Charge ordering in quasi-one dimensional organic conductors

J.P. Pouget & P. Foury-LeylekianLaboratoire 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: 4kF CDW instability in 1D / Charge

ordering (CO) / Wigner localization• In 2:1 salts: influence of the anion sublattice

ORGANIC CHARGE TRANSFER SALTS

1D

2 bands crossing at EF

2kF(A)= 2kF(D)Only a single 2kF

critical wave vector!Acceptor

Donor

D

A

Charge transfer ρ (generally incommensurate): D+ρ A-ρ 2kF=ρ/2

1D metal coupled to the lattice:

PEIERLS’ CHAIN

unstable at 0°K towards a Periodic Lattice Distortion

which provides a new (2kF)-1

lattice periodicity

PLD opens a gap 2at the Fermilevel: insulating ground state

2kF

2kF modulated chain

-2kF

+ 2kF

2kF satellite lines

Fourier transform of a modulated chain: diffuse sheets in reciprocal spacedetected by diffraction methods (X-ray diffuse scattering technics)

Real space

Reciprocal space

Modulation of the electronic density and of the atomic positions

2π/2kF

a*

a

TSF-TCNQ: 2kF CDW / BOW* instability

2kF=ρ/2 b**2kF modulation of the inter-molecular TSF distances

Charge transfer

Yamaji et al J.Physique 42, 1327 (1981)

TTF-TCNQ: 2kF and 4kF CDW/BOW!

T=60K

2kF instability on the TCNQ stack4kF instability on the TTF stack

4kF2kF

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)

b*

Charge transfer

2kF Peierls transition for non interacting Fermions

4kF Peierls transition for spinless Fermions (no double occupancy if U>>t)

The 4kF CDW corresponds at the first Fourier component of a 1D Wigner lattice of localized charges

ground state in electron-phonon coupled systems

Spin degree of freedom = (2) x 2kF

No spin degree of freedom= 4kF Average distance between charges: 1(4kF)-

1

4kF phase diagram for spinless fermions with long range coulomb interactions

J. Hubbard, J. Kondo & K. Yamaji; B. Valenzuela et al PRB 68, 045112 (2003)

organics

4kF=n (d//*)

Generalized Wigner Lattice (GWL)

• Exact determination of the ground state for H0 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≥2Vm convex potential (i.e. 1/R Coulomb repulsion)

Organic conductors

i mi mininmVin

inUHH

0,0

Quantum chemistry calculations on clusters of TMTTF moleculesF. Castet et al J. Phys. I 6, 583 (1996)

m = 1 2 3 V~λ/R with λ~ 13 eVÅ

but V1+V3 close to 2V2

Quarter filled band ρ=1/2with V1 and V2 ; V3=0

• V1>2V2 (convex potential)

1 0 1 0 1 0 1 04kF charge order ( GWL)

• V1<2V2 (non convex potential)

1 1 0 0 1 1 0 0 1 1

2kF charge order

Divergence of the CDW electron-hole response function (U,V1≥0 case)

J.E.Hirsch and D.J.Scalapino PRB 29, 5554 (1984)

T 0: (2kF) diverges

(4kF) diverge

s

T 0: both (2kF) and (4kF) diverge

2kF 2kF

2kF

4kF

4kF

V=0

V ~ U/2

U=0U=0

(2kF) diverges

U T

T

U GWL(Peierls instability)

(Peierls instability)

0

2kF and 4kF CDW / BOW instabilities in quarter filled TMTSF-DMTCNQ

2kF and 4kF BOW instabilities are both located on the TMTSF stack

Charge transfer:ρ=1/2 2kF=1/4a* 4kF=1/2a*

BOW instability on the donor stack DK

0

1

1/2

1/3

2kF BOW

2kF + 4kF BOW

4kF BOW

S Se

two more cycles

TTF

HMTTF

TSF

HMTSF

Increase of the polarizability of the molecule

D-TCNQ charge transfer salts

In charge transfer salts: the 2kF BOW instability drives the Peierls transitionthe 4kF BOW instability is at most weakly divergent

JPP 1988

Crossover from a dominant 2kF instability to a dominant 4kF instability in NMP1-xPhenx TCNQ

2 chains system (interchain screening) 2kF instability dominantsingle chain system (reduced interchain screening) 4kF instability dominant

Reduction of the interchain screening* promotes the divergence of the 4kF instability!

ρ incom2kF only

4kF dominant

ρ=1/2

1:2 TCNQ salts

A.J. Epstein et al PRL 47, 741 (1981)*screening between electron (TCNQ) and hole (NMP) 1D gases

2:1 TCNQ salts

Dominant 4kF lattice instability in 2:1 acceptor quarter filled salts

• Qn(TCNQ)2

• (DI-DCNQI)2Ag

25K

Y. Nogami et al, Synthetic Metals 102, 1778 (1999)

J.P. Pouget, Chem. Scripta (Suède) 17, 85 (1981)

No transition at low T (Qn disorder)

Charge ordering transition at 220K

Qn(TCNQ)2

σ/σRT

T

(TMTTF)2Xno disorder

Mott- Hubbard charge localization

Charge localization due to:- disorder- strong Coulomb interactions

AsF6

PF6

4kF lattice instabilitybut also

thermopower due to localized spins: S~(k/e) ln2

Buravov et al JETP 32, 612 (1971)Chaikin et al PRL 42, 1178 (1979)

(data from Schegolev et al)

4kF charge localization in a quarter filled band (ρ=1/2)

• U,V1 phase diagram(Mila & Zotos EPL 24, 133 (1993))

• In the insulating phase an electron is localized:

- on one bond out of two (4kF BOW: Mott Dimer)

- on one site out of two(4kF CDW: Charge Ordering)

1 0 1 0 1

0 1 0 1 0 1

4kF BOW: Mott dimers(all the sites are equivalent; the bonds are different)

Exemple 1:2 TCNQ salts

MEM (TCNQ)2 : T<335K

(S. Huizinga et al PRB 19, 4723 (1979))

Intradimer overlap

Interdimer overlap

4KF CDW: Wigner charge orderNMR shows that the sites are different: charge disproportionation

NMR evidences of 2 different sites in ¼ filled organic conductors D2X or A2Y:- (TMP)2X-CH2Cl2 (X=PF6,AsF6) (Ilakovac et al PRB 52, 4108 (1995)) but problem of disorder due to solvant

- (DI-DCNQI)2Ag (uniform stack) but structural refinement shows a mixture of CDW and BOW

- (TMTTF)2X (X=PF6,AsF6, SbF6,ReO4,….)

dimerized stack (BOW induced by the anion sublattice)

-δ-(EDT-TTF-CONMe2)2Br nearly non dimerized stack

xx

xx

c

a

δ-(EDT-TTF-CONMe2)2Br

MeC2H4

J. Mater. Chem. 19, 6980-6994 (2009)

Average structure P 2/m 2/n 21/a

2

2

n

2

221

uniform stackalong a

L

K

In fact layers of very weak superstructure reflections!

[0,K,L] X-ray pattern/Synchrotron radiation (SOLEIL)

unit cell doubling along b

q = (0,1/2,0)

superstructure P2nn 2 inequivalent molecules per stack: implies the CO!

Br- displacementtowards the II+ molécule

NMR line splitting

axa

slightly dimerized zig-zag chain of TM

P 1

X centrosymmetrical : AsF6, PF6, SbF6, TaF6, Br

X non centro. : BF4, ClO4, ReO4, NO3,,SCN

:S TMTTF

:Se TMTSF

(TM)2X: BECHGAARD and FABRE SALTS

TM: TMTSF or TMTTF

(TM+1/2)2 X-1

1 hole per 2 TM molecules: 2kF=1/2a*Quarter filled band system

Se or S

Charge ordering transition in (TMTTF)2X• Charge disproportionation at TCO

2 different molecules: NMR line splitting

• Charge disproportionation + incipient lattice dimerization (4kF BOW) no inversion centers:

thus ferroelectricity at TCOMonceau et al PRL 86, 4080 (2001)

Chow et al PRL 85, 1698 (2000)

Symmetry breaking (PĪ →P1) at TCO

Difficulties to be detected because of:- the triclinic symmetry of the lattice- X-ray irradiation damages

P4kF BOW

Lattice anomaly at the CO transition(thermal expansion)

M. De Souza et al PRL 101, 216403 (2008)and ISCOM 2009

Tco

metalinsulator

R. Laversanne et al J. Phys. Lett.45, L393 (1984)

Step anomaly

Lambda anomaly

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

Debye behavior

Neutron scattering evidence of a lattice deformation at the

(PĪ →P1) CO transition of (TMTTF)2PF6 – d12

Tco = 84K

Dielectric measurements at 16.5GHzA. Langlois et al

σeff RPE - C. Coulon et al PRB 76, 085126 (2007)

Tco

Tco

Neutron* powder** spectrum of (TMTTF)2PF6 –d12* to avoid X-ray irradiation damages** to avoid twin misorientation in T

P. Foury-Leylekian et al ISCOM 2009

δI/I0 ~10%

Tco = 84K

ρh

ρe

ρh=0.5+δ

ρe=0.5-δ

PF6-

PF6-

d1

d2

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)

Shift of the anion sublattice required to break the inversion symmetryand to achieve ferroelectricity (S. Brazovski)

Role of the anions in the CO process

In (TMTTF)2X 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 3D CO pattern(numerical simulations : Riera and Poilblanc PRB 63, 241102 (2001))

?

Anion shift modifies the intra-stack interactions• Modulates the one electron site energy εelectron-anion coupling → « Holstein type of electron-phonon coupling » stabilizes the site CDW

• Increases the dimerisation gap (thus the Umklapp scattering)

ΔD²= ΔDb²+ΔD

ε²

• Changes the lattice polarizability Vm→Vmeff

due to the loss of inversion centres

V2

ε

X

Xh

V1

Ferroelectric medium

Quantum chemistry calculation on clusters of TMTTF molecules

intrastack interactions:

V1D~ V1

I ~ U/2

V1~1.5 V2

F. Castet et al J. Phys. I 6, 583 (1996)

The polarisability of the anions and the screening effects are ignored in the calculation

V1+V3~2V2 (curvature of the potential?)

(V1 / V2 )bare ~1.5

but V1eff / V2

eff could be closer to the critical ratio 2at which there is competition between different CDW orders

Vm

Explicit consideration of repulsive V2

in t, U, V1, V2 extended 1D Hubbard model

V2

V1

V1

V2=V1/2 frustration line

Well below this line: 4kF CDW O o O o O o

Well above this line: 2kF CDW O O o o O O

U=10t

For V2~V1/2 frustration: metallic state (Luttinger liquid) preservedHowever frustration effects can be lifted by small perturbations (chain dimerization,

interactions with the anions)

Ground state:

(Ejima et al PRB 72, 033101 (2005))

Simple consideration of the anion potential (V.J. Emery 1986)

aa-b+c

(0,0,0) or (0,1/2,1/2) CO: 4kF anion potential ε

+(1/2,1/2,1/2) AO

2kF anion potential δ

V1

V2

4kF CDW/CO

energy per holeE4kF=V2-ε

2kFCDW/AO

energy per holeE2kF=V1/2-δ

V2crit. =V1/2+ε-δ

I

V1/2V2

εI

δI

4kF CDW 2kF CDW

(0,0,0) CO then (1/2,1/2,1/2) AO in (TMTTF)2ReO4

CO

CO

AO

AO

C. Coulon et al PRB 31, 3583 (1985) and H.H. S. Javadi et al PRB 37, 4280 (1988)idem for (TMTTF)2BF4

Conclusions

• 4kF CO / Wigner instabilities are known since 1976 in the organic conductors!

• In 2:1 salts the 4kF intrastack instability is strenghtened by the reduction of the interchain screening

• Cooperative role of the anion (cation) sublattice to stabilize the 3D CO ground state

Supplementary material

2:1 dimerized salts: 1/4 (3/4) or 1/2 Band filling?

½ or 3/4 filled system if the dimerization gap 2Δ is larger or smaller than W┴ or πkBT

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 1 1), the 2kF CDW ( « neutral-ionic » dimer charge array: 2 0 2 0) or the 2kF p-type density wave (BCDW)

½ filled upper band of the dimerized chain (ρ=1)

¼ filled HOMO band (ρ=1/2)?

Extended Hubbard model at half filling

Mott- Hubbard AF chain

Neutral-Ionic chain N I N I N I

SP resonant chain

Extended Hubbard model for an half filled band

with a staggered site potential Δ

with a 2kF bond dimerization δ

Tsuchiizu & Furusaki PRB 65, 155113 (2002)

Δ coupled to the CDWopen a gap at ±kF

(Band Insulator: BI)

δ induces Peierls Insulator (PI) by modulating the charge on the bonds The SDW is unstable

Superstructure P2nn

Hypothetical charge pattern of ferroelectric TMTTF

a

b

Anion X- points towardshole rich TMTTF

3D Coulomb interactions minimized ?

anion shift seems to be essential to impose

the charge pattern

a,c plane

a,b plane

4kF order does not involves the spin degrees of

freedom which remains free to order at low T

TCO

S not perturbed at the CO transition

Spin pairing

(TMTTF)2X

Spin-Peierls (2kF BOW instability)

4kF CDW (CO)

4kF BOW (Mott dimer)

S=0

MEM- (TCNQ)2

AF

2kF SDW

Magnetic order

4kF order well decoupled from the low Tground state

involving S=1/2 coupling