Organic Electronic Materials: Competing Phases,Spatial Order, and Device Applications

1
Organic Electronic Materials Competing
Phases,Spatial Order, and Device Applications

• David K. Campbell
• Understanding Complex Systems UIUC
• May 2003
• with R.T. Clay, S. Mazumdar, S. Ramasesha, A.
  Sandvik, and P. Sengupta
• Supported by NSF and NCSA

2
Outline

• Motivation and Bottom Line on Organic
  Electronics
• The Past Conducting Polymers
• The Present Organic Charge Transfer Solids
• (CTS)
• The Future Organic Molecular Crystals and
• self-assembled structures
• Conclusions

3
Motivation and Bottom Line

• Organic Electronic Materials (OEM)conducting
  polymers, organic charge transfer salts, and
  organic molecular crystalsbring the richness of
  organic chemistry to solid state physics and
  electronic device applications
• Like high Tc superconductors, OEM typically
  have strong e-e and e-ph interactions. Can hope
  for a unified theoretical approach to whole class
  of materials via Peierls-extended Hubbard (PEH)
  models.
• OEM exhibit a large range of theoretically
  interesting phenomena from the kink solitons
  and bipolarons of conducting polymers through the
  excitonic effects of molecular crystals to CTS
  ground states that exhibit superconductivity (SC)
  and antiferromagnetism (SDW) (as seen in high Tc)
  but also charge density wave (CDW), bond-order
  wave (BOW), and spin-Peierls (SP)phases.
• OEM vary continuously in effective electronic
  dimensionality from 1D (conducting polymers and
  some CTS) through 2D (other CTS) to 3D (typical
  molecular crystal).

4
Motivation and Bottom Line

• Todays talk provides capsule summary of the
  past (conducting polymers), present (charge
  transfer salts), and future (organic molecular
  crystals) of the field, illustrating some
  possible device applications and offering a few
  specific examples from our theoretical studies,
  based on PEH models, that
• Describe the nonlinear excitationskink solitons,
  polarons, bipolaronsin conducting polymers
• Predict novel coexisting BCDW and BCSDW
  density wave ground states in CTS
• Provide an explanation of previously puzzling
  recent experiments in several organic CTS,
  including recent observations of charge order
  (CO)
• Explain differences among 1D, weakly 2D, and
  strongly 2D CTS
• Set stage for a possible approach to the observed
  organic superconductivity

5
The Past Conducting Polymers

• 2000 Nobel Prize in Chemistry awarded for 1976
  discovery of conducting films of (bromine) doped
  poly-acetylene, the first synthetic metal

6
The Past Conducting Polymers

• Polyacetylene, the hydrogen atom of conducting
  polymers to chemists (CHCH)n, a
  dimerized/bond alternating ground state to
  physicists (CH)x, a Bond Order Wave (BOW). By
  either name, a broken symmetry phase. (CH)x
  exists in two isomers
• trans-(CH)x
  cis-(CH)x

7
The Past Conducting Polymers

• Degenerate ground state of trans-(CH)x gt kink
  solitons
• Non-degenerate ground state of cis-(CH)x (and
  most other conducting polymers!) gt no kinks
  possiblewhat then?

8
The Past Conducting Polymers

• Twenty-five year history of theoretical modeling
  in one slide observed properties of conducting
  polymers require inclusion of both
  electron-phonon (e-ph) and electron-electron
  (e-e) interactions. In idealized one-dimensional
  (1D) situation, use Peierls-extended Hubbard
  (PEH) model.
• HPEH H0 Hee
• H0 -S j, s t0 - a(Dj)Bj,j1,s , Ka/2 S
  j(Dj)2
• Hee U S jnj,nj, V S i,njnj1
• Here j is a site index, Bj,k,s cj,s ck,s
  ck, s cj, s, is the kinetic energy/hopping
  operator, uj intersite distortion (phonon),
  Dj (uj uj1).
• Parameters t0 2.5 eV, a ? 3.8 eV/Å, Ka ?
  47eV/Å2, U 10 eV, V 2.5eV Initial studies had
  U0V (SSH model), allowed analytic treatment,
  via continuum limit and mapping to relativistic
  quantum field theory (!).
• Data on optics, as well as comparison to
  oligomers, showed U and V both non-zero gt
  accurate many-body methods needed gt Quantum
  Monte Carlo

9
The Past Conducting Polymers

• Pictorial descriptions of kink solitons

10
The Past Conducting Polymers

• Pictorial descriptions of
• polarons
  bipolarons

11
The Past Conducting Polymers

• Excitons in conventional semiconductors, often
  have bound particle-hole pairs excitons. Here
  the strong e-ph coupling creates accompanying
  lattice distortion implies neutral P-P- or
  BP-BP- - pairs. In singlet state, such pairs
  are unstable against radiative decay gt
  light-emission gt Polymeric LEDs !!
• First constructed by R. Friend and collaborators
  (Cambridge) in February 1989 using
  poly-paraphenylene vinylene (PPV)

12
The Past Conducting Polymers

• Polymeric LEDs are now being commercially
  exploited as the basis for large format,
  inexpensive, flexible, multicolor displays. Such
  displays can be created using inkjet technology
  to polymeric components gt potentially dirt
  cheap and disposable
• Polymer LED
  Organic LED Color TV

13
The Present Organic CTS

• Organic Chemistry offers rich variety of CTS
• Principal molecules are flat
• p-conjugated organics
• Form 11 salts (TTF-TCNQ)
• 12 anionic salts (MEM(TCNQ))2
• 21 cationic salts (TMTSF)2PF6
• From T. Ishiguro and K. Yamaji, Organic
  Superconductors, p. 2
• (Springer Series in Solid State Sciences Volume
  88 (1990).

14
The PresentOrganic CTS

• Crystal structures are stacks of the flat
• organic molecules, counterions lying
• between in parallel segregated stacks.
• In 0th approximation, treat crystals as
• orthorhombic. Largest conductivity
• along stack, called a. For (TMTSF)2PF6,
• ta ' 0.25 eV, tb ' eV, tc ' 0.0015 eV,
• so conductivities are in ratio
• sasbsc 1 (1/100) (1/25000)
• After N. Thorup et al, Acta Crys. B37 1236-1240
  (1981).

15
The Present Organic CTS

• Electronic anisotropies of material are such that
  they range from quasi-1D to quasi-2D. This is
  reflected in the bulk crystals quasi-1D
  materials form needles, quasi-2 form pancakes.
• Photos courtesy of James Brooks, NHMFL

The needle-like crystal of TTF-TCNQ, has a
transition to a CDW at about 100 K.
The flat, slab-like crystal of the k-phase of
(BEDT-TTF)Cu(NCS)2, which is a 10.4 K
superconductor.
16
CTSExperimental Overview

• Generalized phase diagram summarizes properties
  seen in a wide range of 21 cationic CTS,
  including (TMTZF)2X, Z(SuT,SeS), XBr,PF6, .
• Key observation Pressure is known to enhance
  t?, thereby increasing effective electronic
  dimensionality. Recent results on uniaxial
  pressure confirm directly.
• M. Maesato et al, Phys. Rev. B64 155104 (2001).
• 1DCTS ? Quasi-1D/Weakly 2D ? 2D
• Fig 1. Phase Diagram for (TMTZF)2X compounds.
• CL Charge localized state. Lower case letters
• designate locations of specific compounds at
• atmospheric pressure a) ZT, XPF6
• b)ZDTDS, XPF6 c) ZT, XBr
• d) ZS, XPF6 e) ZS, XClO4.
• D. Jerome, Science 252, 1509 (1991).

17
CTS Experimental Overview

• In 1D CTS (TMTTF)2X, experiments establish CO
• NMR-line splitting below TCO shows two different
  site charges.
• D.S. Chow et al, PRL 85, 1698 (2000).

18
CTS Experimental Overview

• In 1D CTS (TMTTF)2X, experiments establish CO
• B. Dielectric permittivity
• Monceau, Nad, Brazovskii, PRL 86, 4080 (2001).

19
CTS Experimental Overview

• In Quasi-1D/Weakly 2D (TMTSF)2PF6 and (TMTTF)2Br,
  X-Ray experiments show
• a mixed CDW-SDW modulation
• develops below TSDW. To our knowledge,
• such a modulated state has never been
• observed before
• J.P. Pouget and S. Ravy, Synth. Metals 85, 1523
  (1997).
• X-Ray satellite intensities from (TMTSF)2PF6
  below TSDW.
• Satellites 1 and 2 are 2kF reflections satellite
  3 is the 4kF
• CDW reflections.

20
CTS Experimental Overview

• In strongly 2D CTS a-(BEDT-TTF)2MHg(SCN)4,
  M(K,Rb,Tl), analysis of cspin, Hall coefficient,
  mSR, NMR, and ADMRO, leads to conclusion
• We arrive at the possibility that the
• ground state below TA.. (' 10K)
• could be SDW (or CDW)
• accompanied by CDW (or SDW).
• T. Sasaki and N. Toyota, Mysterious ground
  states
• in the organic conductor a-(BEDT-TTF)2MHg(SCN)4
• Mixed SDW and CDW? Synth. Metals 70 849 (1995).
• Fig. 2 Temperature dependence of zero-field
• resistance, Hall coefficient, and spin
  susceptibility.

21
CTS Experimental Overview

• In strongly 2D a-(BEDT-TTF)2MHg(SCN)4, 13C NMR
  data show
• the whole NMR results seen above are in favor
  of the picture of a nonmagnetic transition such
  as charge density wave (CDW). However, we have no
  idea which kind of CDW reconciles the
  susceptibility anisotropy observed below 12 K and
  other magnetic properties at present.
• K. Miyagawa, A. Kawamoto, and K. Kanoda, 13C NMR
  study of nesting instability in a
  a-(BEDT-TTF)2RbHg(SCN)4 Physi. Rev. B. 56, R8487
  (1997).

22
CTS Theoretical Models and Concepts

• Strongly correlated electrons low
  dimensionality ) weak-coupling Fermi
  surface-based arguments are suspect (as in high
  Tc materials). Use discrete 2D anisotropic
  lattice model Hamiltonian with e-e and e-ph
  interactions. The
• (quasi-2D) Peierls-extended
  Hubbard (PEH) model
• HPEH H0 Hee Hinter
• H0 -S j,M s t0 - a(Dj,M)Bj,j1,M, M,s b S
  j,Mvj,Mnj,M
• K1/2 S j,M(Dj,M)2 K2/2 S j,Mvj,M2
• HeeU S j,Mnj,M, nj,M, V S i,Mnj,Mnj1,M
• Hinter -t? S j,M,s Bj,j,M,M1, s

23
CTS Theoretical Models and Concepts

• As before, in PEH j is a site index along given
  chain, M is a chain index. Bj,k,L,M,s cj,L,s
  ck,M,s ck,M,s cj,L,s,
• uj,M intersite phonon, Dj,M (uj,M uj1,M),
  vj,M intrasite phonon, present because large
  molecules are deformable
• Parameters e-e are U gtgt V gt t0, e-ph are a, b
• Critical implicit parameter Band-filling, r
  Ne/NL, where NL is the number of sites, and Ne is
  the number of electrons.

24
CTS Theoretical Models and Concepts

• Broken symmetries in 1D PEH at ½-filling
• 2kF BOW, modulation of bj
• (Bj, j1, M, M, s )
• 2kF CDW, modulation of charge nj
• 2kF SDW, modulation of spin nj,
• nj,
• No coexistence of two DWs!!

25
CTS Theoretical Models and Concepts

• Phase Diagram in the U, V gt 0 quadrant
• Schematic ground state phase diagram
• of the pure EHM at ½-filling, showing
• familiar CDW (LRO) and SDW (algebraic
• decay) phases, as well as recently
• confirmed BOW (LRO) phase near
• U ' 2V line at intermediate coupling.
• M. Nakamura, Phys. Soc Jpn 68, 3123 (1999).
• P. Sengupta, A. W. Sandvik, D.K. Campbell,
• Bond-order-wave phase and quantum phase
• transitions I the one dimensional extended
• Hubbard model, Phys. Rev. B 65, 155113/1-18
• (2002).

26
CTS Theoretical Models and Concepts

• Broken Symmetries in the 1D PEH at ¼-filling
• Organic stacks in 12 CTS are ¼-filled electron
  bands ((MEM1)(TCNQ-1/2)2) and in 21 CTS are
  ¼-filled hold bands ((TMTTF1/2)2PF6-1 )
  ¼-filling is very important!
• B1) 2kF BOW1CDW1 for U V 0 and a, b
• ! 0-Familiar Peierls state
• B2) 4kF CDW for a, b ! 0, U gt V gt Vc,
• where Vc 2t Vc 1 for U/t0 !
• 1 Vc gt Vc1 for finite U/t0-Familiar
• 1010 Wigner crystal.
• B3) New coexisting BCDW state-(2kF4kF)
• BOW 2kF CDW for U ¹ 0,V lt Vc-note
• 1100.. charge order
• B4) New 4kF 2kF CDW 2kF BOW for U gt
• V gt Vc and a gt ac-novel SP variant of
• ..1010.. Wigner crystal.

27
CTS Theoretical Models and Concepts

• NB
• B1 and B2 are well-known B3 and B4 are new
  results, to be proven below. Key issue is which
  is the ground state for given parameters.
• B3 has 2 different site charges, 3 different
  bonds B4 has 3 different site charge, 2
  different bonds.
• Question of Charge Order in 1D materials is not
  clear is it ..1010.. or ..1100..?

28
CTS Theory Confronts Experiments

• 1D CTS Key Questions
• Quasi-1D ¼-filled, segregated stack organic CTS
  21 cationic CTS (e.g. (TMTTF)2X), ¼-filled
  holes 12 anionic CTS (e.g., (MEM)(TCNQ)2,
  ¼-filled electrons)
• KQO What is Charge Order (CO)?
• Inhomogenous distribution of charge along organic
  stacks-some sort of density wave. Two models
  proposed for CO
• 1010 CO, obtained by Hartree-Fock, 4kF CDW,
  nearest-neighbor V dominates.
• H. Seo and H. Fukuyama, J. Phys. Soc. Jpn. 66,
  1249 (1997).
• 1100 CO, obtained in (numerically) exact
  many-body study, BCDW, cooperative e-e and e-ph
  effect.
• Mazumdar, Clay, Campbell, PRB 62, 13400 (2000).

29
CTS Theory Confronts Experiments

• 1D CTS Key Questions
• Quasi-1D ¼-filled, segregated stack organic CTS
  21 cationic CTS (e.g. (TMTTF)2X), ¼-filled
  holes 12 anionic CTS (e.g., (MEM)(TCNQ)2,
  ¼-filled electrons
• KQ1 Hartree-Fock vs. Exact many-body? Does
  ..1010.. CO occur for realistic parameters in
  exact calculation?
• KQ2 Combined e-e and e-ph interactions? Is there
  always CO? Always spin-Peierls?
• KQ3 Experimental signature of the two CO states?
  Strong evidence for the one or the other?
• KQ4 Are expected temperature scales in either
  picture consistent with experiment?

30
CTS Theory Confronts Experiments

• Recall PEH model in 1D version with intrasite
  phonons
• HPEH H0 Hee
• H0 -S j, s t0 - a(Dj)Bj,j1,s b S jvjnj,
• Ka/2 S j(Dj)2 KB/2 S jvj2
• HeeU S jnj,nj, V S i,njnj1
• Here j is a site index, Bj,k,s cj,s ck,s ck,
  s cj, s, uj intersite phonon,
• Dj (uj uj1), vj intrasite phonon.
• Parameters e-e are U gtgt V gt t0, e-ph are a, b
• Estimated Values ????
• TMTTF t0 0.1 0.15 eV, U 1.0 eV, V 0.35eV
  (??) a, b ¹ 0
• TMTSF t0 0.2 0.25 eV, U 1.0 eV, ) U/t0
  smaller than in TMTTF, V 0.4 0.5 eV (??) a,
  b ¹ 0
• F. Mila, Phys. Rev. B 52, 4788 (1995).
• Methods applied include Hartree-Fock, ED, and
  QMC Results?

31
CTS Theory Confronts Experiments

• AKQ1 Hartree-Fock vs. Exact many-body? Does
  ..1010.. CO occur for realistic parameters in
  exact calculation? For U ! 1, one finds ..1010..
  only for
• V gt Vc gt 2t0.
• Phase diagram in
  (U,V) plane for a, b ! 0

32
CTS Theory Confronts Experiments

• AKQ1 Hartree-Fock vs. Exact many-body? Does
  ..1010.. CO occur for realistic parameters in
  exact calculation?
• Vc(U) determined by exact methods (strong
  coupling, QMC, and ED) vs. HF
• Shibata, Nishimoto, Ohta, PRB 64, 235107 (2001).
• Clay, Mazumdar, Campbell, cond-mat/0112278 PRB
  67, 115121/1-9 (2003)
• H. Seo and H. Fukuyama, J. Phys. Soc. Jpn. 66,
  1249 (1997).
• For Vc(U) HF gets both magnitude and trend with U
  wrong. For realistic U and V, ..1010.. can be
  reached over only narrow range of parameters.
  From experimental parameters conclude TMTSF is
  strongly in ..1100.. Region, TMTTF may be close
  to 1100/1010 boundary.

33
CTS Theory Confronts Experiments

• AKQ2 Combined e-e and e-ph interactions? Is
  there always CO? Always spin-Peierls?
• Exact many body studies for U gt 6t0, V lt Vc(U)
  show ground state is novel coexisting BCDW with
  ..1100.. CO and WSWS bond orders.
• Data for U 6t0, V t0 on a 16 site open chain
  for a b 0. CO and SP/BOW coexist in a BCDW
  (2kF 4kF) BOW 2kF CDW, which occurs for a,
  b ! 0
• Mazumdar, Clay, Campbell, PRB 62, 13400 (2000) -
  Fig3a.

34
CTS Theory Confronts Experiments

• Can SP/BOW coexist with ..1010.. CO for V gt
  Vc(U)?
• No previous studies of this!
• We have recently show answer is yes provided a
  gt ac gt 0 state is 4kF CDW-SP
• ..1010.. (4kF CDW-SP) bonds SSWW
• NB in 1010.. SP, 0 sites no longer equivalent
  ) slightly different charge on 0 s ) 3
  different site charges!
• Clay, Mazumdar, Campbell, cond-mat/0203266, PRB
  67, 115121/1-9 (2003)
• Bottom Line bond distortion can coexist with
  both 1100 and 1010 states but with different
  patterns
• For V lt Vc(U), unconditional BCDW (1100) CO
  WSWS BOW, 2 sites, 3 bonds
• For V gt Vc(U), conditional 4kF CDW-SP (1010)
  CO SSWW BOW, 3 sites, 2 bonds

35
CTS Theory Confronts Experiments

• Detailed Results for Phase diagram
• with phonons
• Self-consistent Lanczös
• for N 12 and 16 sites
• Dimensions coupling constants
• la a2 / Kat, lb b2 / Kbt
• Results for N 16, U 8t
• NB Undistorted and 4kF BOW
• phases are finite-size artifacts.

36
CTS Theory Confronts Experiments

• Expected Phase diagram for N ! 1
• The expected phase diagram in the la - lb plane
• for (a) V lt Vc and (b) V lt Vc.
• Thus SP behavior at low T is consistent
• with either 1100 or 1010 CO, but with
• key differences
• BCDW state 1100 charge order,
• two site charges, three bond orders
• in WSWS pattern small Dn, strong
• bond distortion.
• 4kF CDW-SP state 1010 charge order
  (actually, three site charges in SP distorted
  state), two bond orders in SSWW pattern large
  Dn, weak bond distortion.

37
CTS Theory Confronts Experiments

• AKQ3 Experimental signature of the two CO
  states? Strong evidence for the one or the other?
• Site Charges?
• NMR data show two different local charge
  environments below TCO dont distinguish clearly
  between 1010 and 1100.
• Spectroscopic Studies of (EDO-TTF)2PF6 show 0110
  CO
• O. Drozdova et al., Yamada Conf LVI, Abstract
  Number S72 (2001).

38
CTS Theory Confronts Experiments

• Bond Orders?
• For 1010, no direct observation of yet of SSWW
  pattern.
• For 1100, considerable evidence for WSWS
  pattern.
• 12 TCNQ bond distortions measured by neutron
  scattering
• Dimerization followed by tetramerization seen
  directly.
• MEM(TCNQ)2 R.J.J. Visser et al., PRB 28, 2074
  (1983).
• TEA(TCNQ)2 Direct evidence of both WSWS and
  1100 CO from X-ray and neutron diffraction H.
  Kobayashi et al. Acta. Cryst. B 26, 459, (1970)
  J. P. Farges, J. Physique 46, 465, (1985).

39
CTS Theory Confronts Experiments

• AKQ4 Are expected temperature scales in either
  picture consistent with experiment?
• In a word NO! Experiments find CO at
  intermediate temperature
• TSP lt TCO lt TMI
• 1010
• T gt TMI 1010, 0101 equal weight ) metal
• T lt TMI 1010, 0101 symmetry broken ) insulator
  but immediately with CO
• Expect 1010 to give TCO TMI
• 1100
• Above TMI 1100, 0011, 0110, 1001, all equal
  weight ) metal
• TSP lt T lt TMI 1010, 0101 equal weight )
  insulator but no CO
• T lt TSP 1100, 0011 symmetry broken ) CO first
  appears
• Expect 1100 to give TCO TSP
• Bottom line Temperature dependence difficult to
  understand in purely 1D model-Recent results
  suggest considering 2D effects may resolve issue.

40
CTS Conclusions and Future Directions

• We have a unified approach to 1D, quasi-1D/weakly
  2D, and 2D organic CTS. Results are based on
  exact many-body studies (strong coupling, QMC,
  ED) of Peierls-extended Hubbard that
  incorporates e-e and e-ph interactions. Focusing
  on the 1D CTS, we have answered four key
  questions (KQ1-KQ4) and can summarize our results
  as follows
• The presence of 1100 CO in 1D systems for most of
  the expected range of parameters U, V. HF
  prediction of large region of 1010 CO is wrong.
• 1100 CO in 1D systems is one aspect of novel
  BCDW (coexisting density wave) ground state.
• Experiments confirm existence of BCDW and 100 in
  12 TCNQ salts. (TMTTF)2 may exhibit 1010 CO.

41
The Future Organic Electronics

• Idea/Dream Build (self-assemble?) structures
  (dots, layers, multi-layers, crystals?) with
  active elements (molecules with 2,3,states,
  intrinsic rectifying properties?) linked by
  network (how to make connections?).

42
The Future Organic Electronics

• Sample idealized molecular devices

43
The Future Organic Electronics

• Optical Micrograph of Actual
  Molecular Circuit, fabricated by
  soft-imprinting and chemical assembly
  techniques

44
The Future Organic Electronics

• How are these for
  possibilities?
• Efficient organic photovoltaic diodes based on
  doped pentacene
• Superconductivity in molecular crystals induced
  by charge injection
• Gate-induced superconductivity in a solution
  processed organic polymer film
• Self-assembled monolayer organic field-effect
  transistors

JH Schön, Ch Kloc, E. Buchler, B. Battlogg JH
Schön, Ch Kloc, B. Battlogg JH Schön, A
Dodabalapur, Z. Bao, Ch Kloc, O. Schenker B.
Battlogg JH Schön, H Meng, Z. Bao,
In the words of Wolfgang Pauli, Schön ist sie
schon, aber leider falsch!
45
Conclusion

• Despite that serious setback, the
  future of organic electronic materials is
  bright as we heard yesterday from John Rogers
  from fundamental theoretical issues (the nature
  of CO and the mechanism of SC in CTS, the
  temperature dependence of mobility in organic
  molecular crystals, the mechanism for
  conductivity in molecules like DNA) through
  commercial applications (cheap plastic active
  displays, flexible organic thin-film transistors,
  self-assembling novel logic and memory circuits),
  this important class of complex materials
  promises to provide challenges and opportunities
  to chemists, physicists, materials scientists and
  engineers for decades to come.

46
Our References

• K. C. Ung, S. Mazumdar, and D. Toussaint,
  Metal-Insulator and Insulator-Insulator
  Transitions in Quarter-Filled Band Organic
  Conductors, Phys. Rev. Lett. 73, 2603 (1994).
• S. Mazumdar, S. Ramasesha, R. T. Clay, and D.K.
  Campbell, Theory of Coexisting Charge and
  Soin-Density Waves in (TMTTF)2Br, (TMTSF)2PF6,
  and a-(BEDT-TTF2MHg(SCN)4, Phys. Rev. Lett. 82,
  1522-1525 (1999).
• S. Mazumdar, D. K. Campbell, R. T. Clay, S.
  Ramasesha Comment on Wigner Crystal Type of
  Charge Ordering in an Organic Conductor with a
  Quarter-Filled Band (DI-DCNQI)2Ag, Phys. Rev.
  Lett. 82, 2411 (1999).
• S. Mazumdar, R. T. Clay, and D. K. Campbell
  Bond and charge density waves in the isotropic
  interacting two-dimensional quarter-filled band
  and the insulating state proximate to organic
  superconductivity,'' Phys. Rev. B 62, 13400-13425
  (2000).
• R. T. Clay, S. Mazumdar, and D. K. Campbell
  Re-Integerization of Fractional Charges in the
  Correlated Quarter-Filled
• Band,'' Phys. Rev. Lett. 86, 4084-4087 (2001).
• R. T. Clay, S. Mazumdar, and D. K. Campbell,
  Charge ordering and spin gap transitions in
  q-(BEDT-TTF)2X
• materials,'' J. Phys. Soc. Jpn 71, 1816-1819
  (2002).
• R. T. Clay, S. Mazumdar, and D. K. Campbell,
  The pattern of charge ordering in
  quasi-one-dimensional organic charge transfer
  solids,'' Phys. Rev. B 67, 115121/1-9 (2003).

47
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48
Theory Confronts Experiments

• Answers to Key Questions
• KQ1 Hartree-Fock vs. Exact many-body? Does
  ..1010.. CO occur for realistic parameters in
  exact calculation?
• Vc(U) determined by exact methods (strong
  coupling, QMC, and ED) vs. HF
• Shibata, Nishimoto, Ohta, PRB 64, 235107 (2001).
• Clay, Mazumdar, Campbell, cond-mat/0112278
• H. Seo and H. Fukuyama, J. Phys. Soc. Jpn. 66,
  1249 (1997).
• For Vc(U) HF gets both magnitude and trend with U
  wrong. For realistic U and V, ..1010.. Be reached
  over only narrow range of parameters. From
  experimental parameters conclude TMTSF is
  strongly in ..1100.. Region, TMTTF may be close
  to 1100/1010 boundary.

49
Theory Confronts Experiments

• Answers to Key Questions
• KQ2 Combined e-e and e-ph interactions? Is there
  always CO? Always spin-Peierls?
• Exact many body studies for U gt 6t0, V lt Vc(U)
  show ground state is novel coexisting BCDW with
  ..1100.. CO and WSWS bond orders.
• Data for U 6t0, V t0 on a 16 site open chain
  for a b 0. CO and SP/BOW coexist in a BCDW
  (2kF 4kF) BOW 2kF CDW, which occurs for a,
  b ! 0
• Mazumdar, Clay, Campbell, PRB 62, 13400 (2000) -
  Fig3a.

50
Theory Confronts Experiments

• Can SP/BOW coexist with ..1010.. CO for V gt
  Vc(U)?
• No previous studies of this!
• We have recently show answer is yes provided a
  gt ac gt 0 state is 4kF CDW-SP
• ..1010.. (4kF CDW-SP) bonds SSWW
• NB in 1010.. SP, 0 sites no longer equivalent
  ) slightly different charge on 0 s ) 3
  different site charges!
• Clay, Mazumdar, Campbell, cond-mat/0203266
• Bottom Line bond distortion can coexist with
  both 1100 and 1010 states but with different
  patterns
• For V lt Vc(U), unconditional BCDW (1100) CO
  WSWS BOW, 2 sites, 3 bonds
• For V gt Vc(U), conditional 4kF CDW-SP (1010)
  CO SSWW BOW, 3 sites, 2 bonds

51
Theory Confronts Experiments

• Detailed Results for Phase diagram
• with phonons
• Self-consistent Lanczös
• for N 12 and 16 sites
• Dimensions coupling constants
• la a2 / Kat, lb b2 / Kbt
• Results for N 16, U 8t
• NB Undistorted and 4kF BOW
• phases are finite-size artifacts.

52
Theory Confronts Experiments

• Expected Phase diagram for N ! 1
• The expected phase diagram in the la - lb plane
• for (a) V lt Vc and (b) V lt Vc.
• Thus SP behavior at low is consistent
• with either 1100 or 1010 CO, but with
• key differences
• BCDW state 1100 charge order,
• two site charges, three bond orders
• in WSWS pattern small Dn, strong
• bond distortion.
• 4kF CDW-SP state 1010 charge order
  (actually, three site charges in SP distorted
  state), two bond orders in SSWW pattern large
  Dn, weak bond distortion.

53
Theory Confronts Experiments

• Answers to Key Questions
• KQ3 Experimental signature of the two CO states?
  Strong evidence for the one or the other?
• Site Charges?
• NMR data show two different local charge
  environments below TCO dont distinguish clearly
  between 1010 and 1100.
• Spectroscopic Studies of (EDO-TTF)2PF6 show 0110
  CO
• O. Drozdova et al., Yamada Conf LVI, Abstract
  Number S72 (2001).

54
Theory Confronts Experiments

• Bond Orders?
• For 1010, no direct observation of yet of SSWW
  pattern.
• For 1100, considerable evidence for WSWS
  pattern.
• 12 TCNQ bond distortions measured by neutron
  scattering
• Dimerization followed by tetramerization seen
  directly.
• MEM(TCNQ)2 R.J.J. Visser et al., PRB 28, 2074
  (1983).
• TEA(TCNQ)2 Direct evidence of both WSWS and
  1100 CO from X-ray and neutron diffraction H.
  Kobayashi et al. Acta. Cryst. B 26, 459, (1970)
  J. P. Farges, J. Physique 46, 465, (1985).

55
Theory Confronts Experiments

• Answers to Key Questions
• KQ4 Are expected temperature scales in either
  picture consistent with experiment?
• In a word NO! Experiments find CO at
  intermediate temperature TSP lt TCO lt TMI
• 1010
• T gt TMI 1010, 0101 equal weight ) metal
• T lt TMI 1010, 0101 symmetry broken ) insulator
  but immediately with CO
• Expect 1010 to give TCO TMI
• 1100
• Above TMI 1100, 0011, 0110, 1001, all equal
  weight ) metal
• TSP lt T lt TMI 1010, 0101 equal weight )
  insulator but no CO
• T lt TSP 1100, 0011 symmetry broken ) CO first
  appears
• Expect 1100 to give TCO TSP
• Bottom line Temperature dependence difficult to
  understand in purely 1D model-recent results
  (c.f. S. Mazumdar, Talk ThuI2) suggest
  considering 2D effects may resolve issue.

56
Theory Confronts Experiments

• Answers to Key Questions
• Quasi-1D/Weakly 2D CTS
• KQ5 What is the alignment of the transverse
  direction?
• With 1100 CO along high conductivity (x) axis
  can have 4 distinct transverse orders.
• Shift by 0 sites between chains ) 0 phase shift
• 110011001100
• 110011001100
• 110011001100
• (Insulating!) stripes in y-direction , 1100, CO
  in x (and diagonals)
• Shift by 1 site between chains ) p / 2 phase
  shift
• 001100110011
• 011001100110
• 110011001100
• 1100 CO in x and y (diagonals (insulating) stripe
  and 1010)

57
Theory Confronts Experiments

• Shift by 2 sites between chains ) p phase shift
• 110011001100
• 001100110011
• 110011001100
• 1100 CO in x, 1010 CO in y (diagonals
  (insulation) stripes)
• Shift by 3 site between chains ) 3p/2 phase shift
• 001100110011
• 100110011001
• 110011001100
• 1100 CO in x and y (diagonals (insulating) stripe
  and 1010)
• Results?

58
Theory Confronts Experiments

• For typical parameters, answer is 3), p phase
  shift and we find coexisting SDW, so state
  becomes BCSDW!
• QMC results for site charges and interchain
• spin-spin correlations on a 12(x)4 lattice, t?
  0.2t0

Schematic structure of the Coexisting BOW-CDW-SDW
BCSDW
59
Theory Confronts Experiments

• Answers to Key Questions
• 2D CTS Consider q-(BEDT-TFF)2X
• KQ6 Crystal/lattice structure? Experimental
  results?
• q-(BEDT-TTF) lattice
• Triangular lattice 6 neighbors
• Tc ltlt tp, but Vc Vp
• q-(BEDT-TFF)2I3 superconductor,
• other X are semiconductors.
• Experiments in non-superconduction q-(ET) also
  show two transitions as function to temperature

60
Theory Confronts Experiments

• (1) High temperature metal-insulator (MI)
  transition
• Seen in all q-(ET) at T 200K
• 2D ¼-filled no MI transition in conventional
  band theory
• The Fermi surface predicted by bandstructure
  calculation is a simple closed cylinder.
  Nevertheless, most of them undergo transitions
  into insulators
• K. Miyagawa, A. Kawamoto, K. Kanoda, PRB 62,
  R7679 (2000).
• NB c-direction dimerization is seen at TMI

61
Theory Confronts Experiments

• Low temperature transition to spin-gap state
  (TSG)
• Data for q-(ET)2RbZn(SCN)4, TSG 50K
• H. Mori, S. Tanaka, T. Mori, PRB 57, 12023
  (1998).
• Spin gap not consistent with 1D spin-Peierls
  transition

62
Theory Confronts Experiments

• (3) Charge ordering (CO) immediately for T lt TMI
• Splitting of NMR line seen
• K. Miyagawa, A. Kawamoto, K. Kanoda, PRB 62 R7679
  (2000) and others.
• No previous theory described all three effects.
  TCO TMI suggests 1010 CO in 2D. Acutlaly, much
  more subtle as we now show

63
Theory Confronts Experiments

• Answers to Key Questions
• KQ7 What are possible CO arrangements in 2D q-ET
  lattice?
• H. Seo, J. Phys. Cos. Jpn. 69, 805 (2000).
• Vertical Diagonal Horizontal
  Converted to square lattice
• Stripes
  added diagonal
• Notice horizontal stripe has 1100 CO with p/2
  phase shift
• Compare Stripe Energies within 2D EH model
• H -t0 åltijgts (cyiscjs cyjscis) Uåi ni"ni
  V åltijgt ni nj
• Parameters for q-ET tp 0.14 eV, tc 0.01
  eV, U 0.7 eV
• Consider range of V 0.15 lt V lt 0.35

64
Theory Confronts Experiments

• Answers to Key Questions
• KQ8 Which stripe CO dominates, and what are its
  characteristics?
• Results are 16-site exact diagonalization
• We find that the horizontal stripe
• has lowest energy for large range
• of V. Previous theoretical work
• incorrectly predicts vertical stripe
• H. Seo, J. Phys. Soc. Jpn. 69, 805 (2000).
• vertical strip favored within HF
• approximation
• R.H. McKenzie et al., PRB 61, 085109 (2001)
• ignores Vc (chooses pure square lattice)

65
Theory Confronts Experiments

• Other characteristics of horizontal stripe CO
• We find strong bond distortions coexisting with
  CO. These are not present in vertical/diagonal
  states.
• Bond distortions will lower energy further when
  phonons included self-consistently

66
Theory Confronts Experiments

• Answers to Key Questions
• KQ9 How do CO and BOW coexist in different spin
  states?
• S0 state (T lt TSG) FM state dominates
  high T
• - Tetramerization along p ! spin gap -
  Dimerization along p
• - Dimerization along c - Dimerizaiton along c

67
Theory Confronts Experiments

• Exact diagonalization results show
• Charge order and c-direction bond dimerization
  present in ferromagnetic state (i.e. above
  spin-gap transition)
• Spin gap transition involves tetramerization of
  p-direction bonds.
• Above spin-gap transition 1-1 and 0-0 bonds
  equivalent
• Below spin-gap transition 1-1 and 0-0 bonds
  different

68
Conclusions and Future Directions

• We have presented a unified approach to 1D,
  quasi-1D/weakly 2D, and 2D organic CTS. Results
  are based on exact many-body studies (strong
  coupling, QMC, ED) of Peierls-extended Hubbard
  that incorporates e-e and e-ph interactions. We
  have answered nine key questions (KQ1-KQ9) and
  can summarize our results as follows
• The presence of 1100 CO in 1D systems for most of
  the expected range of parameters U, V. HF
  prediction of large region of 1010 CO is wrong.
• 1100 CO in 1D systems is one aspect of novel
  BCDW (coexisting density wave) ground state.
• Experiments confirm existence of BCDW and 100 in
  12 TCNQ salts. (TMTTF)2 may exhibit 1010 CO.
• In quasi-1D/weakly 2D CTS, theory predicts novel
  BCSDW in which 1100 CO along chains coexists
  with 1010 transverse order and an SDW. Consistent
  with data in (TMTSF)2PF6.
• In strongly 2D CTS (q -ET)2X, find 1100 order in
  both x and y directions (recall unusual
  lattice). Theory explains two transition and spin
  gap.

69
Conclusions and Future Directions

• Challenges for the future include
• Resolving the T-dependent behavior of (TMTTF)2X
  why is TMI gt TCO gtTSP, TSDW? (2D effects?)
• Understanding the role crystal behavior in
  (ET)-materials differences among q, a and k
  phases, etc. Subtleties of structure in other
  CTS?
• Calculate spin excitation spectra in q-ET
• Establish relation of insulating phases to
  (adjacent?) superconducting phases? Occurrence of
  cooperation, rather than competition, between e-e
  and e-ph interactions in BCDW/BCSDW may be the
  key to understanding unconventional SC in
  organics. Related to ideas in high TC SC but no
  obvious analog of doping.

70
References

• K. C. Ung, S. Mazumdar, and D. Toussaint,
  Metal-Insulator and Unsulator-Insulatr
  Transitions in Quarter-Filled Band Organic
  Conductors, Phsy. Rev. Lett. 73, 2603 (1994).
• S. Mazumdar, S. Ramasesha, R. T. Clay, and D.K.
  Campbell, Theory of Coexisting Charge and
  Soin-Density Waves in (TMTTF)2Br, (TMTSF)2PF6,
  and a-(BEDT-TTF2MHg(SCN)4, Phys. Rev. Lett. 82,
  1522-1525 (1999).
• S. Mazumdar, D. K. Campbell, R. T. Clay, S.
  Ramasesha Comment on Wigner Crystal Type of
  Charge Ordering in an Organic Conductor with a
  Quarter-Filled Band (DI-DCNQI)2Ag, Phys. Rev.
  Lett. 82, 2411 (1999).
• S. Mazumdar, R. T. Clay, and D. K. Campbell
  Bond and charge density waves in the isotropic
  interacting two-dimensional quarter-filled band
  and the insulating state proximate to organic
  superconductivity,'' Phys. Rev. B 62, 13400-13425
  (2000).
• R. T. Clay, S. Mazumdar, and D. K. Campbell
  Re-Integerization of Fractional Charges in the
  Correlated Quarter-Filled
• Band,'' Phys. Rev. Lett. 86, 4084-4087 (2001).
• R. T. Clay, S. Mazumdar, and D. K. Campbell,
  Charge ordering and spin gap transitions in
  q-(BEDT-TTF)2X
• materials,'' J. Phys. Soc. Jpn., in press.
• R. T. Clay, S. Mazumdar, and D. K. Campbell,
  The pattern of charge ordering in
  quasi-one-dimensional organic charge transfer
  solids,'' submitted to Phys. Rev. B.

71
(No Transcript)
72
Broken Symmetry States and Charge Order in
Organic Superconductors

• Understanding Complex Systems UIUC
• May 2003
• with R.T. Clay, S. Mazumdar, and S. Ramasesha
• Supported by NSF DMR97-12765, NSF GRT, NCSA and
  ERATO, Japan Science and Technology Corp.

73
Outline

• Motivation and Bottom Line
• Materials The Organic CTS
• Experimental Overview evidence for change order
  (CO) and novel coexisting density waves
• Theoretical Models and Concepts Peierls
  extended Hubbard (PEH) models, broken symmetry,
  charge order
• Theory confronts Experiment 1D CTS ?
• Quasi-1D/weakly 2D CTS ? 2D CTS
• Conclusions and Future Directions

74
Motivation and Bottom Line

• Organic Charge Transfer Solids (CTS) offer
  richness of organic chemistry in novel electronic
  systems
• Like high Tc superconductors, CTS have strong
  e-e and e-ph interactions
• CTS exhibit superconductivity (SC) and
  antiferromagnetism (SDW) (as seen in high Tc) but
  also charge density wave (CDW), bond-order wave
  (BOW), and spin-Peierls (SP)phases.
• Vary continuously in effective electronic
  dimensionality from 1D to 2D.

75
Motivation and Bottom Line

• Our theoretical studies, based on
  Peierlsextended Hubbard (PEH) models
• Predict novel coexisting BCDW and BCSDW
  density wave ground states
• Provide an explanation of previously puzzling
  recent experiment in several organic CTS,
  including recent observations of charge order
  (CO)
• Explain differences among 1D, weakly 2D, and
  strongly 2D CTS
• Set stage for a possible approach to the observed
  organic superconductivity

76
Materials The Organic CTS

• Organic Chemistry offers rich variety of CTS
• Principal molecules are flat
• p-conjugated organics
• Form 11 salts (TTF-TCNQ)
• 12 anionic salts (MEM(TCNQ))2
• 21 cationic salts (TMTSF)2PF6
• From T. Ishiguro and K. Yamaji, Organic
  Superconductors, p. 2
• (Springer Series in Solid State Sciences Volume
  88 (1990).

77
Materials The Organic CTS

• Crystal structures are stacks of the flat
• organic molecules, counterions lying
• between in parallel segregated stacks.
• In 0th approximation, treat crystals as
• orthorhombic. Largest conductivity
• along stack, called a. For (TMTSF)2PF6,
• ta ' 0.25 eV, tb ' eV, tc ' 0.0015 eV,
• so conductivities are in ratio
• sasbsc 1 (1/100) (1/25000)
• After N. Thorup et al, Acta Crys. B37 1236-1240
  (1981).

78
Materials The Organic CTS

• Electronic anisotropies of material are such that
  they range from quasi-1D to quasi-2D. This is
  reflected in the bulk crystals quasi-1D
  materials form needles, quasi-2 form pancakes.
• Photos courtesy of James Brooks, NHMFL

The needle-like crystal of TTF-TCNQ, has a
transition to a CDW at about 100 K.
The flat, slab-like crystal of the k-phase of
(BEDT-TTF)Cu(NCS)2, which is a 10.4 K
superconductor.
79
Experimental Overview

• Generalized phase diagram summarizes properties
  seen in a wide range of 21 cationic CTS,
  including (TMTZF)2X, Z(S,Se), XBr,PF6, .
• Key observation Pressure is known to enhance
  t?, thereby increasing effective electronic
  dimensionality. Recent results on uniaxial
  pressure confirm directly.
• M. Maesato et al, Phys. Rev. B64 155104 (2001).
• 1DCTS ? Quasi-1D/Weakly 2D ? 2D
• Fig 1. Phase Diagram for (TMTZF)2X compounds.
• CL Charge localized state. Lower case letters
• designate locations of specific compounds at
• atmospheric pressure a) ZT, XPF6
• b)ZDTDS, XPF6 c) ZT, XBr
• d) ZS, XPF6 e) ZS, XClO4.
• D. Jerome, Science 252, 1509 (1991).

80
Experimental Overview

• In 1D CTS (TMTTF)2X, experiments establish CO
• NMR-line splitting below TCO shows two different
  site charges.
• D.S. Chow et al, PRL 85, 1698 (2000).

81
Experimental Overview

• In 1D CTS (TMTTF)2X, experiments establish CO
• B. Dielectric permittivity
• Monceau, Nad, Brazovskii, PRL 86, 4080 (2001).

82
Experimental Overview

• In Quasi-1D/Weakly 2D (TMTSF)2PF6 and (TMTTF)2Br,
  X-Ray experiments show
• a mixed CDW-SDW modulation
• develops below TSDW. To our knowledge,
• such a modulated state has never been
• observed before
• J.P. Pouget and S. Ravy, Synth. Metals 85, 1523
  (1997).
• X-Ray satellite intensities from (TMTSF)2PF6
  below TSDW.
• Satellites 1 and 2 are 2kF reflections satellite
  3 is the 4kF
• CDW reflections.

83
Experimental Overview

• In strongly 2D CTS a-(BEDT-TTF)2MHg(SCN)4,
  M(K,Rb,Tl), analysis of cspin, Hall coefficient,
  mSR, NMR, and ADMRO, leads to conclusion
• We arrive at the possibility that the
• ground state below TZ.. (' 10K)
• could be SDW (or CDW)
• accompanied by CDW (or SDW).
• T. Sasaki and N. Toyota, Mysterious ground
  states
• in the organic conductor a-(BEDT-TTF)2MHg(SCN)4
• Mixed SDW and CDW? Synth. Metals 70 849 (1995).
• Fig. 2 Temperature dependence of zero-field
• resistance, Hall coefficient, and spin
  susceptibility.

84
Experimental Overview

• In strongly 2D a-(BEDT-TTF)2MHg(SCN)4, 13C NMR
  data show
• the whole NMR results seen above are in favor
  of the picture of a nonmagnetic transition such
  as charge density wave (CDW). However, we have no
  idea which kind of CDW reconciles the
  susceptibility anisotropy observed below 12 K and
  other magnetic properties at present.
• K. Miyagawa, A. Kawamoto, and K. Kanoda, 13C NMR
  study of nesting instability in a
  a-(BEDT-TTF)2RbHg(SCN)4 Physi. Rev. B. 56, R8487
  (1997).

85
Theoretical Models and Concepts

• Strongly correlated electrons low
  dimensionality ) weak-coupling Fermi
  surface-based arguments are suspect (as in high
  Tc materials). Use discrete 2D anisotropic
  lattice model Hamiltonian with e-e and e-ph
  interactions.
• (2D) Peierls-extended Hubbard (PEH) model
• HPEH H0 Hee Hinter
• H0 -S j,M s t0 - a(Dj,M)Bj,j1,M, M,s b S
  j,Mvj,Mnj,M
• K1/2 S j,M(Dj,M)2 K2/2 S j,Mvj,M2
• HeeU S j,Mnj,M, nj,M, V S i,Mnj,Mnj1,M
• Hinter -t? S j,M,s Bj,j,M,M1, s

86
Theoretical Models and Concepts

• Here j is a site index along given chain, M is a
  chain index. Bj,k,L,M,s cj,L,s ck,M,s ck,M,s
  cj,L,s, uj,M intersite phonon, vj,M
  intrasite phonon, Dj,M (uj,M uj1,M).
• Parameters e-e are U gtgt V gt t, e-ph are a, b
• Critical implicit parameter Band-filling r
  Ne/NL, where NL is the number of sites, and Ne is
  the number of electrons.

87
Theoretical Models and Concepts

• Broken symmetries in 1D PEH at ½-filling
• 2kF BOW, modulation of bj
• (Bj, j1, M, M, s )
• 2kF CDW, modulation of charge nj
• 2kF SDW, modulation of spin nj,
• nj,
• No coexistence of two DWs!!

88
Theoretical Models and Concepts

• Phase Diagram in the U, V gt 0 quadrant
• Schematic ground state phase diagram
• of the pure EHM at ½-filling, showing
• familiar CDW (LRO) and SCW (algebraic
• decay) phases, as well as recently
• confirmed BOW (LRO) phase near
• U ' 2V line at intermediate coupling.
• M. Nakamura, Phys. Soc Jpn 68, 3123 (1999).
• P. Sengupta, A. W. Sandvik, D.K. Campbell,
• Bond-order-wave phase and quantum phase
• transitions I the one dimensional extended
• Hubbard model, Phys. Rev. B 65, 155113/1-18
• (2002).

89
Theoretical Models and Concepts

• Broken Symmetries in the 1D PEH at ¼-filling
• Organic stacks in 12 CTS are ¼-filled electron
  bands ((MEM1)(TCNQ-1/2)2) and in 21 CTS are
  ¼-filled hold bands ((TMTTF1/2)2PF6-1 )
  ¼-filling is very important!
• B1) 2kF BOW1CDW1 for U V 0 and a, b
• ! 0-Familiar Peierls state
• B2) 4kF CDW for a, b ! 0, U gt V gt Vc,
• where Vc 2t Vc 1 for U/t0 !
• 1 Vc gt Vc1 for finite U/t0-Familiar
• 1010 Wigner crystal.
• B3) New coexisting BCDW state-(2kF4kF)
• BOW 2kF CDW for U ¹ 0,V lt Vc-note
• 1100.. charge order
• B4) New 4kF 2kF CDW 2kF BOW for U gt
• V gt Vc and a gt ac-novel SP variant of
• ..1010.. Wigner crystal.

90
Theoretical Models and Concepts

• NB
• B1 and B2 are well-known B3 and B4 are new
  results, to be proven below. Key issue is which
  is the ground state for given parameters.
• B3 has 2 different site charges, 3 different
  bonds B4 has 3 different site charge, 2
  different bonds.
• Question of Charge Order in 1D materials is not
  clear is it ..1010.. or ..1100..?

91
Theory Confronts Experiments

• 1D CTS Key Questions
• Quasi-1D ¼-filled, segregated stack organic CTS
  21 cationic CTS (e.g. (TMTTF)2X), ¼-filled
  holes 12 anionic CTS (e.g., (MEM)(TCNQ)2,
  ¼-filled electrons)
• KQO What is Charge Order (CO)?
• Inhomogenous distribution of charge along organic
  stacks-some sort of density wave. Two models
  proposed for CO
• 1010 CO, obtained by Hartree-Fock, 4kF CDW,
  nearest-neighbor V dominates.
• H. Seo and H. Fukuyama, J. Phys. Soc. Jpn. 66,
  1249 (1997).
• 1100 CO, obtained in (numerically) exact
  many-body study, BCDW, cooperative e-e and e-ph
  effect.
• Mazumdar, Clay, Campbell, PRB 62, 13400 (2000).

92
Theory Confronts Experiments

• 1D CTS Key Questions
• Quasi-1D ¼-filled, segregated stack organic CTS
  21 cationic CTS (e.g. (TMTTF)2X), ¼-filled
  holes 12 anionic CTS (e.g., (MEM)(TCNQ)2,
  ¼-filled electrons
• KQ1 Hartree-Fock vs. Exact many-body? Does
  ..1010.. CO occur for realistic parameters in
  exact calculation?
• KQ2 Combined e-e and e-ph interactions? Is there
  always CO? Always spin-Peierls?
• KQ3 Experimental signature of the two CO states?
  Strong evidence for the one or the other?
• KQ4 Are expected temperature scales in either
  picture consistent with experiment?

93
Theory Confronts Experiments

• Recall PEH model in 1D Version
• HPEH H0 Hee
• H0 -S j, s t0 - a(Dj)Bj,j1,s b S jvjnj,
• Ka/2 S j(Dj)2 KB/2 S jvj2
• HeeU S jnj,nj, V S i,njnj1
• Here j is a site index, Bj,k,s cj,s ck,s ck,
  s cj, s, uj intersite phonon, vj intrasite
  phonon, Dj (uj uj1).
• Parameters e-e are U gtgt V gt t0, e-ph are a, b
• Estimated Values ????
• TMTTF t0 0.1 0.15 eV, U 1.0 eV, V 0.35eV
  (??) a, b ¹ 0
• TMTTF t0 0.2 0.25 eV, U 1.0 eV, ) U/t0
  smaller than in TMTTF, V 0.4 0.5 eV (??) a,
  b ¹ 0
• F. Mila, Phys. Re. B 52, 4788 (1995).
• Methods applied include Hartree-Fock, ED, and
  QMC Results?

94
Theory Confronts Experiments

• Answers to Key Questions
• KQ1 Hartree-Fock vs. Exact many-body? Does
  ..1010.. CO occur for realistic parameters in
  exact calculation? For U ! 1, finds ..1010.. Only
  for V gt Vc gt 2t0.
• Phase diagram in (U,V) plane for a, b ! 0

95
Theory Confronts Experiments

• Answers to Key Questions
• KQ4 Are expected temperature scales in either
  picture consistent with experiment?
• In a word NO! Experiments find CO at
  intermediate temperature TSP lt TCO lt TMI
• 1010
• T gt TMI 1010, 0101 equal weight ) metal
• T lt TMI 1010, 0101 symmetry broken ) insulator
  but immediately with CO
• Expect 1010 to give TCO TMI
• 1100
• Above TMI 1100, 0011, 0110, 1001, all equal
  weight ) metal
• TSP lt T lt TMI 1010, 0101 equal weight )
  insulator but no CO
• T lt TSP 1100, 0011 symmetry broken ) CO first
  appears
• Expect 1100 to give TCO TSP
• Bottom line Temperature dependence difficult to
  understand in purely 1D model-recent results
  (c.f. S. Mazumdar, Talk ThuI2) suggest
  considering 2D effects may resolve issue.

96
Theoretical Models and Concepts

• Here j is a site index along given chain, M is a
  chain index. Bj,k,L,M,s cj,L,s ck,M,s ck,M,s
  cj,L,s, uj,M intersite phonon, vj,M
  intrasite phonon, Dj,M (uj,M uj1,M).
• Parameters e-e are U gtgt V gt t, e-ph are a, b
• Critical implicit parameter Band-filling r
  Ne/NL, where NL is the number of sites, and Ne is
  the number of electrons.

97
Theoretical Models and Concepts

• Here j is a site index along given chain, M is a
  chain index. Bj,k,L,M,s cj,L,s ck,M,s ck,M,s
  cj,L,s, uj,M intersite phonon, vj,M
  intrasite phonon, Dj,M (uj,M uj1,M).
• Parameters e-e are U gtgt V gt t, e-ph are a, b
• Critical implicit parameter Band-filling r
  Ne/NL, where NL is the number of sites, and Ne is
  the number of electrons.