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Physical review. B, Condensed matter

Electron spectrum and superconductivity in the t−J model at moderate doping

Nikolay M. Plakida, V. S. Oudovenko

Published May 1, 1999• 111 citations
Publisher

Abstract

A microscopical theory of electron spectrum and superconductivity within the two-dimensional $t\ensuremath{-}J$ model in paramagnetic state is proposed. By employing the projection technique for the Green functions in terms of the Hubbard operators self-consistent Eliashberg equations are derived. A strong coupling of electrons with spin and charge fluctuations due to exchange and kinematical interactions is obtained. In the normal state, one-electron spectral functions reveal narrow quasiparticle peaks close to the Fermi surface (FS) with an additional broad incoherent band. The FS changes from holelike at low doping to electronlike for hole concentrations $\ensuremath{\delta}>0.3.$ In the superconducting state we observe d-wave pairing with the maximal ${T}_{c}\ensuremath{\simeq}0.04t$ at optimal doping $\ensuremath{\delta}\ensuremath{\simeq}0.3.$

DOI
10.1103/physrevb.59.11949

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Physical review. B, Condensed matter•Aug 15, 1997•4 citations
A microscopical theory of electron spectrum and superconductivity within the two-dimensional t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model in paramagnetic state is proposed. By employing the projection technique for the Green functions in terms of the Hubbard operators self-consistent Eliashberg equations are derived. A strong coupling of electrons with spin and charge fluctuations due to exchange and kinematical interactions is obtained. In the normal state, one-electron spectral functions reveal narrow quasiparticle peaks close to the Fermi surface (FS) with an additional broad incoherent band. The FS changes from holelike at low doping to electronlike for hole concentrations \ensuremathδ>0.3.\ensuremath{\delta}>0.3.\ensuremathδ>0.3. In the superconducting state we observe d-wave pairing with the maximal Tc\ensuremath≃0.04t{T}_{c}\ensuremath{\simeq}0.04tTc​\ensuremath≃0.04t at optimal doping \ensuremathδ\ensuremath≃0.3.\ensuremath{\delta}\ensuremath{\simeq}0.3.\ensuremathδ\ensuremath≃0.3.
A microscopic theory of electronic spectrum and superconducting pairing within the Hubbard model is formulated.The Dyson equation for the normal and anomalous Green functions in terms of the Hubbard operators is derived by applying the Mori-type projection technique.The self-energy is evaluated in the noncrossing approximation for electron scattering on spin and charge fluctuations induced by kinematic interaction for Hubbard operators.Numerical results for electron dispersion in the strong correlation limit are presented.Superconducting pairing mediated by antiferromagnetic exchange and spin fluctuations is discussed.
The theory of superconducting pairing due to the exchange and kinematical interactions in the t - J model in a paramagnetic state is developed. \nThe Dyson equation for the matrix Green functions in terms of the Hubbard \noperators is obtained in the noncrossing approximation. The linearized self-сonsistent system of Eliashberg equations is proposed to study the temperature and doping dependence of the quasi-particle hole spectrum in \nthe normal state and to calculate the temperature of the superconducting \nphase transition and the symmetry of the gap function.
A microscopic theory of the electronic spectrum and of superconductivity within the t-J model on the honeycomb lattice is developed. We derive the equations for the normal and anomalous Green functions in terms of the Hubbard operators by applying the projection technique. Superconducting pairing of d + id′-type mediated by the antiferromagnetic exchange is found. The superconducting Tc as a function of hole doping exhibits a two-peak structure related to the van Hove singularities of the density of states for the two-band t-J model. At half-filling and for large enough values of the exchange coupling, gapless superconductivity may occur. For small doping the coexistence of antiferromagnetic order and superconductivity is suggested. It is shown that the s-wave pairing is prohibited, since it violates the constraint of no-double-occupancy.
A microscopic theory of the electronic spectrum and of superconductivity within the t-J model on the honeycomb lattice is developed. We derive the equations for the normal and anomalous Green functions in terms of the Hubbard operators by applying the projection technique. Superconducting pairing of d + id-type mediated by the antiferromagnetic exchange is found. The superconducting T-c as a function of hole doping exhibits a two-peak structure related to the van Hove singularities of the density of states for the two-band t-J model. At half-filling and for large enough values of the exchange coupling, gapless superconductivity may occur. For small doping the coexistence of antiferromagnetic order and superconductivity is suggested. It is shown that the s-wave pairing is prohibited, since it violates the constraint of no-double-occupancy.
Quasiparticle bands of the two-dimensional Hubbard model are calculated using the Roth two-pole approximation to the one-particle Green's function. Excellent agreement is obtained with recent Monte Carlo calculations, including an anomalous volume of the Fermi surface near half-filling, which can possibly be explained in terms of a breakdown of Fermi liquid theory. The calculated bands are very flat around the (\ensuremath{\pi},0) points of the Brillouin zone in agreement with photoemission measurements of cuprate superconductors. With doping there is a shift in spectral weight from the upper band to the lower band. The Roth method is extended to deal with superconductivity within a four-pole approximation allowing electron-hole mixing. It is shown that triplet p-wave pairing never occurs. A self-consistent solution with singlet ${\mathit{d}}_{{\mathit{x}}^{2}\mathrm{\ensuremath{-}}{\mathit{y}}^{2}}$-wave pairing is found and optimal doping occurs when the van Hove singularity, corresponding to the flat band part, lies at the Fermi level. Nearest-neighbor antiferromagnetic correlations play an important role in flattening the bands near the Fermi level and in favoring superconductivity. However, the mechanism for superconductivity is a local one, in contrast to spin-fluctuation exchange models. For reasonable values of the hopping parameter the transition temperature Tc{\mathit{T}}_{\mathit{c}}Tc​ is in the range 10--100 K. The optimum doping ${\mathrm{\ensuremath{\delta}}}_{\mathit{c}}$ lies between 0.14 and 0.25, depending on the ratio U/t. The gap equation has a BCS-like form and 2${\mathrm{\ensuremath{\Delta}}}_{\mathrm{max}}$/kTc{\mathit{kT}}_{\mathit{c}}kTc​\ensuremath{\simeq}4.
Electronic states in the two-dimensional Hubbard model are studied in the doped paramagnetic states by use of the auxiliary boson approach. Four auxiliary bosons are introduced by means of the Hubbard-Stratonovich transformation within the functional integral treatment. These bosons correspond to one charge and three spin fluctuations. An effective model is formulated. Going beyond the boson fluctuations around the saddle point, the single-electron Green's function including one-loop self-energy effects of fermion-boson interaction is derived. The behavior of the fermion self-energy, spectral functions, and density of states are investigated for several values of the Coulomb interaction UUU within the limit imposed by the Stoner criterion and also for small and moderate doping concentrations $\ensuremath{\delta}$. For small doping $(\ensuremath{\delta}=0.2)$, as UUU approaches a value determined by the Stoner criterion, the spin-boson spectrum has a striking low-energy enhancement around $\mathbf{q}\ensuremath{\sim}2{\mathbf{k}}_{F}.$ This enhancement of the spin fluctuation causes a non-Fermi-liquid-like low-energy $\ensuremath{\omega}$ linear dependence in the imaginary part of the self-energy. Due to the self-energy effects, band splittings and a band narrowing are produced in the spectral functions. As a consequence of this, the density of states has pseudogap structures around the quasiparticle band with a narrow bandwidth on the Fermi energy. These features seem to be precursors of the metal-insulator (Mott-Hubbard) transition and they might be related to the spin-gap phenomena observed in high-Tc{T}_{c}Tc​ materials. Our results for the density of states, the spectral function, and the band dispersions show qualitative agreement with the data of finite-size cluster simulations.