ b Dot limit k,γ << GF-F approach U F U < n > Fock space density-matrix approach L R single particle energy states 0 0 Fock space energy states 00 trong coupling regime Weak coupling regime aroli et. al., 97 7

18 U Γ << k B, ± ± ± j j i j i j i i ij i j i r ij j i j a ji Q j i i j i j i j P R P R dt dp P R P R P R P R q tot tot ] [ ] [ ] [,,,,,,,,,,,,, 0 +U +U,U +U, app V Bi V, 0 V app P in Q out Q Formalism

19 hermoelectric operation:power hort ircuit, 0, V app 0, 0, V app Open ircuit, 0, V app V P 0 0 V app 0 V app P V V app 0 V app P 0 V, 0 P max V app V Region of positive Power work done by system

20 hermoelectric operation: fficiency η V app app V max 0, Q 0, V η η η 0 arnot ngine η max η V app V Bi

21 Δ, app V V, 0 Δ f f 0 Open ircuit tot Q Q η η Δ Δ + Δ Δ + + Δ Δ Δ 0 0 Ideal QD-nano-arnot ngine Q Δ Δ OFO MAA RMOLRI

22 Linear response picture: z in Q Ĥ, 0 out Q, V app V σv Q app σv + σδ app + L Δ σ V app Q 0 V Δ 0 κ el Q Δ 0 κ ph Q Δ ph η max η + z + z + z σ κ + κ el ph Ioffe 947 ofo and Mahan PA 996

23 Ideas to improve z z z σ κ + κ el ph lectron engineering Phonon engineering DO engineering Other exotic ideas anostructuring ngineering anharmoicity etx? Quantum Dots Molecules

24 Best hermoelectric, U U 0 δ κ el 0 σ z κ + κ el ph η max η + z + z + η, 0 Γ << k B, U, V app V Bi OLY W 0, Δ 0 0 Q Reversible limit Mahan and ofo PA 996

25 η η max η <η max η 0 0, app V V, 0., / f f dd f f dd q D Q γ γ γ γ γ γ γ γ γ γ γ γ π Max fficiency approaches arnot limit at finite power operating point different from open circuit Realistic QD efficiency

26 hermoelectric operation: Finite U,U η 0.3 +U V app, 0, Γ << k B, U on-trivial variation of maximum efficiency with U Maximum efficiency operating point shifts non trivially B Muralidharan and M Grifoni, PRB 0

27 Maximum fficiency and U Max efficiency -> arnot - small and large U z based linear response calculation not correct at higher arnot values B Muralidharan and M Grifoni, PRB 0

28 RAP +U,, V app,, V app, 0, V app Ideal non-interacting ase of nano-arnot engine Real non-interacting Role of line-width Interacting on-trivial role of U ow to improve power efficiency trade-off 8

29 ffect of flattening the DO- Power-efficiency trade-off Maximum efficiency reduces But more power can be drawn at max efficiency Power efficiency trade-off 9

30 A Bulk example-lesson learnt DO engineering of Pb eremans et al., cience 008

31 he RD thermoelectric A Agarwal and B Muralidharan, APL, 05,

32 mbedded nano structures. A ingha D Mahanti and B Muralidharan, AIP Adv, 5,

33 Molecular heat engines coupled to vibrionic degrees 33

34 Quantum ano-nergy-pin ransport ARG pin nergy 34

35 , ˆ ˆ ˆ,, + R L r q B m m p m p q dt d τ QD pin dynamics v/s L L, R R, +U L m L p, R R m p, + Γ π f U f d m p B ˆ ' Precession Damping Injection Relaxation Precession 35 B Muralidharan and M Grifoni, PRB 03

36 L m L p, R R m p, y z x B L B R B + hermoelectrically induced spin precession Pure spin current due to spin precession + τ B m m p m p q r q, ˆ ˆ ˆ Injection Relaxation Precession pin precession-spin current B Muralidharan and M Grifoni, PRB 03 36

37 ano-device demons + info battery 0 0 Δ Δ Δ Δ F tot Δ v/s RGY IFORMAIO 37

38 Other complicated nanoscale demons he case of ntanglement and quantum information: r[ ρ ln ρ] Universe at 0 Universe at 0, i 0 / ab + β0 / ab + ξ0 / aa + δ 0 / bb

39 World of Quantum transport 0. mm 0 m m 0. m 0 nm nm 0. nm Macroscopic dimensions <--- L --> Atomic dimensions ource Σ s + U Σ Σ Unified formalism For quantum transport F Drain ^ many electron levels