Understanding the complete temperature-pressure phase diagrams of organic charge-transfer solids

Transcription

1 Understanding the complete temperature-pressure phase diagrams of organic charge-transfer solids Collaborators: R. Torsten Clay Department of Physics & Astronomy HPC 2 Center for Computational Sciences Mississippi State University Sumit Mazumdar, Hongtao Li (Univ. of Arizona) Rahul Hardikar (MSU, now Butler University) References: S. Mazumdar and R.T. Clay, Phys. Rev. B 77, (R) (2008) R.T. Clay, H. Li, S. Mazumdar, Support: US Department of Energy DE-FG02-06ER46315

2 Outline of talk 1 No superconductivity in triangular lattice 1 2-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 of correlated-electron superconductivity

3 Organic Superconductors SC adjacent to exotic insulating state: not just AFM; spin liquid, charge/bond order κ-(et) 2 X: triangular/frustrated lattice T 4kF Temperature T 2kF 4k 1010 F AFM SP 1100 AFM SC Pressure SbF 6 AsF 6 PF 6 Br PF 6 (TMTCF) 2 X κ-(et) 2 Cu 2 (CN) 3 Clay, Hardikar, Mazumdar, Y. Kurosaki et al, PRL 95, (2005) PRB (2007) EtMe 2 P[Pd(dmit) 2 ] 2 Y. Shimizu et al, PRL 99, (2007)

4 1. RVB Theories of SC in 1 2-filled triangular Hubbard model Proposed t t 1 -filled Hubbard model 2 1 unfrustrated system has AFM order 2 frustration destroys AFM order 3 claim Ψ RVB = superposition of singlet dimers superconductor Approaches: variational, mean field, etc. Kyung, Tremblay, PRL 97, (2006) Cluster DMFT, 4-site cluster Powell, McKenzie, PRL 98, (2007) RVB variational ansatz

5 1. Our results: NO superconductivity in this model arxiv: Necessary conditions for SC: U enhances pair-pair correlations must have at least short-range order Our work: 1 exact diagonalization 2 tried s, d x 2 y2, dxy, s + dxy U AFM PM NMI π, t 4 4 Phase diagram: no SC P dx 2 -y 2(r) P dx 2 -y 2(r) d-wave pair-pair correlation t = 0.5 Pair-pair correlations decrease monotonically from U = 0 Absence of even short range order 0.5 t'=0.5 U=1 U=3 0.4 U=5 0.3 U= r t'=0.5 PM AFM r= r=2.24 r= U

6 2. Configuration space pairing in the insulating state Effective 1 2-filled Hubbard model is oversimplified filled model: n = 1 carrier per site 2 real system: n = 1 2 carrier per molecule Specifically at the concentration of 1 2 carrier/molecule, a singlet paired state with nearest-neighbor bonding is either the ground state or very competitive to the ground state. (The existence of a singlet competitive with AFM is the key idea/assumption of Anderson s RVB theory)

7 2. Configuration space pairing in the insulating state: 1D Hamiltonian Hamiltonian for 1D systems H = H SSH + H Hol + H e e H SSH = t X [1 + α(x i+1 x i )](c i+1,σ c i,σ + h.c.) K SSH i,σ H Hol = g X ν i n i K Hol i X i ν 2 i X (x i+1 x i ) 2 i H e e = U X i n i, n i, + V X i n i+1 n i Inter- and Intra-molecular phonons, electron-electron interactions

8 2. Configuration space pairing in the insulating state: 1D Dominant ground state in 1D: Bond-Charge-Density Wave T 4kF Temperature T 2kF 4k 1010 F AFM SP 1100 AFM SC Pressure SbF 6 AsF 6 PF 6 Br PF 6 (TMTCF) 2 X phase diagram RT Clay, S Mazumdar, DK Campbell, PRB 67, (2003) RT Clay, RP Hardikar, S Mazumdar, PRB 76, (2007) In (TMTSF) 2 X, coexisting CDW-SDW: P. Pouget, S. Ravy, Synth. Met. 85, 1523 (1997) Theory: Mazumdar et al., PRL 82, 1522 (1999).

9 2. Configuration space pairing in the insulating state: 2D 1 BCDW in n = 1 2 ladders 2 θ-(et) 2 X : horizontal stripe CO 3 Valence-bond solid (VBS): [Pd(dmit) 2 ] The VBS is identical to our BCDW! zigzag ladder BCDW PRL 94, (2005) Clay et al, JPSJ 71, 1816 (2002).037 θ-(et) 2 RbZn(SCN) 4 X-ray analysis Watanabe et al., JPSJ 73, 116 (2004) [Pd(dmit) 2 ] Tamura, Nakao, Kato, JPSJ 75, (2006)

10 3. Mapping BCDW to negative-u model: Our recent work: Theory of BCDW SC transition: 1 with frustration pairs in BCDW aquire mobility 2 construct effective negative-u extended Hubbard model (a) (b) 1 -filled BCDW Effective model 4 Filled circle=double occupancy Key components of effective model 1 -U 2 V 3 lattice frustration: t, t tuned by pressure Increasing frustration pair mobility, SC without doping

11 3. Negative U effective Hamiltonian Hamiltonian for 1D systems H = H SSH + H Hol + H e e H SSH = t X [1 + α(x i+1 x i )](c i+1,σ c i,σ + h.c.) K SSH i,σ H Hol = g X ν i n i K Hol i X i ν 2 i X (x i+1 x i ) 2 i H e e = U X i n i, n i, + V X i n i+1 n i Effective -U Hamiltonian: -U, +V, frustration H eff = t X ij,σ(c i,σ c j,σ + h.c.) t X (c k,σ c l,σ + h.c.) [kl],σ U X n i, n i, + V X n i n j + V X n k n l i ij [kl]

12 3. Phase diagram of Effective -U model P(r max ) S(π,π) Charge order SC transition tuned by frustration t SC over broad region of parameters, unlike spin-fluctuation theories (a) (b) t (a) Charge structure factor, bond order (b) pair-pair correlations B t t (a) (b) SC CDW U CDW V t, U and t, V phase diagrams SC

13 4. Discussion of experiments 1 The negative-u model is s-wave This need not be true within the actual 1 -filled Hamiltonian 4 2 What about antiferromagnetism? (a) AFM gives way to proximate singlet BCDW state. Such an AFM singlet transition essential precondition even within RVB theories. Here: we have proved the existence of this low lying singlet. AND these singlets can be mobile. (b) Within CTS superconductors, also have CDW-SC, spin-liquid-sc, and valence-bond-solid-sc transitions. 3 The so-called checkerboard CO-to-SC transition is also a BCDW-to-SC transition with charge order CO state in β (meso-dmbedt-ttf) 2 PF 6 S. Kimura et al., JACS 128, 1456 (2006)

14 4. Discussion of experiments 4 Role of lattice - M. de Souza et al. (κ-et) PRL 99, (2007),.. intricate role of the lattice in the Mott transition for the present materials Our work: 1 at 1 filling, MI and Mott transition are different 4 2 CO and SC involve cooperation electron-electron and electron-phonon 5 Pseudogap: formation of configuration space pairs 6 High H c2 : due to extreme type II local pairs Micnas, Ranninger, Robaszkiewicz, RMP 62, 113 (1990)

15 5. Relationship to other materials: 1/4-filled vanadates n = 1 BCDW/SC transition as a generic model of correlated electron SC 2 (A) Pressure-induced superconductivity in β-na 0.33 V 2 O 5 beyond charge ordering Yamauchi et al., PRL 89, (2002) Yamauchi et al. phase diagram β-na 0.33 V 2 O 5: 1 -filled chains and ladders 4 Earlier conclusion: The localized Cooper pairs... that we have invoked in these vanadium bronzes, may indeed be a genuine precurson to true superconductivity. BK Chakraverty et al., PRB 17, 3781 (1978)

16 5. Relationship to other materials: 1/4-filled spinels (B) Superconducting LiTi 2 O 4, CuRh 2 S 4 Related CuIr 2 S 4 undergoes coupled Jahn-Teller-Peierls distortion with charge ordering Ir 3+ -Ir 3+ -Ir 4+ -Ir 4+ and singlet formation between Ir 4+ -Ir 4+. This is same as our 0011 BCDW. D.I. Khomskii and T. Mizokawa, PRL 94, (2005)

17 5. Relationship to other materials: Other candidates? (C) Key features of model: e-e interactions, 1 -filling, frustration 4 1 Na xcoo 2 : CO at x = 0.5, triangular lattice 2 LaOFeAs Frustration: Strong correlations and magnetic frustration in the high T c iron pnictides, Q. Si and E. Abrahms, PRL 101, (2008) (and others) Warren Pickett on Fe configuration: ()...the minority states are almost exactly half-filled, giving 7.5 3d electrons filled?

18 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 massive bipolarons 2 Our theory: pairing driven by both antiferromagnetism and e-p interactions (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 without virtual breaking of pairs. Large bandwidth. Square lattice: must break bipolaron to move Triangular lattice: crab motion without breaking Hague et al PRL 98, (2007)

19 Conclusions 1 No SC in U > 0 triangular lattice 1 2-filled Hubbard model 2 SC transition in organics is a BCDW/SC transition with pair mobility due to frustration 3 Model applies to all 1 4 -filled CTS SC: (TMTCF) 2X, κ-(et) 2 X, θ-(et) 2 X,... 4 Possible application to other materials References: 1 arxiv: PRB 77, (R) (2008)