Les instabilités d ordre de charge dans les conducteurs organiques quasi-unidimensionnels

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1 Les instabilités d ordre de charge dans les conducteurs organiques quasi-unidimensionnels J.P. POUGET Laboratoire de Physique des Solides CNRS- Université Paris Sud F Orsay

2 outline Focus on organic conductors undergoing important electron-electron interactions Charge density wave electronic instability and its coupling with the lattice In particular: 4k F CDW instability in 1D / Charge ordering (CO) / Wigner localization In 2:1 salts: influence of the anion sublattice* Quarter band filling effect? * S. Brazovski, V. J. Emery, V.M. Yakovenko

3 ONE DIMENSIONAL CONDUCTORS Structural anisotropy : d // <d d // Anisotropy of overlap of wave functions π organics: pπ σ t perp t // t // >> t inorganics: dz² d Anisotropy of electronic properties: charge transport σ // (ω)>> σ (ω) real 1D conductor: no coherent interchain electronic transfert imply: t <<π k B T (Fermi surface thermal broadening)

4 ORGANIC CHARGE TRANSFERT SALTS 1D Donor A 2 bands crossing at Acceptor Charge transfer ρ: D +ρ A -ρ 2k F =ρ/2 D EF 2kF(A)= 2kF(D) Only a single 2kF critical wave vector!

5 (TM)2X: BECHGAARD and FABRE SALTS Se or S TM: TMTSF or TMTTF :S TMTTF (TM +1/2 ) 2 X -1 1 hole per :Se formula TMTSF unit: 2k F =1/2a* P 1 a x a X centrosymmetrical : AsF 6, PF 6, SbF 6, TaF 6, Br zig-zag chain of TM X non centro. : BF 4, ClO 4, ReO 4, NO 3,,SCN

6 PEIERLS CHAIN 1D metal coupled to the lattice: unstable at 0 K towards a Periodic Lattice Distortion which provides a new (2k F ) -1 lattice periodicity 2k F PLD opens a gap 2Δ at the Fermi level: insulating ground state

7 Charge density wave ground state Charge density wave has two components*: Periodic Lattice Distortion u(x) (PLD)** observed by diffraction (information in reciprocal space: u(q)) Modulation of the electronic density ρ(x) (electronic CDW): observed by STM (information in direct space) u(x) ρ(x) coupled by the electronphonon interaction (g) ρ(x) = - u(x)/ x **in practice the PLD modulates the inter-site (bond) distance one has a 2k F bond order wave (BOW) * not always the case if 2k F =1/2: the BOW and CDW can be decoupled a*/2 BOW: (CH) x : = = = all the C atoms have the same environment: no CDW idem for a a*/2 CDW: O o O o all the bonds are identical: no BOW

8 χe = CDW instability: driven by the divergence of the electron-hole response function χ(q) k f ( Ek + q) f ( Ek) Ek + q Ek (for non interacting electrons) Divergence of χ(q) for q such that E k+q ~E k 2k F χ(q) χ(q) 2k F PLD fingerprint of q wave vectors at which χ(q) diverges

9 2k F modulated chain -2k F Satellite lines: + 2k F Fourier transform of a modulated chain: diffuse sheets in reciprocal space detected by diffraction methods (X-ray diffuse scattering: Guinier school)

10 TSF-TCNQ: 2kF CDW / BOW* instability Charge transfer ρ=0.63 *2k F modulation of the TSF intra-molecular distance 2k F =ρ/2 b* Yamaji et al J.Physique 42, 1327 (1981)

11 TTF-TCNQ: 2kF and 4kF CDW/BOW! b* Charge transfer ρ=0.59 T=60K 2kF 4kF 2kF instability on the TCNQ stack 4kF instability on the TTF stack J.-P. Pouget et al PRL 37, 873 (1975); S.K. Khanna et al PRB 16, 1468 (1977)

12 Τ= 0 Κ ground state in electron-phonon coupled systems Spin degree of freedom ρ = (2) x 2kF 2kF Peierls transition for non interacting Fermions (exists whatever the strength of the electronphonon coupling) 4kF Peierls transition for spinless Fermions (no double occupancy U>>t) (exists only if the electron-phonon coupling is strong enough) No spin degree of freedom ρ = 4kF Average distance between charges: 1/ρ=(4k F ) -1 The 4kF CDW can correspond at the first Fourier component of a 1D Wigner lattice of localized charges

13 4k F phase diagram for spinless fermions with long range coulomb interactions 4k F =n (d // *) organics J. Hubbard, K. Yamaji & J. Kondo; B. Valenzuela et al PRB 68, (2003)

14 V 1 Extended Hubbard Model: H = H + U 0 ORGANIC CONDUCTORS U «experimentally» U~4t // ~1eV; U/V 1 ~2-3; V 2 relevent? n n + V i m n n i i i, m > 0 i i + 1D correlated fermion gas: no quasiparticle only CDW, SDW and supraconductivity fluctuations The most diverging fluctuation at low T depends upon: The strength and range of Coulomb interactions: Kρ (>0 ) Kρ<1 density waves / Kρ>1 superconductivity The sign of the 2kF Fourier transform of the Coulomb interaction: g1 (= U+2V1cosπρ) If repulsion (g1>0): Tomonaga Luttinger Liquid If attraction (g1<0): Luther Emery Liquid m

15 PHASE DIAGRAM OF THE 1D INTERACTING ELECTRON GAS Charge sector (Kσ =1) Coexistence of 2kF and 4kF CDW! (H. Schultz) 2kF incommensurate no unklapp scattering

16 Divergence of the CDW electron-hole response function (U,V 1 0 case) U=0 2kF V=0 2kF U=0 χ(2kf) diverges 4kF T T 0: χ(2kf) diverges U U 2kF χ(4kf) diverges 4kF V ~ U/2 T 0: both χ(2kf) and χ(4kf) diverge J.E.Hirsch and D.J.Scalapino PRB 29, 5554 (1984) T

17 2k F and 4k F CDW / BOW instabilities in TMTSF-DMTCNQ Charge transfer:ρ=1/2 2k F =1/4a* 4k F =1/2a* 2k F and 4k F BOW instabilities are both located on the TMTSF stack

18 1 Kρ BOW instability on the donor stack Increase of the polarizability of the molecule 1/2 HMTSF 2kF BOW TSF S Se 1/3 2kF + 4kF BOW HMTTF two more cycles 4kF BOW TTF 0

19 In charge transfer salts: the 2k F BOW instability drives the Peierls transition the 4k F BOW instability is at most weakly divergent JPP 1988

20 Crossover from a dominant 2k F instability to a dominant 4k F instability in NMP 1-x Phen x TCNQ ρ incom 2k F only 4k F dominant ρ=1/2 Reduction of the interchain screening* promotes the divergence of the 4k F instability! 2 chains system: screening thus 2k F instability dominant single chain system: no screening, 4k F instability dominant A.J. Epstein et al PRL 47, 741 (1981) *screening between electron (TCNQ) and hole (NMP) 1D gas

21 2k F BOW instability on the TMTSF stack diverges in TMTSF-DMTCNQ Charge transfer salt with ρ=0.5 vanishes in (TMTSF) 2 PF 6 2:1 cation radical salt: ρ=0.5 What about the 4k F instability in ¼ filled single chain organic salts?

22 4k F charge localization in a quarter filled band (ρ=1/2) U,V 1 phase diagram (Mila & Zotos EPL 24, 133 (1993) In the insulating phase the electrons are localized: - on one bond out of two (4k F BOW: Mott Dimer) - on one site out of two (4k F CDW: Charge Ordering)

23 4k F BOW: Mott dimers (all the sites are equivalent; the bonds are different) Exemple 1:2 TCNQ salts MEM (TCNQ) 2 : T<335K Intradimer overlap Interdimer overlap (S. Huizinga et al PRB 19, 4723 (1979))

24 4K F CDW: Wigner charge order NMR shows that the 2 sites are different: charge disproportion First experimental evidences in ¼ filled organic conductors D 2 X or A 2 Y: -(TMP) 2 X-CH 2 Cl 2 (X=PF 6,AsF 6 ) (Ilakovac et al PRB52, 4108 (1995)) but problem of disorder due to solvant - (DI-DCNQI) 2 Ag (uniform stack) c (TMTTF) 2 X (X=PF 6,AsF 6, SbF 6,ReO 4,.) (dimerized stack) x x x x Role of the cationic/anionic sublattice in the stabilization of the CO? a

25 (DI-DCNQI) 2 Ag 13 K l =3 l =2 l =1 201 K 100 K 213 K NMR : inequivalent molecular sites: charge disproportion below ~210K (K. Hiraki et al PRL 80,4737 (1998)) 4k F =1/2c* X-ray scattering: quasi-1d at RT chain dimerization below~ 220K (Y. Nogami et al Synth. Met. 102, 1778 (1999)) 156 K 176 K T CO 226 K R. T.

26 4k F CO and BOW in (DI-DCNQI) 2 Ag shift of Ag + towards charge rich DCNQI charge pattern reveals 3 kinds of stack in the CO state! Charge rich aeras form a body centered tetragonal structure charge on the sites charge on the bonds intermediate situation Charge pattern imposed by the interchain Coulomb coupling? Kakiuchi et al PRL 98, (2007)

27 Charge ordering transition in (TMTTF) 2 X Charge disproportion at T CO 2 different molecules :NMR line splitting Chow et al PRL 85, 1698 (2000) Charge disproportion + incipient lattice dimerization (4k F BOW) no inversion centers: ferroelectricity at T CO Monceau et al PRL 86,4080 (2001) Symmetry breaking at T CO Difficulties to detect it due to: - the very low symmetry of the lattice - X-ray irradiation damages

28 Lattice anomaly at the CO transition (thermal expansion) β/t ~ δ²f/δt² c* soft direction: softening could be achieved by a transverse shift of the anions Additional transition at T int? M. De Souza et al PRL 101, (2008)

29 Shift of the anion sublattice X with respect to TMTTF sublattice ) TMTTF hole rich (contracted) * TMTTF electron rich (elongated) 1 ρ e d 1 8 ρ h 1 11 d 2 =? 11 ρ e =0.5-δ PF 6 - > ρ h =0.5+δ Shift of the anion sublattice required to break the inversion symmetry and to achieve ferroelectricity (S. Brazovski) PF 6 -

30 Hypothetical charge pattern of ferroelectric TMTTF a,c plane Anion X - points towards hole rich TMTTF a,b plane a b 3D Coulomb interactions minimized? anion shift seems to be essential to impose the charge pattern

31 2:1 salts with 1/4 (3/4) or 1/2 Band filling (DI-DCNQI) 2 Ag - uniform stack ¼ filled system undergoing a 4k F CDW instability (TMTT(S)F) 2 X - zig-zag dimerized ½ or 3/4 filled system if the dimerization gap 2Δ is larger or smaller than W or πk B T (TMTTF) 2 PF 6 : 2Δ ~88meV W b ~55meV 1/2 filled system (TMTSF) 2 PF 6 : 2Δ ~86meV W b ~130meV 3/4 filled system Ducasse et al J. Phys. C 19, 3805 (1986)

32 δ-(edt-ttf-conme 2 ) 2 Br «average structure» Pmna approximate symmetry: non planar molecule located on the miror m ( no stack dimerization: approximate statement) glide plane a all molecules are identical (no CO) close to 3/4 filled system at RT in fact superlattice modulation (0,1/2,0) at RT strucural refinement weak dimerization + CO at RT (DMtTTF) 2 ClO 4 - uniform zig-zag (2 1 screw axis symmetry) ¾ filled

33 (DMtTTF) 2 ClO 4 2 1? C2/c Coulon et al J. Physique 47, 157 (1986)

34 X-ray diffuse scattering investigation of (DMtTTF) 2 ClO 4 Short range incommensurate anharmonic Modulation q=(-0.58, 0, 0.275) Stack periodicity Diffuse spots Main Bragg reflections S. Ravy et al J. Phys. IV, 114, 81 (2004)

35 4k F order does not involves the spin degrees of freedom which remains free to order at low T (TMTTF) 2 X χ S not perturbed at the CO transition T CO 4k F order well decoupled from the low T ground state involving S=1/2 coupling AF Magnetic order Spin pairing Spin-Peierls (2k F BOW instability) 2k F SDW 4k F CDW (CO) 4k F BOW (Mott dimer) S=0 MEM- (TCNQ) 2

36 Partial conclusions 4k F or CO instability are not new in the organic conductors: known since 1976 in the charge transfer salts! In 2:1 salts 4k F intrastack instability strenghtened by the reduction of the interchain screening Cooperative role of the anion (cation) sublattice to stabilize the CO ground state Is there any thing special for ¼ band filling? more the order of commensurability n of the filling increases more the V n coulomb interactions must be important to induce a Wigner charge localization in 1D

37 Indirect contribution to V 2 interaction via Coulomb coupling with the anion sublattice Contribution to the polarisability of the anion sublattice λ ea V 2 V 2 eff V 2 + (λ ea )² FT[χ Α (q,ω)] i-j=a which can be high near a structural transition involving an anionic shift Quantum chemistry calculations on clusters of TMTTF molecules for intrastack interactions: V 1D ~ V I 1 ~ U/2 V 1 ~1.5 V 2 V i F. Castet et al J. Phys. I 6, 583 (1996) i=1 2 The polarisability of the anions and the screening effects are ignored

38 Explicit consideration of repulsive V 2 t, U, V 1, V 2 extended 1D Hubbard model Ground state: U=10t V 1 V 2 V 1 V 2 =V 1 /2 frustration line Well below this line: 4k F CDW Well above this line: 2k F CDW O o O o O o O O o o O O (Ejima et al PRB72, (2005)) For V 2 ~V 1 /2 frustration: metallic state (TLL) preserved However frustration effects can be lifted by small perturbations (chain dimerization, anion ordering)