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
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

2. 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) ?

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

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

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) t’/t ~
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unpublished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., PRL 104 (2010)
Thermal conductivity
M. Yamashita et al.,
Nature Phys. 5 (2009) 44
NMR Relaxation rate
Shimizu et al.,
PRB 70 (2006)

7. 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

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

11. Mott transition seen in spin degrees of freedom
NMR
k-(ET)2Cu[N(CN)2]Cl
t’/t=
k-(ET)2Cu2(CN)3
t’/t=
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 SLJ AF
U-V(r) +8J
Exotic charge excitations in spin liquid state
fermionic; Ng & P.A. Lee, PRL 99 (2007)
bosonic; Qi & Sachdev: PRB 77 (2008)
U-V(r) +J SL

13. 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

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
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

17. 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)

18. 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)

19. 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

20. Doped triangular lattice
k-(ET)4Hg2.89Br % hole doped/ET2
Hg3-dX8 (X=Br, Cl)
(ET)2+1+d
Hole doping
ET layer
X layer
k-(ET)4Hg2.89Br 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)
k-(ET)2Cu[N(CN)2]Cl
k-(ET)2Cu[N(CN)2]Br
k-(ET)2Cu(NCS)
k-(ET)2I
Mott insulator
Mott insulator
(U/t)critical
Metal/SC

21. Conductivity of k-(ET)4Hg2
Conductivity of k-(ET)4Hg2.89Br 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
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

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