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: 4kF CDW instability in 1D / Charge
ordering (CO) / Wigner localization
• In 2:1 salts: influence of the anion sublattice
ORGANIC CHARGE TRANSFER SALTS
1D
Donor
A 2 bands crossing at EF
2kF(A)= 2kF(D)
Only a single 2kF
D critical wave vector!
Acceptor
Charge transfer ρ (generally incommensurate): D+ρ A-ρ
2kF=ρ/2
PEIERLS’ CHAIN
1D metal coupled to the lattice:
unstable at 0°K towards a
Periodic Lattice Distortion
which provides a new (2kF)-1
lattice periodicity
2kF
PLD opens a gap 2D at the Fermi
level: insulating ground state
2kF modulated chain
Modulation of the electronic density and of the atomic positions
Real space
Reciprocal space
a
2π/2kF
a*
-2kF
2kF satellite lines
+ 2kF
Fourier transform of a modulated chain: diffuse sheets in reciprocal space
detected by diffraction methods (X-ray diffuse scattering technics)
TSF-TCNQ: 2kF CDW / BOW* instability
Charge transfer
r=0.63
2kF=ρ/2 b*
*2kF modulation of the inter-molecular TSF distances
Yamaji et al J.Physique 42, 1327 (1981)
TTF-TCNQ: 2kF and 4kF CDW/BOW!
b*
Charge transfer
r=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)
S. Kagoshima et al JPSJ, 41, 2061 (1976)
T= 0K ground state in electron-phonon
coupled systems
2kF Peierls transition for non interacting
Fermions
Spin degree of freedom
r = (2) x 2kF

4kF Peierls transition for spinless
Fermions (no double occupancy if U>>t)
No spin degree of freedom
r = 4kF
Average distance between charges: 1/r=(4kF)-1
The 4kF CDW corresponds at the first Fourier component of a 1D
Wigner lattice of localized charges
4kF phase diagram for spinless fermions with
long range coulomb interactions
4kF=n (d//*)
organics
J. Hubbard, J. Kondo & K. Yamaji; B. Valenzuela et al PRB 68, 045112 (2003)
Generalized Wigner Lattice (GWL)
H = H U  n n 
0
i i i
 V m ni ni  m
i ,m  0
• 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
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 eVÅ
but V1+V3 close to 2V2
Quarter filled band ρ=1/2
with V1 and V2 ; V3=0
• V1>2V2 (convex potential)
10101010
4kF charge order ( GWL)
• V1<2V2 (non convex potential)
1100110011
2kF charge order
Divergence of the CDW electron-hole response function (U,V1≥0 case)
U=0
c(2kF)
2kF U=0 diverges
2kF
(Peierls instability)
V=0
0
4kF
T
T 0: c(2kF) diverges

U
(Peierls instability)
V ~ U/2
T 0: both c(2kF) and c(4kF)
diverge
T
J.E.Hirsch and D.J.Scalapino PRB 29, 5554 (1984)
c(4kF)
U  diverges
GWL
2kF
4kF
2kF and 4kF CDW / BOW instabilities
in quarter filled TMTSF-DMTCNQ
Charge transfer:ρ=1/2
2kF=1/4a* 4kF=1/2a*
2kF and 4kF BOW instabilities are both located on the TMTSF stack
BOW instability on the donor stack D
Kr
1
Increase of the polarizability of the molecule
HMTSF
2kF BOW
TSF
1/2
S
Se
2kF + 4kF BOW
HMTTF
two more cycles
1/3
4kF BOW
0
TTF
D-TCNQ charge transfer salts
In charge transfer salts:
the 2kF BOW instability drives the Peierls transition
the 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
Reduction of the interchain screening* promotes
the divergence of the 4kF instability!
ρ incom
2kF only
4kF dominant
ρ=1/2
1:2 TCNQ salts
2 chains system (interchain screening) 2kF instability dominant
single chain system (reduced interchain screening)
A.J. Epstein et al
4kF instability dominant
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
25K
No transition at low T (Qn disorder)
J.P. Pouget, Chem. Scripta (Suède) 17, 85 (1981)
• (DI-DCNQI)2Ag
Charge ordering transition at 220K
Y. Nogami et al, Synthetic Metals 102, 1778 (1999)
Qn(TCNQ)2
T
σ/σRT
AsF6
PF6
(data from Schegolev et al)
Charge localization due to:
- disorder
- strong Coulomb interactions
4kF lattice instability
but also
thermopower due to localized spins: S~(k/e) ln2
Buravov et al JETP 32, 612 (1971)
Chaikin et al PRL 42, 1178 (1979)
(TMTTF)2X
no disorder
Mott- Hubbard charge localization
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)
1
0
1
0
1
- on one site out of two
(4kF CDW: Charge Ordering)
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
Intradimer overlap
Interdimer overlap
(S. Huizinga et al PRB 19, 4723 (1979))
4KF CDW: Wigner charge order
NMR 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)
c
but structural refinement shows a mixture of CDW and BOW
- (TMTTF)2X (X=PF6,AsF6, SbF6,ReO4,….)
x
dimerized stack
(BOW induced by the anion sublattice)
-δ-(EDT-TTF-CONMe2)2Br
nearly non dimerized stack
x
x
a
x
δ-(EDT-TTF-CONMe2)2Br
C2H4
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 P2nn
2 inequivalent molecules per stack: implies the CO!
NMR line splitting
Br- displacement
towards the II+ molécule
(TM)2X: BECHGAARD and FABRE SALTS
Se or S
(TM+1/2)2 X-1
TMTTF 2kF=1/2a*
1 hole per 2 TM:S
molecules:
Quarter filled band system
:Se TMTSF
TM: TMTSF or TMTTF
P1
a
x
a
X centrosymmetrical : AsF6,
PF6, SbF6, TaF6, Br
slightly dimerized zig-zag
chain of TM
X non centro. : BF4, ClO4, ReO4,
NO3,,SCN
Charge ordering transition in (TMTTF)2X
• Charge disproportionation at TCO
2 different molecules: NMR line splitting
Chow et al PRL 85, 1698 (2000)
4kF BOW
P
• Charge disproportionation + incipient lattice dimerization
(4kF BOW)
no inversion centers:
thus ferroelectricity at TCO
Monceau et al PRL 86, 4080 (2001)
Symmetry breaking (PĪ →P1) 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, L393 (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 →P1) CO transition of (TMTTF)2PF6 – d12
Tco
Tco
Dielectric measurements at 16.5GHz
A. Langlois et al
σeff RPE - C. Coulon et al PRB 76, 085126 (2007)
Tco = 84K
Neutron* powder** spectrum of (TMTTF)2PF6 –d12
* to avoid X-ray irradiation damages
** to avoid twin misorientation in T
δI/I0 ~10%
Tco = 84K
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
d1
d2
ρh
ρe=0.5-δ
PF6-
ρh=0.5+δ
Shift of the anion sublattice required to break the inversion symmetry
and to achieve ferroelectricity (S. Brazovski)
PF6-
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 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
V2
X
V1
h
X
Ferroelectric medium
Quantum chemistry calculation on clusters of TMTTF
molecules
intrastack interactions:
Vm
V1D~ V1I ~ 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 / V2eff could be closer to the critical ratio 2
at which there is competition between different CDW orders
Explicit consideration of repulsive V2
in t, U, V1, V2 extended 1D Hubbard model
Ground state:
U=10t
V1
V2
V1
V2=V1/2 frustration line
(Ejima et al PRB 72, 033101 (2005))
Well below this line: 4kF CDW O o O o O o
Well above this line: 2kF CDW
OOooOO
For V2~V1/2 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)
V1
a
(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
V2
a-b+c
2kFCDW/AO
4kF CDW/CO
energy per hole
E2kF=V1/2-δ
energy per hole
E4kF=V2-ε
V2crit. =V1/2+ε-δ
δ
ε
I
4kF CDW
I
V1/2
I
V2
2kF CDW
(0,0,0) CO then (1/2,1/2,1/2) AO
in (TMTTF)2ReO4
CO
AO
CO
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 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 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)
Extended Hubbard model at half filling
Neutral-Ionic chain
N I 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 2kF bond
dimerization δ
Δ coupled to the CDW
open a gap at ±kF
(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 P2nn
Hypothetical charge pattern of ferroelectric TMTTF
a,c plane
a,b plane
3D Coulomb
interactions minimized ?
anion shift seems
to be essential to impose
the charge pattern
Anion X- points towards
hole rich TMTTF
a
b
4kF order does not involves the spin degrees of
freedom which remains free to order at low T
cS not perturbed at the
CO transition
(TMTTF)2X
TCO
4kF order well decoupled
from the low T
ground state
involving S=1/2 coupling
Spin pairing
AF
Magnetic order
Spin-Peierls (2kF BOW instability)
4kF CDW (CO)
2kF SDW
S=0
4kF BOW (Mott dimer)
MEM- (TCNQ)2