Rudolf Torsten Clay

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

We present a study of the effects of simultaneous charge- and spin-frustration on the two-dimensional strongly correlated quarter-filled band on an anisotropic triangular lattice. The broken-symmetry states that dominate in the weakly frustrated region near the rectangular lattice limit are the well known antiferromagnetic state with in-phase lattice dimerization along one direction, and the Wigner crystal state with the checkerboard charge order. For moderate to strong frustration, however, the dominant phase is a novel spin-singlet paired-electron crystal (PEC), consisting of pairs of charge-rich sites separated by pairs of charge-poor sites. The PEC, with coexisting charge-order and spin-gap in two dimension, is the quarter-filled band equivalent of the valence bond solid (VBS) that can appear in the frustrated half-filled band within antiferromagnetic spin Hamiltonians. We discuss the phase diagram as a function of on-site and intersite Coulomb interactions as well as electron-phonon coupling strength. We speculate that the spin-bonded pairs of the PEC can become mobile for even stronger frustration, giving rise to a paired-electron liquid. We discuss the implications of the PEC concept for understanding several classes of quarter-filled band materials that display unconventional superconductivity, focusing in particular on organic charge transfer solids. Our work points out the need to go beyond quantum spin liquid (QSL) concepts for highly frustrated organic charge-transfer solids such as kappa-(BEDT-TTF)_2Cu_2(CN)_3 and EtMe_3Sb[Pd(dmit)_2]_2, which we believe show frustration-induced charge disproportionation at low temperatures. We discuss possible application to layered cobaltates and 1/4-filled band spinels.

Absence of superconductivity in the half-filled band hubbard model on the anisotropic triangular lattice

We report exact calculations of magnetic and superconducting pair-pair correlations for the half-filled band Hubbard model on an anisotropic triangular lattice. Our results for the magnetic phases are similar to those obtained with other techniques. The superconducting pair-pair correlations at distances beyond nearest neighbor decrease monotonically with increasing Hubbard interaction U for all anisotropy, indicating the absence of frustration-driven superconductivity within the model.

The paired-electron crystal in the two-dimensional frustrated quarter-filled band.

The competition between antiferromagnetic and spin-singlet ground states within quantum spin models and the ½-filled band Hubbard model has received intense scrutiny. Here we demonstrate a frustration-induced transition from Néel antiferromagnetism to a spin-singlet state in the interacting ¼-filled band on an anisotropic triangular lattice. While the antiferromagnetic state has equal charge densities, 0.5, on all sites, the spin-singlet state is a paired-electron crystal, with pairs of charge-rich sites separated by pairs of charge-poor sites. The paired-electron crystal provides a natural description of the spin-gapped state proximate to superconductivity in many organic charge transfer solids. Pressure-induced superconductivity in these correlated-electron systems is likely a result of a transition from the ¼-filled band valence bond solid to a valence bond liquid.

Phase diagram of the one-dimensional Hubbard-Holstein model at half and quarter filling

The Hubbard-Holstein model is one of the simplest to incorporate both electron-electron and electron-phonon interactions. In one dimension at half filling the Holstein electron-phonon coupling promotes onsite pairs of electrons and a Peierls charge density wave while the Hubbard onsite Coulomb repulsion U promotes antiferromagnetic correlations and a Mott insulating state. Recent numerical studies have found a possible third intermediate phase between Peierls and Mott states. From direct calculations of charge and spin susceptibilities, we show that (i) As the electron-phonon coupling is increased, first a spin gap opens, followed by the Peierls transition. Between these two transitions the metallic intermediate phase has a spin gap, no charge gap, and properties similar to the negative-U Hubbard model. (ii) The transitions between Mott/intermediate and intermediate/Peierls states are of the Kosterlitz-Thouless form. (iii) For larger U the two transitions merge at a tritical point into a single first order Mott/Peierls transition. In addition we show that an intermediate phase also occurs in the quarter-filled model.

Quantum critical transition from charge-ordered to superconducting state in the negative- U extended Hubbard model on a triangular lattice

Spatial broken symmetries such as antiferromagnetism (AFM) and charge ordering (CO) are proximate to superconductivity (SC) in a number of exotic systems, including the cuprates, NaxCoO2 · yH2O , βNa0.33V2O5 3 and organic charge-transfer solids (CTS) such as (TMTCF)2X (here C=S or Se, and X are closedshell anions), (BEDT-TTF)2X (hereafter ET2X) 4 and EtMe3Z[Pd(dmit)2]2, Z = P, As . Unlike in the cuprates, SC in the CTS is reached not by doping, but on application of hydrostatic or uniaxial pressure. CTS crystals often consist of anisotropic triangular lattices of dimers of the active cationic or anionic molecules. The average number of charge carriers n per molecule is 1 2 , indicating that n per dimer unit cell is 1. Since the n = 1 triangular lattice provides the classic template for the resonating valence bond (RVB) electronic structure within the nearest-neighbor (n.n.) Heisenberg Hamiltonian, the idea that spin frustration drives an AFM-to-SC or spin liquid-to-SC transition in the CTS has acquired popularity. Within this picture, pressure makes the effective anisotropic n = 1 triangular lattice more isotropic, and SC occurs over a narrow range of anisotropy between the more robust AFM and the paramagnetic metal (PM). Numerical quantum Monte Carlo and exact diagonalization calculations, however, have failed to find superconducting correlations in the the triangular lattice repulsive n = 1 Hubbard model, casting doubt on the mean-field techniques that find SC within the Hamiltonian. Experimentally, the situation is complex. (i) SC in certain CTS is proximate to CO instead of AFM. This has led to yet other mean-field models with additional Coulomb parameter of charge-fluctuation mediated SC. (ii) The insulating phase proximate to SC in EtMe3[Pd(dmit)2]2 is not an AFM but a valence bond solid (VBS), with charge disproportionation between molecules. (iii) AFM is missing in the insulating state of κ−ET2Cu2(CN)3 with a nearly isotropic triangular lattice. There occur inhomogeneous charge localization and sharp decrease in spin susceptibility below 10 K, which may also be signatures of a static or fluctuating VBS-like state. Whether or not frustration can drive transition to SC from an ordered state therefore remains an open and intriguing question. In the present paper we demonstrate a robust frustration-driven SC within the n = 1 negative-U extended Hubbard model (EHM) with n.n. Coulomb repulsion V . Although the literature on the negative-U Hubbard Hamiltonian is vast, the model has been investigated primarily for bipartite lattices. With repulsive V , there is strong tendency to CO in bipartite lattices and SC is absent. Frustrated lattices have been investigated within the Hamiltonian for V = 0 only. Now SC dominates and CO is absent. Here we begin with the square lattice with n.n. V and electron hopping, when the ground state is a checkerboard CO with alternate double occupancies and vacancies in the square lattice. As the Coulomb interaction and electron hopping along one diagonal of the square lattice increase from zero, charge frustration in the emergent triangular lattice leads to first-order transition to a superconducting state. While our primary goal is to demonstrate the frustrationdriven CO-to-SC transition, we also point out that our work provides insight for understanding unconventional SC in n = 1 2 correlated electron systems including the CTS. We consider the two-dimensional (2D) Hamiltonian,

Temperature-driven transition from the Wigner crystal to the bond-charge-density wave in the quasi-one-dimensional quarter-filled band

It is known that within the interacting electron model Hamiltonian for the one-dimensional

Absence of long-range superconducting correlations in the frustrated half-filled-band Hubbard model

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The chemical physics of unconventional superconductivity

-filled band, the singlet ground state is a Wigner crystal only if the nearest-neighbor electron-electron repulsion is larger than a critical value. We show that this critical nearest-neighbor Coulomb interaction is different for each spin subspace, with the critical value decreasing with increasing spin. As a consequence, with the lowering of temperature, there can occur a transition from a Wigner crystal charge-ordered state to a spin-Peierls state that is a bond-charge-density wave with charge occupancies different from the Wigner crystal. This transition is possible because spin excitations from the spin-Peierls state in the

Absence of superconductivity and valence bond order in the Hubbard–Heisenberg model for organic charge-transfer solids

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Cooperative orbital ordering and Peierls instability in the checkerboard lattice with doubly degenerate orbitals

-filled band are necessarily accompanied by changes in site charge densities. We apply our theory to the