1. Sumit Mazumdar University 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

2. Plan of talk: 1.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

3. 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 (a)non-1/2-filled bands, --- need also charge confinement ! (b)Dimensionality > 1 ?

4. Materials of interest ORGANIC INORGANIC 1/4-FILLED BAND CTS (i) 1-D anionic: 1:2 TCNQ, DCNQI (ii) 1-D cationic, (iii) Weakly 2-D (iv) Strongly 2-D (v) Organic ``ladder’’ compounds,

5. THEORY, START WITH 1-D Obvious broken symmetry: 4kF CDW, occupancies ….1010…. HOWEVER, THIS CDW IS OBTAINED ONLY FOR U > 4|t|, V > V C V C = 2|t| for infinite U, V C > 2|t| for finite U Coulomb interactions SSH + Holstein Force constants

6. 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

7. 4kF BOW (2kF+4kF) BCDW 4kF CDW 4kF CDW + SP PHASE DIAGRAM WITH NONZERO e-p COUPLING U 8t, (a) V = 2t, (b) V = 3t, (c) V = 4t Bond lengths in BCDW: SW ’ SW Bond lengths in 4kF CDW + SP: SSWW R.T. Clay, S.M. and D.K. Campbell, PR B 67, 115121 (2003).

8. EXPERIMENTAL EVIDENCE FOR THE …1100… BCDW (1)MEM(TCNQ)2, Bond length pattern SW’SW, R.J.J. Visser et al., PR B 28, 2074 (1983) (2)TEA(TCNQ)2, Bond length patters SW’SW 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). (3)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?

9. Weakly 2-D system, add nonzero interchain hopping to Hamiltonian, coexisting BOW-CDW-SDW, -- BCSDW. 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). S. Mazumdar et al., PRL 82, 1522 (1999).

10. 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).

11. 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).

12. Recent ¼-filled band ``molecular ladder’’ systems (1) (DT-TTF) 2 [Au(mnt) 2 ], E. Ribera at al., Chem Eur J 5, 2025 (1999). (2) (BDTFP) 2 X[PhCl] 0.5, T. Nakamura et al., JPSJ 71, 2022 (2002). DT-TTF Au(mnt) 2 BDTFP Characteristic feature of molecular ladder systems: insulator-insulator transitions accompanied by spin gaps (SG). T SG in ladder systems extremely large, 70 K in (DT-TTF) 2 X, 175 K in BDTFP. To be compared with spin-Peierls transitions at 10-20 K in quasi-1D ¼-filled CTS.

13. Bond-charge density wave in the zigzag electron ladder: 2k F CDW + 2k F BOW along Zigzag, 4k F CDW + 4k F BOW along stacks 1D Z-Z ladder SG versus charge disproportionation in zizag ladder and 1D chain. SG much larger in z-z ladder.

14. 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 V 4+ 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 VO 2 or V 4 O 7. `` ``The localized Cooper pairs that one has seen in Ti 4 O 7, and that we have invoked in these vanadium bronzes, may indeed be a genuine precursor to true superconductivity

15. CONCLUSIONS (1)Configuration space p a iring, 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 > 1.