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 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 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

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

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

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 Similar QC behavior at high T 0.33 >10 1 R/Rc Dissimilar at low T

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unpublished Spin liquid

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., PRL 104 (2010) 016403 Thermal conductivity M. Yamashita et al., Nature Phys. 5 (2009) 44 NMR Relaxation rate Shimizu et al., PRB 70 (2006) 060510

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

 Degenerate spinons (Motrunich, P.A. Lee, Senthil) Spin liquid in k-(ET)2Cu2(CN)3; Gapless or marginally gapped Specific heat  gapless (g = 13-14 mJ/K2mol) Nuclear Shottky  Degenerate spinons (Motrunich, P.A. Lee, Senthil) 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

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

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

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

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

Not pseudo-gapped nearby spin liq. Pseudo-gapped nearby AFM Not pseudo-gapped nearby spin liq. Spin liquid ~T3 TC Not pseudo-gapped 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

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

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)

DMFT of Hubbard model at high temperatures Quantum Critical Transport Near the Mott Transition H. Terletska et al., PRL 107 (2011) T - t/U phase diagram T T0∝ δ zv T Zv=0.57 Mott Ins. Fermi Iiq. t/U δ=(t/U)-(t/U)c r vs T calc. r vs T/T0　calc. 相図の食い込みいれてもいいかもしれない Resistivities r(T,δ) are scaled with the one parameter, T/T0 Characteristic energy, T0∝δzv  quantum criticality 16

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

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 T0=c d zv f(T/T0)= exp[(T/T0)1/zv] cf. zv =0.57 (DMFT)

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

Doped triangular lattice k-(ET)4Hg2.89Br8 ---11% hole doped/ET2 Hg3-dX8 (X=Br, Cl) (ET)2+1+d Hole doping ET layer X layer k-(ET)4Hg2.89Br8 10.01 1.02 Metal/SC Doped triangular lattice Lyubovslaya (1986) Hall coefficient P (GPa) d(1/RH)/dP (C/cm3/GPa) 10K Compressibility of 1/RH 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

Conductivity of k-(ET)4Hg2 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)

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

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