Casimir Friction Aleksandr Volokitin Research Center Jülich and Samara State Technical University

Transcription

1 p 1 Casimir Friction Aleksandr Volokitin Research Center Jülich and Samara State Technical University Fluctuational Electrodynamics Casimir Forces Near-Field Radiative Heat Transfer Casimir Friction Non-Contact Friction Frictional Drag

2 Fluctuation-Dissipation Theorem p 2 mẍ+mω 2 0x+Γẋ = F(t) Γ = (k B T) 1 Re 0 dt ˆF(t)ˆF(0) The detection of single spins by MRFM for: (a) 3D atomic imaging (b) quantum computation Measurements of gravitation force at short length scale Measurements of Casimir forces

3 Rytov s Theory p 3 E = i ω c B H = i ω c D+4π c jf j f i (r)jf k (r ) = ω (2π) 2 ( ) 1 2 +n(ω) ω 2 Imε ik (r,r,ω) n(ω) = [e ω/k BT 1] 1

4 Origin of Non-Contact Friction p 4 AI Volokitin and BNJ Persson, RevModPhys, 79, 1291 (2007)

5 Non-contact Friction Experiment: Stipe BC etal PRL, 87, (2001) F friction = Γv, Γ kg/s at d nm Γ d n with n = 13±03 and n = 05±03, Γ V 2 Theory: AI Volokitin and BNJ Persson, PRB, 73, (2006) p 5

6 p 6 Electronic versus Phononic Friction Experiment: M Kisiel etal Nat Materials, 10, 119 (2011)

7 p 7 Electronic versus Phononic Friction Theory: AI Volokitin and BNJ Persson, PRB, 73, (2006)

8 p 8 Casimir Friction v ω+q v x ω-q v x Pendry JB JPCM 9, (1997) AI Volokitin and BNJ Persson, JPCM, 11, 345 (1999)

9 p 9 Frictional Stress σ xz = 0 dω 2π i=(s,p) d 2 q (2π) 2 q xsgn(ω ) ( n 2 (ω ) n 1 (ω) ) Γ i (ω,q), 1 Γ i (ω,q) = 2k z 1 e 2ikzd R 1i (ω)r 2i (ω ) 2 [ (k z +kz)(1 R 1i (ω) 2 )(1 R 2i (ω 2 ) ] +4(k z kz)imr 1i (ω)imr 2i (ω )e 2dImk z ω = ω q x v, n i (ω) = [exp( ω/k B T i ) 1] 1, k z = (ω/c) 2 q 2 AI Volokitin and BNJ Persson, JPCM, 11, 345 (1999)

10 p 10 Small Velocities v v T = k B Td/, d λ T = c /k B T, γ = 2 8π 3 k B T 0 σ xz = γv, dω sinh( ω/k B T) i=p,s d 2 qq 2 xe 2qd ImR 1i (ω)imr 2i (ω) 1 e 2qd R 1i (ω)r 2i (ω) 2, Γ = dsγ(z(x, y))

11 p 11 Adsorbate enhancement of Casimir friction log Γ (kg/s) log d (Angstrom) Cs/Cu(100) AI Volokitin and BNJ Persson, PRB, 73, (2006)

12 p 12 Radiative Heat Transfer log (S / Jm -2 s -1 ) clean surfaces with adsorbates o log (d / A) K/Cu(001) log (S / 1Jm -2 s -1 ) o log (d / 1A) SiC T 1 = 273 K, T 2 = 0 K Volokitin AI and Persson BNJ PRB, 69, (2004)

13 Two ways to study Casimir friction p 13 v 2 J 2= n 2ev U 1 Left:Upper block is sliding relative to block at the bottom Right: The current is induced in the upper block

14 Frictional Drag in 2D-systems p 14 Layer 1 J 1 d Layer 2 E 2 (J =0) 2 V Theory - Coulomb Drag M B Pogrebenskii SovPhysSecond,11 (1977) 372, P J Price Physica B+C,117 (1983) 750 Experiment - Quantum wells T J Gramila etal PRL,66 (1991) 1216, U Sivan etal PRL,68 (1992) 1196 Experiment - Graphene Sheets S Kim etal PRB,83 (2011) , RV Gorbachev etal NatPhys,8 (2012) 896 Theory - Casimir Friction AI Volokitin and BNJ Persson, JPhys:CondensMatter, 13, 859 (2001); ibid, EPL (2013)

15 Quantum Friction p 15 q x v = ω 1 +ω 2 Pendry JB JPCM 9, (1997) Volokitin AI and Persson BNJ JPCM, 11, 345 (1999) Volokitin AI and Persson BNJ PRB, 78, (2008)

16 Anomalous Doppler Effect p 16 v ω+q v x ω-q v x Normal Doppler effect ω = ω q x v > 0 Anomalous Doppler effect ω = ω q x v<0 Thermal fluctuations dominate at v < v T = k B Td/ Quantum fluctuations dominate at v > v T = k B Td/

17 p 17 Classical Vavilov-Cherenkov Radiation Cherenkov PA Dokl Akad Nauk SSSR, 2, 451 (1934) Resonant condition: q x v = cq/n > v 0 = cq x /n Threshold velocity: v > c/n

18 p 18 Quantum Vavilov-Cherenkov Radiation Frank MI JPhysUSSR, 7, 49 (1943) Doppler effect (a): ω ph = ω 0 g x v > 0 Doppler effect (b): ω 0 g x v < 0;ω ph = q x v ω 0

19 p 19 The Landau criterion for the critical velocity of a superfluid ε(p) p E = Mv2 2 +ε(p) pv ε(p) pv < 0 v > v c = min ( ε(p) p Landau LD, Zh Eksp Teor Fiz 11, 592 (1941) )

20 Radiation at shearing two transparent plates p 20 Pendry JB JMO 45, 2389 (1998) Magreby FM, Golestian R, and Kardar M, PRA 88, (2013) Volokitin AI and Persson BNJ PRB 93, (2016)

21 Non-Relativistic Theory F s 1x [normalized] Resonant condition: ω ph = q x v cq/n = cq/n,v > v 0 = 2c/n F1x s = v 0 π 3 d F s 4 1x [normalized] v/v o R s = (ω/c) 2 q 2 (nω/c) 2 q 2 (ω/c) 2 q 2 + (nω/c) 2 q 2 Magreby FM, Golestian R, and Kardar M, PRA 88, (2013) Volokitin AI and Persson BNJ PRB 93, (2016) p 21

22 Relativistic Theory p F 1x [normalized] F 1x [normalized] v/c v/c ω ph = q x v cq /γn = cq/n,v > v 0 = 2cn/(n 2 +1) Volokitin AI and Persson BNJ PRB 78, (2008) Volokitin AI and Persson BNJ PRB 93, (2016)

23 Radiation From Moving Neutral Particle p 23 2 a) v b) c) v v ω ph = q x v ω 0 /γ = cq/n,v > v 0 = c/n Pieplow G and Henkel C, JPCM 27, (2015) Volokitin AI and Persson BNJ arxivorg/abs/ (2016)

24 Quantum Friction for Particle p 24 log 10 f friction (N) (a) (b) v/c log 10 γ

25 p 25 Polar Dielectric SiO F friction, 10 5 N/m v, 10 5 m/s Resonant condition: ω ph = q x v ω 0 = ω 0 Threshold velocity: v > 2ω 0 /q xmax 2ω 0 d m/s

26 p 26 Graphene on SiO 2 electrode graphene SiO 2 Threshold velocity: v > v F +ω 0 /q xmax v F 10 6 m/s Resonant condition: ω ph = q x v v F q = ω 0 Experiment:Freitag M,Steiner M, Martin Y, Perebeinos V, Chen Z, Tsang JC, and Avouris P, Nano Lett 9, 1883 (2009) Theory:Volokitin AI and Persson BNJ PRL (2011)

27 p 27 Current density-electric field dependence in graphene on SiO 2 16 a) 9 b) 16 T=300 K J (ma/µm) T = 150 K 300 K 450 K J (ma/µm) T=0 K E (V/µm) F x, 10 3 N/m K E (V/µm) v, 10 5 m/s v sat v F 10 6 m/s J sat = en s v sat 1mA/µm

28 Frictional Drag between Graphene Sheets p F x, N/m a) T=600 K 300 K 0 K F x, N/m b) T=300 K 100 K 0 K v, 10 5 m/s v, 10 5 m/s d=1 nm d=10 nm At l v v F induced electric field E = ρ D J = µ 1 v ρ D = Γ (ne) 2 = h πζ(3) e 2 32 ( kb T ǫ F ) 2 1 (k F d) 2 1 (k TF d) 2, F x0 = v 15ζ(5) d 4 128π 2 ( v v F ) 2 1 (k TF d) 2 Volokitin AI and Persson BNJ EPL (2013)

29 p 29 Acoustic Phonon Emission solid 0solid 0 solid 0 d + u - u eq 0 1 z solid 1 σ(x,t) = K[u 0 (x vt,t) u 1 (x,t)], Persson BNJ, Volokitin AI and Ueba H, JPCM (2011)

30 p 30 Acoustic Phonon Emission σ, N/m v, m/s

31 p 31 Summary Casimir friction can be studied using modern experimental setups for observation of frictional drag in graphene systems The challenging problem is to study frictional drag for graphene for strong electric field (large drift velocity) when Casimir friction is dominated by quantum fluctuations (quantum friction) The challenging problem for experimentalists is to develop setup for mechanical detection of Casimir friction using AFM Quantum friction is strongly enhanced above the threshold velocity The threshold velocity is determined by a type of excitations which are responsible for quantum friction