Charge ordering in quasi-one dimensional organic conductors J

Charge ordering in quasi-one dimensional organic conductors J. P. Pouget & P. Foury-Leylekian Laboratoire de Physique des Solides I. F. Schegolev Memorial Conference « Low- Dimensional Metallic and Superconducting Systems » October 11 -16, Chernogolovka, Russia

outline • Focus on organic conductors experiencing important electron-electron interactions • Charge density wave (CDW) electronic instability and its coupling with the lattice • In particular: 4 k. F CDW instability in 1 D / Charge ordering (CO) / Wigner localization • In 2: 1 salts: influence of the anion sublattice

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

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

2 k. F modulated chain Modulation of the electronic density and of the atomic positions Real space Reciprocal space a 2π/2 k. F a* -2 k. F satellite lines + 2 k. F Fourier transform of a modulated chain: diffuse sheets in reciprocal space detected by diffraction methods (X-ray diffuse scattering technics)

TSF-TCNQ: 2 k. F CDW / BOW* instability Charge transfer r=0. 63 2 k. F=ρ/2 b* *2 k. F modulation of the inter-molecular TSF distances Yamaji et al J. Physique 42, 1327 (1981)

TTF-TCNQ: 2 k. F and 4 k. F CDW/BOW! b* Charge transfer r=0. 59 2 k. F T=60 K 4 k. F 2 k. F instability on the TCNQ stack 4 k. F instability on the TTF stack J. -P. Pouget et al PRL 37, 873 (1975); S. K. Khanna et al PRB 16, 1468 (1977) S. Kagoshima et al JPSJ, 41, 2061 (1976)

T= 0°K ground state in electron-phonon coupled systems 2 k. F Peierls transition for non interacting Fermions Spin degree of freedom r = (2) x 2 k. F No spin degree of freedom r = 4 k. F Peierls transition for spinless Fermions (no double occupancy if U>>t) Average distance between charges: 1/r=(4 k. F)-1 The 4 k. F CDW corresponds at the first Fourier component of a 1 D Wigner lattice of localized charges

4 k. F phase diagram for spinless fermions with long range coulomb interactions 4 k. F=n (d//*) organics J. Hubbard, J. Kondo & K. Yamaji; B. Valenzuela et al PRB 68, 045112 (2003)

Generalized Wigner Lattice (GWL) • Exact determination of the ground state for H 0 or t =0 and U→∞ (at most one spinless fermion per site) (J. Hubbard PRB 17, 494 (1978)) GWL if Vm→ 0 as m→∞ and Vm+1+Vm-1≥ 2 Vm convex potential (i. e. 1/R Coulomb repulsion) Organic conductors Quantum chemistry calculations on clusters of TMTTF molecules F. Castet et al J. Phys. I 6, 583 (1996) m = 1 2 3 V~λ/R with λ~ 13 e. VÅ but V 1+V 3 close to 2 V 2

Quarter filled band ρ=1/2 with V 1 and V 2 ; V 3=0 • V 1>2 V 2 (convex potential) 1 0 1 0 4 k. F charge order ( GWL) • V 1<2 V 2 (non convex potential) 1 1 0 0 1 1 2 k. F charge order

Divergence of the CDW electron-hole response function (U, V 1≥ 0 case) U=0 c(2 k. F) 2 k. F U=0 diverges 2 k. F (Peierls instability) V=0 0 4 k. F T T 0: c(2 k. F) diverges U (Peierls instability) V ~ U/2 T 0: both c(2 k. F) and c(4 k. F) diverge T J. E. Hirsch and D. J. Scalapino PRB 29, 5554 (1984) c(4 k. F) U diverges GWL 2 k. F 4 k. F

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

BOW instability on the donor stack D Kr 1 1/2 Increase of the polarizability of the molecule HMTSF 2 k. F BOW TSF S Se 2 k. F + 4 k. F BOW HMTTF two more cycles 1/3 4 k. F BOW 0 TTF D-TCNQ charge transfer salts

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

Crossover from a dominant 2 k. F instability to a dominant 4 k. F instability in NMP 1 -x. Phenx TCNQ Reduction of the interchain screening* promotes the divergence of the 4 k. F instability! ρ incom 2 k. F only 4 k. F dominant ρ=1/2 1: 2 TCNQ salts 2 chains system (interchain screening) 2 k. F instability dominant single chain system (reduced interchain screening) A. J. Epstein et al 4 k. F instability dominant PRL 47, 741 (1981) *screening between electron (TCNQ) and hole (NMP) 1 D gases

2: 1 TCNQ salts

Dominant 4 k. F lattice instability in 2: 1 acceptor quarter filled salts • Qn(TCNQ)2 25 K No transition at low T (Qn disorder) J. P. Pouget, Chem. Scripta (Suède) 17, 85 (1981) • (DI-DCNQI)2 Ag Charge ordering transition at 220 K Y. Nogami et al, Synthetic Metals 102, 1778 (1999)

Qn(TCNQ)2 T σ/σRT As. F 6 PF 6 (data from Schegolev et al) Charge localization due to: - disorder - strong Coulomb interactions 4 k. F lattice instability but also thermopower due to localized spins: S~(k/e) ln 2 Buravov et al JETP 32, 612 (1971) Chaikin et al PRL 42, 1178 (1979) (TMTTF)2 X no disorder Mott- Hubbard charge localization

4 k. 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 an electron is localized: - on one bond out of two (4 k. F BOW: Mott Dimer) 1 0 1 - on one site out of two (4 k. F CDW: Charge Ordering) 0 1 0 1

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

4 KF CDW: Wigner charge order NMR shows that the sites are different: charge disproportionation NMR evidences of 2 different sites in ¼ filled organic conductors D 2 X or A 2 Y: - (TMP)2 X-CH 2 Cl 2 (X=PF 6, As. F 6) (Ilakovac et al PRB 52, 4108 (1995)) but problem of disorder due to solvant - (DI-DCNQI)2 Ag (uniform stack) c but structural refinement shows a mixture of CDW and BOW - (TMTTF)2 X (X=PF 6, As. F 6, Sb. F 6, Re. O 4, …. ) dimerized stack (BOW induced by the anion sublattice) -δ-(EDT-TTF-CONMe 2)2 Br nearly non dimerized stack x x a

δ-(EDT-TTF-CONMe 2)2 Br C 2 H 4 Me J. Mater. Chem. 19, 6980 -6994 (2009)

Average structure P 2/m 2/n 21/a 2 uniform stack along a 2 2 n 2 21

In fact layers of very weak superstructure reflections! L unit cell doubling along b q = (0, 1/2, 0) K [0, K, L] X-ray pattern/Synchrotron radiation (SOLEIL)

superstructure P 2 nn 2 inequivalent molecules per stack: implies the CO! NMR line splitting Br- displacement towards the II+ molécule

(TM)2 X: BECHGAARD and FABRE SALTS Se or S (TM+1/2)2 X-1 : S TMTTF 1 hole per 2 TM molecules: 2 k. F=1/2 a* Quarter filled band system : Se TMTSF TM: TMTSF or TMTTF P 1 a x a X centrosymmetrical : As. F 6, PF 6, Sb. F 6, Ta. F 6, Br slightly dimerized zig-zag chain of TM X non centro. : BF 4, Cl. O 4, Re. O 4, NO 3, , SCN

Charge ordering transition in (TMTTF)2 X • Charge disproportionation at TCO 2 different molecules: NMR line splitting Chow et al PRL 85, 1698 (2000) 4 k. F BOW P • Charge disproportionation + incipient lattice dimerization (4 k. F BOW) no inversion centers: thus ferroelectricity at TCO Monceau et al PRL 86, 4080 (2001) Symmetry breaking (PĪ →P 1) at TCO Difficulties to be detected because of: - the triclinic symmetry of the lattice - X-ray irradiation damages

Lattice anomaly at the CO transition (thermal expansion) Step anomaly Lambda anomaly insulator metal Tco M. De Souza et al PRL 101, 216403 (2008) and ISCOM 2009 R. Laversanne et al J. Phys. Lett. 45, L 393 (1984)

Debye behavior c* soft direction: lattice softening above Tco achieved by translational fluctuations of the anion in its metyl group cavity?

Neutron scattering evidence of a lattice deformation at the (PĪ →P 1) CO transition of (TMTTF)2 PF 6 – d 12 Tco Dielectric measurements at 16. 5 GHz A. Langlois et al σeff RPE - C. Coulon et al PRB 76, 085126 (2007) Tco = 84 K

Neutron* powder** spectrum of (TMTTF)2 PF 6 –d 12 * to avoid X-ray irradiation damages ** to avoid twin misorientation in T δI/I 0 ~10% Tco = 84 K P. Foury-Leylekian et al ISCOM 2009

Crude analysis of δI consistent with a shift of the anion sublattice X with respect to TMTTF sublattice TMTTF hole rich (contracted) TMTTF electron rich (elongated) ρe d 1 d 2 ρh ρe=0. 5 -δ PF 6 - ρh=0. 5+δ Shift of the anion sublattice required to break the inversion symmetry and to achieve ferroelectricity (S. Brazovski) PF 6 -

Role of the anions in the CO process ? In (TMTTF)2 X Tco strongly depends upon: - the nature of the anion (mass MX, electron-anion coupling, etc…. ) - the shape and volume of the methyl group cavity where the anion is located (strong deuteration effect) (J. P. Pouget et al J. Low Temp. Phys. 142, 147 (2006)) Anion shift stabilises the 3 D CO pattern (numerical simulations : Riera and Poilblanc PRB 63, 241102 (2001))

Anion shift modifies the intra-stack interactions • Modulates the one electron site energy ε electron-anion coupling → « Holstein type of electron-phonon coupling » stabilizes the site CDW • Increases the dimerisation gap (thus the Umklapp scattering) ΔD²= ΔDb²+ΔDε² due to the loss of inversion centres • Changes the lattice polarizability Vm→Vmeff ε V 2 X V 1 h X Ferroelectric medium

Quantum chemistry calculation on clusters of TMTTF molecules intrastack interactions: Vm V 1 D~ V 1 I ~ U/2 V 1~1. 5 V 2 F. Castet et al J. Phys. I 6, 583 (1996) The polarisability of the anions and the screening effects are ignored in the calculation V 1+V 3~2 V 2 (curvature of the potential? ) (V 1 / V 2 )bare ~1. 5 but V 1 eff / V 2 eff could be closer to the critical ratio 2 at which there is competition between different CDW orders

Explicit consideration of repulsive V 2 in t, U, V 1, V 2 extended 1 D Hubbard model Ground state: U=10 t V 1 V 2=V 1/2 frustration line (Ejima et al PRB 72, 033101 (2005)) Well below this line: 4 k. F CDW O o O o Well above this line: 2 k. F CDW OOoo. OO For V 2~V 1/2 frustration: metallic state (Luttinger liquid) preserved However frustration effects can be lifted by small perturbations (chain dimerization, interactions with the anions)

Simple consideration of the anion potential (V. J. Emery 1986) V 1 a (0, 0, 0) or (0, 1/2) CO: 4 k. F anion potential ε + (1/2, 1/2) AO 2 k. F anion potential δ V 2 a-b+c 2 k. FCDW/AO 4 k. F CDW/CO energy per hole E 4 k. F=V 2 -ε energy per hole E 2 k. F=V 1/2 -δ V 2 crit. =V 1/2+ε-δ δ ε I 4 k. F CDW I V 1/2 I V 2 2 k. F CDW

(0, 0, 0) CO then (1/2, 1/2) AO in (TMTTF)2 Re. O 4 CO AO C. Coulon et al PRB 31, 3583 (1985) and H. H. S. Javadi et al PRB 37, 4280 (1988) idem for (TMTTF)2 BF 4

Conclusions • 4 k. F CO / Wigner instabilities are known since 1976 in the organic conductors! • In 2: 1 salts the 4 k. F intrastack instability is strenghtened by the reduction of the interchain screening • Cooperative role of the anion (cation) sublattice to stabilize the 3 D CO ground state

Supplementary material

2: 1 dimerized salts: 1/4 (3/4) or 1/2 Band filling? ½ filled upper band of the dimerized chain (ρ=1) ¼ filled HOMO band (ρ=1/2) ? ½ or 3/4 filled system if the dimerization gap 2Δ is larger or smaller than W┴ or πk. BT But in the ½ filled band limit (strongly dimerized system) the carriers are in the bonding (anti-bonding) state of the dimer. There is no possibility of charge disproportion inside the dimer (no CO ground state as found for ¼ filling) The instabilities are towards the Mott-Hubbard (one carrier per dimer: 1 1), the 2 k. F CDW ( « neutral-ionic » dimer charge array: 2 0) or the 2 k. F p-type density wave (BCDW)

Extended Hubbard model at half filling Neutral-Ionic chain N I N I SP resonant chain Mott- Hubbard AF chain

Extended Hubbard model for an half filled band with a staggered site potential Δ with a 2 k. F bond dimerization δ Δ coupled to the CDW open a gap at ±k. F (Band Insulator: BI) δ induces Peierls Insulator (PI) by modulating the charge on the bonds The SDW is unstable Tsuchiizu & Furusaki PRB 65, 155113 (2002)

Superstructure P 2 nn

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

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