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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

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

mott physics in 2d organics

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)

k et 2 x quasi triangular lattice systems
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)

mott phase diagrams of quasi triangular lattices

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

separation of charge localization and spin ordering on triangular lattice

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unpublished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 2 cu 2 cn 3
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

13 c nmr under a parallel field

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

degenerate spinons motrunich p a lee senthil

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

strong mott transition from antiferromagnet
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

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

slide11

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

holon doublon pair excitation costs more in af than in sl
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

not pseudo gapped nearby spin liq

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

pseudo gap killed by field and pressure
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
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)

slide16

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

high t scaling of resistivity for k et 2 cu 2 cn 3

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)

high t scaling of resistivity for k et 2 cu n cn 2 cl

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)

slide19

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

doped triangular lattice

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

conductivity of k et 4 hg 2 89 br 8 measured by contactless method under pressure
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
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)

conclusion
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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