Antiferromagnetism and Superconductivity in Layered Organic Conductors: Variational Cluster Approach

Abstract

The κ-(ET)2X layered conductors (where ET stands for BEDT-TTF) are studied within the dimer model as a function of the diagonal hopping t ′ and Hubbard repulsion U . Antiferromagnetism and d-wave superconductivity are investigated at zero temperature using variational cluster perturbation theory (V-CPT). For large U , Néel antiferromagnetism exists for t ′ < t ′ c2 , with t ′ c2 ∼ 0.9. For fixed t ′ , as U is decreased (or pressure increased), a d x 2 −y 2 superconducting phase appears. When U is decreased further, the a dxy order takes over. There is a critical value of t ′ c1 ∼ 0.8 of t ′ beyond which the AF and dSC phases are separated by Mott disordered phase.The proximity of antiferromagnetism (AF) and d-wave superconductivity (dSC) is a central and universal feature of high-temperature superconductors, and leads naturally to the hypothesis that the mechanisms behind the two phases are intimately related. This proximity is also observed in the layered organic conductor κ-(ET) 2 Cu-[N(CN) 2 ]Cl, an antiferromagnet that transits to a superconducting phase upon applying pressure[1] (here ET stands for BEDT-TTF). Other compounds of the same family, κ-(ET) 2 Cu(NCS) 2 and κ-(ET) 2 Cu[N(CN) 2 ]Br, are superconductors with a critical temperature near 10K at ambient pressure. However, another member of this family, κ-(ET) 2 Cu 2 (CN) 3 , displays no sign of AF order, but becomes superconducting upon applying pressure [2,3]. The character of the superconductivity in these compounds is still controversial. While many experiments indicate that the SC gap has nodes (presumably d-wave), others are interpreted as favoring a nodeless gap. The literature on the subject is rich, and we refer to a recent review article[4] for references.The interplay of AF and dSC orders, common to both high-T c and κ-ET materials, cannot be fortuitous and must be a robust feature that can be captured in a simple model of these strongly correlated systems. κ-ET compounds consist of orthogonally aligned ET dimers that form conducting layers sandwiched between insulating polymerized anion layers. The simplest theoretical description of these complex compounds is the so-called dimer Hubbard model [5,6] (Fig. 1A) in which a single bonding orbital is considered on each dimer, occupied by one electron on average, with the Hamiltonianwhere c rσ (c † rσ ) creates an electron (hole) at dimer site r on a square lattice with spin projection σ, and n rσ =c † rσ c rσ is the hole number operator. rr ′ ([rr ′ ]) indicates nearest-(next-nearest)-neighbor bonds. As the ratio t ′ /t grows from 0 towards 1, Néel AF is increasingly

Spin-liquid phase due to competing classical orders in the semiclassical theory of the Heisenberg model with ring exchange on an anisotropic triangular lattice

“…It is well known that the perfect nesting of the square lattice means that is insulating for arbitrarily small U/t. For t = t, it is found, numerically, that the Mott transition occurs at around U/t = 10-15, depending on the method used [3,[15][16][17][18][19][20][21]79]. The metal-insulator transition line in Fig.…”

“…This model contains three parameters: U the effective on-site Coulomb repulsion, t the nearest-neighbor hopping integral, and t the next-nearest-neighbor hopping integral along one diagonal only. The Hubbard model on the anisotropic triangular lattice has been studied via a number of approaches [15][16][17][18][19][20][21]. Some methods have suggested that a spin liquid is realized in the insulating phase.…”

Chirald-wave superconductivity in doped graphene

“…[199,195] and references therein. The interplay between antiferromagnetism, the Mott transition, and d-wave superconductivity has been studied by different theoretical methods [200,201,202]. Also chiral d-wave superconductivity has been proposed for lattice structures close to the isotropic triangular lattice, when the nearest and next nearest neighbor hopping amplitudes are of similar size [184].…”

Paired electron crystal: Order from frustration in the quarter-filled band

“…What is interesting though is that the proposed scenario can give a unified approach to SC in all organic CTS, irrespective of whether the insulating state proximate to SC is AFM 102 , CO 67,103 or VBS 82 . Recall that within existing mean field theories the AFM-to-SC transition is driven by spin fluctuations [13][14][15][16][17][18][19][20][21][22][23] , while the CO-to-SC transition is driven by charge fluctuations 65 . Even if we ignore that recent precise numerical calculations [25][26][27] have demonstrated the absence of SC within the proposed spin-fluctuation models in this context (thereby raising doubts also about mean-field theory of charge-fluctuation mediated superconductivity), different mechanisms of SC for structurally related materials with identical or nearidentical molecular components appear to be unrealistic.…”

“…An extension of the RVB theory of dopant-induced SC in ρ = 1 is the proposal that frustration-induced SC occurs in the anisotropic triangular lattice within the simple Hubbard model even for ρ exactly 1, where a narrow superconducting phase is straddled on both sides by broader PM and AFM insulator phases [13][14][15][16][17][18][19][20][21][22][23] . It has been claimed that this transition explains the SC in the CTS [13][14][15][16][17][18][19][20][21][22][23][24] . Recent numerical work by us and others, however, have determined that SC is absent within the ρ = 1 triangular lattice Hubbard model [25][26][27] and the earlier results are artifacts of mean-field approximations.…”