The two-dimensional t-t'-U model as a minimal model for cuprate materials

Abstract

The addition to the Hubbard Hamiltonian of a t' diagonal hopping term, which is considered to be material dependent for high-T c cuprate superconductors, is generally suggested to obtain a model capable to describe the physics of high-T c cuprate materials. In this line of thinking, the two-dimensional t-t'-U model has been studied by means of the Composite Operator Method, which allows to determine the dynamics in a fully self-consistent way by use of symmetry requirements, as the ones coming from the Pauli principle. At first, some local quantities have been calculated to be compared with quantum Monte Carlo data. Then, the structure of the energy bands, the shape of the Fermi surface and the position of the van Hove singularity have been computed as functions of the model parameters and studied by the light of the available experimental data. The results of our study show that there exists two sets of parameters that allows the model to describe the relevant features of the 1-layer compounds Nd2-xCexCuO4 and La2-xSrxCuO4. On the other hand, for the 2-layer compound YBa2Cu3O 7 - δ is not possible to find a reasonable set of parameters which could reproduce the position of the van Hove singularity as predicted by ARPES experiments. Hence, it results questionable the existence of an unique model that could properly describe the variety of cuprate superconductors, as the two-dimensional t-t'-U model was thought to be

Composite Operator Method Analysis of the Underdoped Cuprates Puzzle

“…The formalism is based on two main ideas: (i) use of propagators of relevant composite operators as building blocks for any subsequent approximate calculations and (ii) use of algebra constraints to fix the representation of the relevant propagators in order to properly preserve algebraic and symmetry properties; these constraints will also determine the unknown parameters appearing in the formulation due to the noncanonical algebra satisfied by the composite operators. In the last fifteen years, COM has been applied to several models and materials: Hubbard [36][37][38][39][40][41][42][43][44][45][46][47], - [48][49][50][51], - [52], -- [53][54][55], extended Hubbard ( --) [56,57], Kondo [58], Anderson [59,60], two-orbital Hubbard [61][62][63], Ising [64,65], 1 − 1.2. Underdoped Cuprates.…”

Equation of motion method for composite field operators

“…The corresponding calculations are reported in Ref. 33 where is shown that these two channels do not carry any new unknown ZFC. The self-consistence scheme closes; by considering the four channels (i.e., fermionic, spin-charge, pair and double occupancy-charge) we can set up a system of coupled selfconsistent equations for all the parameters.…”

“…where the summation range only over two sites at distance a from each other and the rest of notation is standard 33 . The hopping matrix t ij is defined by…”

Exact solution of the 1D Hubbard model with NN and NNN interactions in the narrow-band limit

“…In 2D, various extended HMs (EHMs) have been proposed as key models to explain the mechanisms for unconventional superconductivity in cuprates 16,[19][20][21] . The variety of phenomena predicted in the EHMs in 2D ranges from d-wave superconductivity and spin-/chargedensity waves to antiferromagnetism, ferromagnetism, and Mott metal-insulator transition at commensurate fillings 16,[18][19][20][21]27,[33][34][35] . However, even in 1D, the EHMs present an unexpected richness of properties.…”