Sumit Mazumdar University of Arizona

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Sumit MazumdarUniversity of Arizona

• CHARGE ORDERING AND LOCAL SINGLET FORMATION IN
  ¼-FILLED BAND CHARGE-TRANSFER SOLIDS AND OXIDES
  OF EARLY TRANSITION METALS

Collaborators R. Torsten Clay, Mississippi
State University David Campbell, Boston
University S. Ramasesha, I. I. Sc.
Bangalore Yongguo Yan, University of Arizona
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Plan of talk

• Focus on SPIN GAPS (SG), -- why?
• 2. Materials that are of interest (so far).
• 3. Theory of local singlet formation in
• (a) 1-dimension
• (b) weakly 2-D lattice
• (c) 2-D triangular lattice
• (d) zigzag ladders
• (e) rectangular ladders

K. Ung, S.M. and D. Toussaint, PRL 1994
S.M., Ramasesha, Clay, Campbell, PRL 1999
Clay, S.M., Campbell, JPSJ 71, 1816 (2002).
Clay and S.M., PRL 2005
Yan, Ramasesha and S.M. 2005
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WHY FOCUS ON SG??

• I. SG necessary though not sufficient for
  superconductivity (SC). Most complex SC usually
  proximate to complex magnetic behavior.
• II. ANY energy gap a signature of confinement.
  Standard theories
• of SG are usually in the context of spin-Peierls
  transitions, where
• there occur confinement of SPIN excitations. How
  do we
• understand SG transitions in
• non-1/2-filled bands, --- need also charge
  confinement !
• Dimensionality gt 1 ?

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Materials of interest
ORGANIC
INORGANIC

1/4-FILLED BAND CTS (i) 1-D anionic 12 TCNQ,
DCNQI (ii) 1-D cationic, (iii) Weakly 2-D
(iv) Strongly 2-D

(v) Organic ladder compounds,
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THEORY, START WITH 1-D
Coulomb interactions
SSH Holstein
Force constants
Obvious broken symmetry 4kF CDW, occupancies
.1010.
HOWEVER, THIS CDW IS OBTAINED ONLY FOR U gt 4t,
V gt VC VC 2t for infinite U, VC gt 2t
for finite U
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PHASE DIAGRAM OF 1d EXTENDED HUBBARD MODEL FOR
ZERO ELECTRON-PHONON COUPLING
F. Mila and X. Zotos, Europhys Lett 24, 133 H.Q.
Lin et al, Proc NATO ARW Y. Shibata et al., PR B
64, 235107 (2001) R.T. Clay, S.M. and D.K.
Campbell, PR B 67, 115121
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PHASE DIAGRAM WITH NONZERO e-p COUPLING
4kF BOW
(2kF4kF) BCDW
4kF CDW
4kF CDW SP
U 8t, (a) V 2t, (b) V 3t, (c) V 4t Bond
lengths in BCDW SWSW Bond lengths in 4kF CDW
SP SSWW
R.T. Clay, S.M. and D.K. Campbell, PR B 67,
115121 (2003).
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EXPERIMENTAL EVIDENCE FOR THE 1100 BCDW

• MEM(TCNQ)2, Bond length pattern SWSW, R.J.J.
  Visser et al., PR B 28, 2074 (1983)
• TEA(TCNQ)2, Bond length patters SWSW AND charge
  distribution 1100, --
• A. Filhol and M. Thomas, Acta
  Crystallogr., Sect B, Struct. Sci. B 40, 44
  (1984)
• A. Filhol et al., ibid, B 36, 2719
  (1980).
• Ag (DI-DCNQI)2, CDW of the 1100 type,
• M. Meneghetti et al., J. Sol. St. Chem.
  168, 632 (2002).
• K. Yamamoto et al., PR B 71, 045118
  (2005).
• (4) (TMTTF)2X below the spin-Peierls
  transition?

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Weakly 2-D system, add nonzero interchain hopping
to Hamiltonian, coexisting BOW-CDW-SDW, -- BCSDW.
S. Mazumdar et al., PRL 82, 1522 (1999).
Periodic 12 x 4 lattice, put in bond distortions,
calculate charge densities, Interchain spin-spin
correlations using constrained path quantum Monte
Carlo
Experiment (TMTSF)2X, coexisting CDW-SDW, with
SAME periodicities For CDW and SDW, J.P. Pouget
and S. Ravy, Synth. Metals 85, 1523 (1997).
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Strongly 2-D system, charge-ordering in
H. Mori et al., Bull. Chem Soc. Jpn. 71, 797
and PR B 57, 12023 K. Miyagawa et al., PR B 62,
7679 R. Chiba et al., Synth. Metals 120, 919
Possible CO patterns
H. Seo, J. Phys. Soc. Jpn. 69, 805 (2000).
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Theoretical calculations, R.T. Clay, SM and
D.Campbell, J. Phys Soc Jpn 71, 1816 (2002)
Horizontal stripe with 1100 CO along p-axes
wins. Predict bond tetramerization along p-axes
as well as dimerization along c-axis. These bond
distortions absent in vertical and diagonal
stripe structures.
c-axis dimerization experimentally observed H.
Mori et al., PR B 57, 12023 (1998). M. Watanabe
et al., JPSJ, 68, 2654 (1999). Y. Nogami et al.,
Synth. Metals 102, 1778 (1999). T. Nakamura et
al., JPSJ 69, 594. M. Watanabe et al., JPSJ 74,
2011 (2005).
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Recent ¼-filled band molecular ladder
systems (1) (DT-TTF)2Au(mnt)2, E. Ribera at
al., Chem Eur J 5, 2025 (1999). (2)
(BDTFP)2XPhCl0.5 , T. Nakamura et al., JPSJ 71,
2022 (2002).
BDTFP
Au(mnt)2
DT-TTF
Au(mnt)2
Characteristic feature of molecular ladder
systems insulator-insulator transitions
accompanied by spin gaps (SG). TSG in ladder
systems extremely large, 70 K in (DT-TTF)2X, 175
K in BDTFP. To be compared with spin-Peierls
transitions at 10-20 K in quasi-1D ¼-filled CTS.
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Z-Z ladder
Bond-charge density wave in the zigzag electron
ladder 2kF CDW 2kF BOW along Zigzag, 4kF CDW
4kF BOW along stacks
1D
SG versus charge disproportionation in zizag
ladder and 1D chain. SG much larger in z-z ladder.
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Low-temperature specific heat and magnetic
susceptibility of nonmetallic vanadium bronzes
B.K. Chakraverty, M.J. Sienko, and J. Bonnerot,
PR B 17, 3781 (1978)
The low-temperature magnetic susceptibility is
equally anomalous and points to a singlet or
diamagnetic ground state. It is postulated that
the V4 centers in these bronzes from
near-neighbor pairs or bipolarons through
deformation-induced
attraction.
The pairing interactions that we have proposed
here for the vanadium bronzes is not without
analogy with its more well-known siblings as seen
in VO2 or V4O7. The localized Cooper pairs
that one has seen in Ti4O7, and that we have
invoked in these vanadium bronzes,
may indeed be a genuine precursor to true
superconductivity
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CONCLUSIONS

• Configuration space pairing, or local dimer
  formation is common
• in ¼-filled band systems, independent of
  dimensionality, due to
• strong co-operative interactions between
  antiferromagnetic coupling
• and electron-phonon interactions.

(2) Local dimer formation, -- a new paradigm for
the occurrence of spin gaps in dimensionality gt
1.