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Bulletin of the Russian Academy of Sciences Physics

Effect of interstitial Coulomb interaction on the occurrence of a gapless superconducting phase of Hubbard fermions on a triangular lattice

Valerii Vladimirovich Val'kov, T. A. Val’kova, Vitaly A. Mitskan

Published Jun 1, 2016• 0 citations
Publisher

Abstract

The concentration dependence of the position of nodal points of a superconducting order parameter is investigated using the t – J – V model for a triangular lattice with regard to the exchange and Coulomb interactions in two coordination spheres. The conditions for a topological quantum transition are established.
DOI
10.3103/s1062873816060393

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In the framework of the t–J 1–J 2–V model, the integral equation determining the order parameter Δ(p) of the superconducting phase is derived for an ensemble of strongly correlated fermions on a triangular lattice using the diagram technique for the Hubbard operators. Taking into account the interaction between the Hubbard fermions within two coordination spheres, we demonstrate that the exact analytical solution Δ2(p) of this equation for the superconducting phase with the ( (dx2−y2+idxy)\left( {{d_{{x^2} - {y^2}}} + i{d_{xy}}} \right)(dx2−y2​+idxy​) ) symmetry can be expressed as a superposition of two chiral basis functions. This gives rise to a new set of nodal points for the complex parameter Δ2(p). Moreover, at some critical value x c of the charge carrier density, we obtain a gapless phase with six Dirac points. The passing of x through x = x c is accompanied by the topological quantum transition corresponding to the change in the topological parameter Q.
The model of localized fermions on the triangular lattice is analyzed in means of the Monte Carlo simulations in the grand canonical ensemble. The Hamiltonian of the system has a form of the extended Hubbard model (at the atomic limit) with nearest-neighbor Ising-like magnetic J interactions and onsite Coulomb U interactions. The model is investigated for both signs of J, arbitrary U interaction, and arbitrary chemical potential μ (or, equivalently, arbitrary particle concentration n). Based on the specific heat capacity and sublattice magnetization analyses, the phase diagrams of the model are determined. For ferromagnetic case (J<0), the transition from the ordered phase (which is a standard ferromagnet and can be stable up to k_{B}T/|J|≈0.61) is found to be second order (for sufficiently large temperatures k_{B}T/|J|≳0.2) or first order (for -1<U/|J|<-0.65 at the half-filling, i.e., n=1). In the case of J>0, the ordered phase occurs in a range of -1/2<U/|J|<0 (for n=1), while for larger U the state with short-range order is also found (also for n≠1). The ordered phase is characterized by an antiferromagnetic arrangement of magnetic moments in two sublattices forming the hexagonal lattice. The transition from this ordered phase, which is found also for μ≠0 (n≠1) and U/|J|>-1/2 is always second order for any model parameters. The ordered phase for J>0 can be stable up to k_{B}T/|J|≈0.06.
Abstract The properties of the bound states on a lattice is an interesting problem related to the properties of superconductivity and Bose–Einstein condensation in a given model. By means of the exact solution of the Schrödinger equation the properties of the bound pairs on a frustrated, triangular lattice are examined within extended Hubbard model. Dispersion curves and mobilities are calculated for both positive and negative sign of the hopping integral. The possibility of increasing the mobility with increasing intersite Coulomb interaction is found. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
We investigate a semimetal-superconductor phase transition of two-dimensional Dirac electrons at zero temperature by large-scale and essentially unbiased quantum Monte Carlo simulations for the half-filled attractive Hubbard model on the triangular lattice, in the presence of alternating magnetic $\ensuremath{\pi}$ flux, that is introduced to construct two Dirac points in the one-particle bands at the Fermi level. This phase transition is expected to describe quantum criticality of the chiral XY class in the framework of the Gross-Neveu model, where, in the ordered phase, the U(1)U(1)U(1) symmetry is spontaneously broken and a mass gap opens in the excitation spectrum. We compute the order parameter of the sss-wave superconductivity and estimate the quasiparticle weight from the long-distance behavior of the single-particle Green's function. These calculations allow us to obtain the critical exponents of this transition in a reliable and accurate way. Our estimate for the critical exponents is in good agreement with those obtained for a transition to a Kekul\'e valence bond solid, where an emergent U(1)U(1)U(1) symmetry is proposed [Z.-X. Li et al., Nat. Commun. 8, 314 (2017)].
The extended Hubbard model in the atomic limit, which is equivalent to lattice S=1/2 fermionic gas, is considered on the triangular lattice. The model includes onsite Hubbard U interaction and both nearest-neighbor (W1) and next-nearest-neighbor (W2) density–density intersite interactions. The variational approach treating the U term exactly and the Wl terms in the mean-field approximation is used to investigate thermodynamics of the model and to find its finite temperature (T>0) phase diagrams (as a function of particle concentration) for W1>0 and W2<0. Two different types of charge-order (i.e., DCO and TCO phases) within 3×3 unit cells as well as the nonordered (NO) phase occur on the diagram. Moreover, several kinds of phase-separated (PS) states (NO/DCO, DCO/DCO, DCO/TCO, and TCO/TCO) are found to be stable for fixed concentration. Attractive W2<0 stabilizes PS states at T=0 and it extends the regions of their occurrence at T>0. The evolution of the diagrams with increasing of |W2|/W1 is investigated. It is found that some of the PS states are stable only at T>0. Two different critical values of |W2|/W1 are determined for the PS states, in which two ordered phases of the same type (i.e., two domains of the DCO or TCO phase) coexist.
The triangular-lattice Fermi-Hubbard model has been extensively investigated in the literature due to its connection to chiral spin states and unconventional superconductivity. Previous simulations of the ground state of the doped system rely on quasi-one-dimensional lattices where true long-range order is forbidden. Here we simulate two-dimensional and quasi-one-dimensional triangular lattices using state-of-the-art Auxiliary-Field Quantum Monte Carlo. Upon doping a non-magnetic chiral spin state, we observe evidence of chiral superconductivity supported by long-range order in Cooper-pair correlation and a finite value of the chiral order parameter. With this aim, we first locate the transition from the metallic to the non-magnetic insulating phase and the onset of magnetic order. Our results pave the way towards a better understanding of strongly correlated lattice systems with magnetic frustration.