understanding the complete temperature-pressure phase ...clay, hardikar, mazumdar, y.kurosakietal,...

Understanding the complete temperature-pressure phasediagrams of organic charge-transfer solids

R. Torsten ClayDepartment of Physics & Astronomy

HPC2 Center for Computational SciencesMississippi State University

Collaborators:Sumit Mazumdar, Hongtao Li (Univ. of Arizona)

Rahul Hardikar (MSU, now Butler University)

References:S. Mazumdar and R.T. Clay, Phys. Rev. B 77, 180515(R) (2008)

R.T. Clay, H. Li, S. Mazumdar, http://arxiv.org/abs/0805.0590

Support: US Department of Energy DE-FG02-06ER46315

ECRYS 2008 R. T. Clay

Outline of talk

1 No superconductivity in triangular lattice 12 -filled Hubbard

2 Configuration space pairing in the insulating state.Bond-Charge Density Wave (BCDW) / Valence Bond Solid(VBS)

3 Effective model for VBS/SC transition

4 Discussion of experiments

5 Relationship to other materials and other models ofcorrelated-electron superconductivity


Organic Superconductors

SC adjacent to exotic insulating state:not just AFM; spin liquid, charge/bond or-der

T2kF

T4kF

AsF6 PF6SbF6 PF6

4k 1010F

AFM11010

AFM21100

SP1100

Tem

pera

ture

PressureBr

SC

(TMTCF)2X κ-(ET)2Cu2(CN)3

Clay, Hardikar, Mazumdar, Y. Kurosaki et al, PRL 95, 17701 (2005)PRB76 205118(2007)

κ-(ET)2X: triangular/frustrated lattice

EtMe2P[Pd(dmit)2]2Y. Shimizu et al, PRL 99, 256403 (2007)


1. RVB Theories of SC in 12 -filled triangular Hubbard model

Proposed t − t ′ 12 -filled Hubbard model

1 unfrustrated system has AFM order2 frustration destroys AFM order3 claim |ΨRVB〉 = superposition of singlet

dimers ≡ superconductor

Approaches: variational, mean field, etc.Kyung, Tremblay, PRL 97, 046402 (2006)

Cluster DMFT, 4-site cluster

Powell, McKenzie, PRL 98, 027005 (2007)RVB variational ansatz


1. Our results: NO superconductivity in this model arXiv:0805.0590

Necessary conditions for SC:

U enhances pair-pair correlations

must have at least short-rangeorder

Our work:1 exact diagonalization2 tried s, dx2−y2 , dxy , s + dxy

0 0.2 0.4 0.6 0.8 1 1.2t’

0

4

8

12

16

U

AFM

PM

π,0

NMI

4×4 Phase diagram: no SC

d-wave pair-pair correlation t ′ = 0.5Pair-pair correlations decreasemonotonically from U = 0

Absence of even short range order

0 0.5 1 1.5 2 2.5r

00.10.20.30.40.5

P d x2 -y2(r

)

U=1U=3U=5U=7

0 2 4 6U

0

0.05

0.1

P d x2 -y2(r

)

t'=0.5

t'=0.5

AFMr=2

r=2.24

r=2.83

PM


2. Configuration space pairing in the insulating state

Effective 12 -filled Hubbard model is oversimplified

1 12 -filled model: n = 1 carrier per site

2 real system: n = 12 carrier per molecule

Specifically at the concentration of 12 carrier/molecule, a singlet

paired state with nearest-neighbor “bonding” is either theground state or very competitive to the ground state.

(The existence of a singlet competitive with AFM is the key idea/assumptionof Anderson’s RVB theory)


2. Configuration space pairing in the insulating state: 1D Hamiltonian

Hamiltonian for 1D systems

H = HSSH + HHol + He−e

HSSH = −tXi,σ

[1 + α(xi+1 − xi)](c†i+1,σci,σ + h.c.) +12

KSSH

Xi

(xi+1 − xi)2

HHol = gX

i

νini +12

KHol

Xi

ν2i

He−e = UX

i

ni,↑ni,↓ + VX

i

ni+1ni

Inter- and Intra-molecular phonons, electron-electron interactions


2. Configuration space pairing in the insulating state: 1D

Dominant ground state in 1D: Bond-Charge-Density Wave

T2kF

T4kF

AsF6 PF6SbF6 PF6

4k 1010F

AFM11010

AFM21100

SP1100

Tem

pera

ture

PressureBr

SC

(TMTCF)2X phase diagram

RT Clay, S Mazumdar, DK Campbell, PRB 67, 115121 (2003)

RT Clay, RP Hardikar, S Mazumdar, PRB 76, 205118 (2007)

In (TMTSF)2X, coexisting CDW-SDW: P. Pouget, S. Ravy, Synth. Met. 85, 1523 (1997)Theory: Mazumdar et al., PRL 82, 1522 (1999).


2. Configuration space pairing in the insulating state: 2D

1 BCDW in n = 12 ladders

2 θ-(ET)2X : horizontal stripe CO3 Valence-bond solid (VBS): [Pd(dmit)2]

The VBS is identical to our BCDW!

.192

.383

.284

.180

.037

Clay et al, JPSJ 71, 1816 (2002) θ-(ET)2RbZn(SCN)4 X-ray analysisWatanabe et al., JPSJ 73, 116 (2004)

zigzag ladder BCDWPRL 94, 207206 (2005)

[Pd(dmit)2]Tamura, Nakao, Kato,JPSJ 75, 093701 (2006)


3. Mapping BCDW to negative-U model:

Our recent work: Theory of BCDW–SC transition:1 with frustration pairs in BCDW aquire mobility2 construct effective negative-U extended Hubbard model

(b)(a)

14 -filled BCDW Effective model

Filled circle=double occupancyKey components of effective model

1 -U2 V3 lattice frustration: t , t ′ tuned by pressure

Increasing frustration → pair mobility, SC without doping


3. Negative U effective Hamiltonian

Hamiltonian for 1D systems

H = HSSH + HHol + He−e

HSSH = −tXi,σ

[1 + α(xi+1 − xi)](c†i+1,σci,σ + h.c.) +12

KSSH

Xi

(xi+1 − xi)2

HHol = gX

i

νini +12

KHol

Xi

ν2i

He−e = UX

i

ni,↑ni,↓ + VX

i

ni+1ni

Effective -U Hamiltonian: -U, +V , frustration

Heff = −tX〈ij〉,σ

(c†i,σcj,σ + h.c.)

− t ′X[kl],σ

(c†k,σcl,σ + h.c.)

− |U|X

i

ni,↑ni,↓ + VX〈ij〉

ninj + V ′X[kl]

nk nl


3. Phase diagram of Effective -U model

Charge order–SC transition tuned by frustration t ′

SC over broad region of parameters, unlike spin-fluctuation theories

0

2

4

6

8

10

S(π

,π)

0

0.1

0.20

0.30

B0 0.2 0.4 0.6 0.8 1

t’

0

0.01

0.02

0.03

P(r m

ax)

(a)

(b)

1 2 3 4|U|

0

0.2

0.4

0.6

0.8

1

t’0.5 1 1.5 2

V

0

0.2

0.4

0.6

0.8

1

t’

CDW

SC

CDW

SC

(a)

(b)

(a) Charge structure factor, bond order t′, U and t ′, V phase diagrams(b) pair-pair correlations


4. Discussion of experiments

1 The negative-U model is s-waveThis need not be true within the actual 1

4 -filled Hamiltonian2 What about antiferromagnetism?

(a) AFM gives way to proximate singlet BCDW state. Such an AFM→ singlettransition essential precondition even within RVB theories. Here: we haveproved the existence of this low lying singlet. AND these singlets can bemobile.

(b) Within CTS superconductors, also have CDW-SC, spin-liquid-SC, andvalence-bond-solid-SC transitions.

3

The so-called checkerboard CO-to-SC tran-sition is also a BCDW-to-SC transition with..1100.. charge order

CO state in β−(meso-DMBEDT-TTF)2PF6

S. Kimura et al., JACS 128, 1456 (2006)


4. Discussion of experiments

4 Role of lattice - M. de Souza et al. (κ-ET) PRL 99, 037003 (2007), “..intricate role of the lattice in the Mott transition for the present materials”Our work:

1 at 14 filling, MI and Mott transition are different

2 CO and SC involve cooperation electron-electron and electron-phonon5 Pseudogap: formation of configuration space pairs6 High Hc2: due to extreme type II local pairs

Micnas, Ranninger, Robaszkiewicz, RMP 62, 113 (1990)


5. Relationship to other materials: 1/4-filled vanadates

n = 12 BCDW/SC transition as a generic model of correlated electron SC

(A) “Pressure-induced superconductivity inβ-Na0.33V2O5 beyond charge ordering”Yamauchi et al., PRL 89, 057002 (2002)

β-Na0.33V2O5: 14 -filled chains and ladders

Earlier conclusion: “The localized Cooperpairs ..... that we have invoked in thesevanadium bronzes, may indeed be a gen-uine precurson to true superconductivity.”BK Chakraverty et al., PRB 17, 3781 (1978)

Yamauchi et al. phase diagram


5. Relationship to other materials: 1/4-filled spinels

(B) Superconducting LiTi2O4, CuRh2S4

Related CuIr2S4 undergoes coupled Jahn-Teller-Peierls distortion with chargeordering Ir3+-Ir3+-Ir4+-Ir4+ and singlet formation between Ir4+-Ir4+. This issame as our 0011 BCDW.

D.I. Khomskii and T. Mizokawa, PRL 94, 156402 (2005)


5. Relationship to other materials: Other candidates?

(C) Key features of model: e-e interactions, 14 -filling, frustration

1 Nax CoO2: CO at x = 0.5, triangular lattice2 LaOFeAs

Frustration: ”Strong correlations and magnetic frustration in the high Tc ironpnictides”, Q. Si and E. Abrahms, PRL 101, 076401 (2008) (and others)Warren Pickett on Fe configuration: () “...the minority states are almostexactly half-filled, giving 7.5 3d electrons...” → 1

4 -filled?


5. Arguments against the model

“Bipolaron theory of SC does not work - bipolaron mass too large”

1 Applies to standard bipolaron theory, where electron-phonon (e-p)interactions overscreen electron-electron repulsion giving massivebipolarons

2 Our theory: pairing driven by both antiferromagnetism and e-pinteractions (cooperative). CDW → SC an additional/key requirement -not all systems will exhibit this behavior.

3 Triangular lattice plays a key role: “Crab” motion of bipolarons withoutvirtual breaking of pairs. Large bandwidth.

Square lattice:must break bipolaron to move

Triangular lattice:“crab” motion without breaking

Hague et al PRL 98, 037002 (2007)


Conclusions

1 No SC in U > 0 triangular lattice 12 -filled Hubbard model

2 SC transition in organics is a BCDW/SC transition with pairmobility due to frustration

3 Model applies to all 14 -filled CTS SC: (TMTCF)2X, κ-(ET)2X,

θ-(ET)2X, ...

4 Possible application to other materials

References:1 arXiv:0804.33552 PRB 77, 180515(R) (2008)


understanding the complete temperature-pressure phase ...clay, hardikar, mazumdar, y.kurosakietal,...

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