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Spin frustration and Mott criticality in triangular-lattice organics under controlled Mottness

2013 Hangzhou Workshop on Quantum Matter, April 22, 2013. Spin frustration and Mott criticality in triangular-lattice organics under controlled Mottness. K. Kanoda, Applied Physics, Univ. of Tokyo.

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Spin frustration and Mott criticality in triangular-lattice organics under controlled Mottness

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  1. 2013 Hangzhou Workshop on Quantum Matter, April 22, 2013 Spin frustration and Mott criticality in triangular-lattice organics under controlled Mottness K. Kanoda, Applied Physics, Univ. of Tokyo H. Oike, T. Furukawa, Y. Shimizu (Nagoya Univ.), H. Hashiba, Y. Kurosaki, K. Umeda, K. Miyagawa, S. Yamashita, Y. Nakazawa M. Maesato, G. Saito (Meijo Univ.) H. Taniguchi Univ. of Tokyo Osaka Univ. Kyoto Univ. Saitama Univ. 1. Ground states: SL vs AFM 2. Weak/strong Mott transitions from SL/AFM 3. Quantum criticality at high temperatures (4. Doped triangular lattice) Outline

  2. Charge/Spin ? Mott insulator Metal Temperature Superconductivity Pairing origin ? AF/SL SC U/W (Mottness) Mott physics in 2D organics All in one material Charge Mott transition Criticality ? N. Mott (1949) Anderson (1973) Spin Frustration AF or Spin Liq. ? Onnes (1911)

  3. k-(ET)2X; quasi-triangular lattice systems ET+0.5 X-1 0.80 0.44 Ab initio Kandpal et al.(2009) Nakamura et al.(2009)

  4. Similar QC behavior at high T R/Rc >10 0.33 Dissimilar at low T 1 Mott phase diagrams of quasi-triangular lattices k-(ET)2Cu2(CN)3 t’/t=0.80-1.0 k-(ET)2Cu[N(CN)2]Cl t’/t=0.44-0.75 less frustrated frustrated

  5. k-(ET)2Cu[N(CN)2]Cl t’/t~ 0.44-0.75 Kagawa et al., Nature 2005 , PRL 2004; PRB 2004, Separation of charge localization and spin ordering on triangular lattice k-(ET)2Cu2(CN)3 t’/t~ 0.80-1.06 Kurosaki et a., PRL 2005, Furukawa et al.unpublished Spin liquid

  6. Thermodynamic anomaly at 6K in k-(ET)2Cu2(CN)3 Specific heat S. Yamashita et al., Nature Phys. 4 (2008) 459 Thermal expansion coefficient Manna et al., PRL104 (2010) 016403 Thermal conductivity M. Yamashita et al., Nature Phys. 5 (2009) 44 NMR Relaxation rate Shimizu et al., PRB70 (2006) 060510

  7. a decrease in local c 13C NMR under a parallel field line shift a axis B line broadening Field-induced spin texture ? 6K line width

  8. Spin liquid in k-(ET)2Cu2(CN)3; Gapless or marginally gapped Degenerate spinons (Motrunich, P.A. Lee, Senthil) Specific heat gapless (g = 13-14 mJ/K2mol) Nuclear Shottky k-(ET)2Cu2(CN)3 S. Yamashita et al., , Nature Phys. 4 (2008) 459 g= 13-14 mJ/K2mol Spin liquid k-(ET)2Cu2(CN)3 AF insulator k-(ET)2X, b’-(ET)2ICl2 Thermal conductivity gapped; 0.46 K M. Yamashita et a., Nature Phys. 5 (2009) 44

  9. Strong Mott transition from antiferromagnet k-(ET)2Cu[N(CN)2]Cl Conductivity Resistance Kagawa et al., Nature 436 (2005) 534

  10. Spin liquid P T k-(ET)2Cu2(CN)3 Weak Mott transition from spin liquid Phase diagram T-dependence of r P-dependence of r Quantum Mott transition from spin liquid Senthil et al., PRB (2008) and pfreprint r-rm=rcf(dzv/T) zv =0.68 ~8h/e2

  11. Mott transition seen in spin degrees of freedom NMR k-(ET)2Cu2(CN)3 t’/t=0.80-1.0 k-(ET)2Cu[N(CN)2]Cl t’/t=0.44-0.75 less frustrated frustrated NMR spectra P P NMR spectra metal Mott trans Mott trans insulator

  12. Holon-doublon pair excitation costs more in AF than in SL J AF U-V(r) +8J U-V(r) +J Exotic charge excitations in spin liquid state fermionic; Ng & P.A. Lee, PRL 99 (2007) 156402. bosonic; Qi & Sachdev: PRB 77 (2008) 165112 SL

  13. TC ~T3 Not pseudo-gapped Pseudo-gapped nearby AFM Not pseudo-gapped nearby spin liq. Spin liquid Deuterated k-Br Miyagawa et al., PRL89 (2002) 017003 Pseudo-gapped 3-4 K 13C NMR 1/T1T k-Cu2(CN)3 12K Shimizu et al., PRB 81 (2010) 224508

  14. Pseudo-gap killed by field and pressure Field dependence Pressure dependence PG has connection with superconductivity as well as spin fluctuations

  15. Ground states of with half-filling Strong Mott from AF Pseudo-gapped High Tc t’/t <1 PG k-(ET)2Cu[N(CN)2]Cl AF SC toward square lattice Frustration (t’/t) Metal k-(ET)2Cu2(CN)3 gapless SL t’/t =1 Weak Mott from SLgapless Not pseudo-gapped low Tc (U/W)critical triangle Mottness (U/W)

  16. DMFT of Hubbard model at high temperatures T0∝δ zv Quantum Critical Transport Near the Mott Transition H. Terletskaet al., PRL 107 (2011) T - t/U phase diagram T T Zv=0.57 Mott Ins. Fermi Iiq. t/U δ=(t/U)-(t/U)c rvs T/T0calc. rvs T calc. Resistivities r(T,δ) are scaled with the one parameter, T/T0 Characteristic energy, T0∝δzv  quantum criticality

  17. 35K, 40K, 45K, 50K, 55K, 60K, 65K, 70K, 75K, 80K, 90K, 100K, 110K T0∝ δ zv P>Pc ~T 2 T/T0 d = T0=c dzv High-T scaling of resistivity for k-(ET)2Cu2(CN)3 k-(ET)2Cu2(CN)3 Nearly perfect ! P<Pc 35K, 40K, 45K, 50K, 55K, 60K, 65K, 70K, 75K, 80K, 90K, 100K, 110K P>Pc T/T0 r(T, d)=rc(T)f(T/T0) Zv=0.60±0.05 f(T/T0)= exp[(T/T0)1/zv] cf. zv =0.57 (DMFT)

  18. T0=c dzv High-T scaling of resistivity for k-(ET)2Cu[N(CN)2]Cl k-(ET)2Cu2(CN)3 P<Pc P<Pc P>Pc T/T0 r(T, d)=rc(T)f(T/T0) Zv=0.50±0.05 f(T/T0)= exp[(T/T0)1/zv] cf. zv =0.57 (DMFT)

  19. Quantum phase transition Mott Heavy electrons Kinetic energ vs Coulomb RKKY vs Kondo Doniach W ~5000 K U T (K) T (K) QCP Fermi liq. Mott ins. Fermi Liq. AF 20 K t Mott transition

  20. Hg3-dX8 (X=Br, Cl) X layer Compressibility of 1/RH Hall coefficient (ET)2+1+d Hole doping ET layer 10K k-(ET)4Hg2.89Br8 ---11% hole doped/ET2 d(1/RH)/dP (C/cm3/GPa) k-(ET)4Hg2.89Br8 10.01 1.02 Metal/SC P(GPa) Doped triangular lattice Lyubovslaya (1986) U/t t’/t <1/2-filled systems> k-(ET)2Cu2(CN)3 8.20 1.06 k-(ET)2Cu[N(CN)2]Cl 7.58 0.74 k-(ET)2Cu[N(CN)2]Br 7.20 0.68 k-(ET)2Cu(NCS)2 6.98 0.86 k-(ET)2I3 6.48 0.58 Mott insulator Mott insulator (U/t)critical Metal/SC

  21. Conductivity of k-(ET)4Hg2.89Br8 measured by contactless method under pressure R = r0 + aT Non-Fermi liq.  Fermi liq. by pressure Non-Fermi liq. r//- ro∝T r//- ro(mWcm) r//- ro∝T 2 Fermi liq. Temperature(K)

  22. Possible quantum phase transition high-Tc cuprate k-(ET)4Hg2.89Br8 U>W U<W Double occupancy forbidden Small FS ? (Doped Mott; t-J) Double occupancy allowed Large FS ? (Hubbard metal)

  23. Conclusion ½-filled systems with variable frustration 1) variation at low temperatures (gapless) SL vs AFM weak Mott strong Mott pseudo-gap no pseudo-gap higher Tc lower Tc 2) universality at high temperatures Mott criticality ---- quantum Even under doped systems A QPT or sharp crossover at (U/W)critical

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