Disorder Effects on the Charge Density Wave Structure: Friedel Oscillations and Charge Density Wave Pinning

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1 Disorder Effects on the Charge Density Wave Structure: Friedel Oscillations and Charge Density Wave Pinning Sylvain Ravy a,b, Stéphane Rouzière b, Jean-Paul Pouget b and Serguei Brazovskii c a Synchrotron SOLEIL, l Orme des Merisiers, Saint-Aubin, F Gif-sur-Yvette b Laboratoire de Physique des Solides, CNRS UMR 8502, Université Paris-sud, F Orsay c Laboratoire de Physique Théorique et Modèles Statistiques, CNRS UMR 8626, Université Paris-sud, F Orsay Recent developments in low dimensional charge density wave conductors Skradin, Croatia 29 th June - 3 rd July 2006

2 CDW pinning + - 2e Δϕ < 0 strong (local) pinning or weak (collective) pinning (Fukuyama, Lee, Rice, 1978/79) Δϕ > 0 Local phase deformation (Friedel oscillations)... or Collective

3 Impurity primary effect Peak broadenig:loss of long range order L = (HWHM) -1 (size of the average coherent domain) textured CDW pattern? Intensity (counts/s) Intensity (counts/s) ( ) LURE-DW22 V % k 5000 (13 k -6.5) ESRF-TROÏKA 4000 V % Intensity (counts per monitor counts) 10 3 W-K 0.3 MoO (-1 k 0.5) k (b*) in chain direction 2π k No local informations...

4 Local informations deduced from X-ray scattering: outline Diffraction from a modulated structure in a substitued crystal Interference effect: +2k F /-2k F intensity asymmetry: «white line» holographic effect organic conductors Profile asymmetry of the 2k F superlattice spots: scattering by the Friedel oscillations doped blue bronzes

5 Intensity diffracted by a disordered crystal σ n = 1 if site n is occupied by an impurity u n CDW (Peridic Lattice Displacement) difference of structure factor: Average structure factor: scattering due to disorder: scattering due to PLD: (Laüe scattering) interference term: antisymmetric in q

6 Intensity asymmetry between the +2k F /4k F and -2k F /4k F scattering!

7 TTF=D TCNQ=A TTF-TCNQ and its family E A c D E F b π/b k -k F k F π/b charge transfer = 0.59 a T P = 38 K, 49 K, 54 K defect of substitution on the donor stack

8 4kF SCATTERING in TTF-TCNQ Pure TTF-TCNQ TTF-TCNQ alloyed with 3% TSF destructive/constructive interferences of the 4kF scattering with No interference for the 2kF scattering the Laue scattering due to the TSF The 4kF CDW is located on the TTF stack! impurity The 2kF CDW is located on the TCNQ stack!

9 HMTTF-TCNQ (HMTTF) x (HMTSF) 1-x -TCNQ x=0% x ~ 5% -2k F +2k F white diffuse line Coherence between the impurity position and the phase of the CDW LOCAL PINNING

10 From the sign of the intensity asymmetry one deduces the phase φ 0 of the CDW on the impurity site! local pinning mechanism: size effect versus electronic effect

11 Analysis of the intensity asymmetry of the 2k F scattering size HMTSF>HMTTF Molecular displacements charge density Charge: max on HMTSF (ρ=0.74 in HMTSF-TCNQ) min on HMTTF (ρ=0.72 in HMTTF-TCNQ) Size and charge effects act cooperatively

12 White line effect for the 1+4k F scattering in TTF 0.97 TSF 0.03 TCNQ. The dotted lines represents the Laüe scattering background due to the TTF/TSF substitution disorder.

13 «holographic diffraction» and the phase problem J. M. Cowley, Surf. Sci. 298 (1993) 336. J. M. Cowley, Phys. Rev. Lett., 84 (2000) the «holographic diffraction» is a scattering process in which the diffracted waves by one kind of atom are taken as référence, and from which the statistic of the atomic distribution around this atom of reference can be deduced. Optical holography Reference wave Detector Diffracted waves Object Image I = A ref +A object exp(iφ) 2 = A ref 2 + A ref A object exp(iφ) + c.c. + Aobject 2 Detector Reference wave Laüe scattering Diffracted wave Object Satellite reflections «White line» effect

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15 The thermal dependence of the extra (4k F ) CDW scattering is governed by the CDW response function intensity asymmetry I A extra peak intensity χ ρ χ² ρ TTF/TSF alloys irradiated TTF-TCNQ

16 In irradiated samples: ~ 0 no «white line» effect but extra scattering: formation of Friedel Oscillations?

17 T>T P =42K 4k F 0.1% mol. defects 0.7% mol. defects pure formation of FOs around irradiation defects gives rise to extra 2k F and 4k F lattice displacements 2k F 0.7% mol. defects pure

18 blue bronze: K 0.3 MoO 3 (or Rb 0.3 MoO 3 ) 2k F wave vector of the charge density wave Potassium (Rubidium) // 2a*-c* a b MoO 6 c Substitution defect: V or W on the Mo site a+2c (~2a*+c*)

19 Substitution: 3d V 4d 5d Mo W W 6+ : isoelectronic of Mo 6+ ~ same size as Mo 6+ (0.60Å) V 5+ : one electron less than Mo 6+ smaller size than Mo 6+ (0.54Å) preferentially substitutes the Mo(2) sites Threshold field at 77K: 2.8%-V ~20V/cm 2%-W ~0.25V/cm «pure» ~0.1V/cm

20 V-2.8% doped blue bronze chain direction +2kF -2kF

21 V-doped blue bronze K 0.3 MoO 3 (V 5+ /Mo 6+ ) Intensity (counts/s) (13 k -6.5) V - 2.8% 6 scans in chain direction 1-spot bradening 2-2k F shift 3-profil asymmetry Intensity (counts/s) k 120 ( ) LURE-DW V % k F k 5000 (13 k -6.5) ESRF-TROÏKA -2k F 1000 Intensity (counts/s) V % k k k

22 Regular part of the CDW No Peierls long range order at low temperature in doped blue bronzes!

23 2kF variations 2%-W 0.28%-V 1.44%-V pure K0.3MoO3 2.8%-V V concentration c:

24 Profile asymmetry of +/- 2kF diffuse spots in A 0.3 (Mo 1-X V X )MoO 3 Scans in chain direction

25 2% W-doped blue bronze Lorentzian squared profile Intensity (counts per monitor counts) W-K 0.3 MoO (-1 k 0.5) Intensity (counts per monitor counts) (-1 k 0.5) W-K 0.3 MoO k (b*) k (b*) Profile asymmetry

26 Lorentzian square profile Scans perpendicular to chain direction V-1.44% V-0.28% W-2% No Bragg glass behavior

27 T<<T MF the satellite profile is due to spatial variations of the phase φ(r) of the CDW modulation in the gaussian approximation: in the framework of the FLR theory: its 3D Fourier transform gives rise to a lorentzian squared (L²) profile, whose:

28 +/- 2kF diffuse spot doublet in A0.3(Mo1-XVX )MoO3 X=2.8% Intensity asymmetry X=1.44% Profile asymmetry X=0.28% +2kF Scans in chain direction -2kF

29 Intensity asymmetry of + 2kF /-2kF diffuse spots in A0.3(Mo1-XVX )MoO3 (with respect to pure blue bronze) (1, 8+δk, -0.5) (1, 10+δk, -0.5) Intensité (unité arb.) k F -2k F δk (b*) electronic effect opposite to size effect! Mo V Mo

30 Intensity asymmetry Phase on the impurity site Calculation with experimental phason velocity T Debye phasons

31 Profile asymmetry of + 2kF /- 2kF diffuse spots in A 0.3 (Mo 1-X V X )MoO 3 Scans in chain direction

32 X ray scattering :Fourier transform of Regular CDW Friedel oscillations FOs give rise to profile asymmetry!

33 Friedel oscillations - phase shift Scattering theory -Quantum mechanics: phase shift of the wave function caused by an external potential -applied to solid state physics (Friedel 52) In a metal: screening of an impurity potential by a charge oscillation: δρ(r) r D exp(-r/ξ) cos(2k F r + η) η: phase shift of the wave function at E F Phase Densité de charge Pi/2 0 -Pi/ e - Δϕ=2η ξ Charge Z to screen: Friedel sum rule Z= 2η/π n

34 Friedel oscillations in 1D metallic phase: Gap: Peierls ground state: : FOs of the metal : damped FOs regular CDW: regular CDW dominates the FOs for x>x 0 with In thebluebronze: V c ~0.5eV: V 2kF ~1eV for V-doped: x 0 >d important FOs V 2kF ~0.1eV for W-doped: x 0 <d no FOs

35 phase (screening) Z= 1 η= π/2 amplitude (damping ξ) + phase regular CDW (dotted line) FOs Mo Electron density as a function of the unit cell n showing FOs merging into the regular CDW The FOs is calculated with a phase shift 2φ=-π (top) which screens the negative charge (Z= 1) provided by the V 5+ with respect to the W 6+ background and a damping length ξ=8å [Arrows indicate that the effect of the phase shift is to expend the CDW, which makes the oscillation loose half a period (i.e. one electron) close to the defect located in n=0]

36 Friedel oscillations amplitude oscillations (damping ξ) phase shift Z= ±1 case (η= ± π/2) ξ Blue bronze case ξ~b

37 Profile asymmetry: CDW Pinning with Friedel oscillations Mo 6+ V 5+ substitution: phase shift of π (screening of the defect of charge on the V) χ(n) 2 0 2η=π Intensité (unité arb.) δq (1, 8+δk, -0.5) (1, 10+δk, -0.5) δk (b*) -2 Friedel oscillations -8-6 on -42ξ=16-2 Å in the vicinity of the V impurity Charge density π phase shift n 2ξ Misfit between the Friedel oscillations and the regular CDW Regular CDW at larger distances Δq fonction of η and ξ Fourier transform S. Rouziére, S. Ravy, JPP, S. Brazovskii PRB 62, R16231 (2000) and submitted

38 X ray scattering :Fourier transform of Regular CDW Friedel oscillations Δq FOs give rise to profile asymmetry!

39 total Fourier transform

40 CDW pinning + - 2e Δϕ < 0 strong (local) pinning or weak (collective) pinning (Fukuyama, Lee, Rice, 1978/79) Δϕ > 0 Local phase deformation (Friedel oscillations)... or Collective

41 φ(n) 40 random impurities on sites (c=0.4%) strong pinning model (φ 0 =ηi=0) strong pinning (φ 0 =0) and phase shift (ηi= π/4) n phase shift only model (ηi= π/2) (φ 0 random ) B D Fourier transforms Intensité (exact calculation) (S. Ravy) k(b*) x number of impurities per coherent domain

42 number of impurities per coherent domain profile asymmetry intensity asymmetry * *** ** + * ** *** + not yet a theory

43 Microscopic theory (basic) PLD : u(r)=u 0 sin(2k f.r+ϕ(r)) CDW : ρ(r)= ρ 0 + δρ cos(2k f.r+ϕ(r)) Interaction between the phase of the CDW and the potential of the defect : H= dr(c // /2( x ϕ) 2 + C /2( ϕ) 2 + V(r - r m ) x ϕ/π + U cos(2k f.r+ϕ(r))δ(r - r m ) ) elastic energy of deformation of the phase of the CDW Fourier transform: Σ m Coupling between the CDW and the impurity potential: (r)ρ(r)dr Σq (-q)ρ(q): 2 scattering processes q~2k F : backward scattering process k f -k f (U interaction term) Pinning and intensity asymmetry q~0: forward scattering process k f k f (V interaction term) Interaction between the impurity and the non oscillating part of the CDW phase shift and profile asymmetry

44 summary X-ray scattering effects : -give access the local properties of the CDW including the pinning and phase shift around impurities -allow to propose a complete scenario of the (weak/strong) pinning Main message:in any case the local effects cannot be neglected Main reference: 35 pages paper submitted to Phys. Rev. B

45 Détermination expérimentale des déphasages 2*déphasage «Coraux quantiques» faits par STM. Atomes de Fe sur une surface de Cu(111) M. F. Crommie, C. P. Lutz, D. M. Eigler, Nature 363, 524 (1993) M. F. Crommie, C. P. Lutz, D. M. Eigler, Science 262, 218 (1993)