Qualitative understanding of the sign oft′asymmetry in the extendedt−Jmodel and relevance for pairing properties

Abstract

Numerical calculations illustrate the effect of the sign of the next nearest-neighbor hopping term t ′ on the 2-hole properties of the t-t ′ -J model. Working mainly on 2-leg ladders, in the -1.0 ≤t ′ /t ≤ 1.0 regime, it is shown that introducing t ′ in the t-J model is equivalent to effectively renormalizing J, namely t ′ negative (positive) is equivalent to an effective t-J model with smaller (bigger) J. This effect is present even at the level of a 2×2 plaquette toy model, and was observed also in calculations on small square clusters. Analyzing the transition probabilities of a hole-pair in the plaquette toy model, it is argued that the coherent propagation of such hole-pair is enhanced by a constructive interference between both t and t ′ for t ′ >0. This interference is destructive for t ′ <0.PACS numbers: 74.20.Mn, 75.25.Dw One of the most important unsolved problems in theoretical physics is the clarification of the nature of high temperature superconductors. A popular approach in this context is the use of the t-J model, with holes moving in an antiferromagnetic (AF) spin background. In recent years, mainly due to an increase in the sensitivity and resolution of angle resolved photoemission spectroscopy (ARPES), it has been shown that extra hole hoppings beyond nearest-neighbor (NN) are important in the t-J model, giving origin to the "extended" t-J model. For example, ARPES measurements in Sr 2 CuO 2 Cl 2 [1], and their subsequent interpretation [2], have shown the importance of those extra hoppings to reproduce the experimental results. Subsequent efforts have concentrated on the effect of the extra hoppings on various properties of planar and ladder systems, such as stripe stability [3], competition between pairing and stripes [4], spin-charge separation in 2-d [5], stripe formation mechanism [6], spin gap evolution [7], and current-current correlations [8]. Most of these papers have compared and contrasted the dependence of different properties of the extended t-J model with the sign of the next NN (NNN) hopping t ′ . Currently it is well established that a positive t ′ enhances hole pairing and AF correlations, while the opposite occurs for t ′ negative [4,9]. Nevertheless, to the best of our knowledge, these previous publications have not provided an intuitive mechanism that can explain why this happens, namely, for what reason there is an asymmetry between positive and negative t ′ . This is particularly puzzling considering the limit t=0, since in the t ′ -J model the sign of t ′ is irrelevant [10].It is the purpose of this paper to provide a qualitative explanation to this phenomenon, i. e., the sign of t ′ asymmetry. Our main result is that a quantum interference between NN and NNN hoppings identified in the hole-pair propagation was found to be constructive (destructive) for t ′ positive (negative); this accounts for the observed dependence of the hole-pair properties with the sign of t ′ . The t-t ′ -J model used here is defined aswhere t im is t for NN, t ′ for NNN, and zero otherwise. T...

Antiferromagnetism and superconductivity of the two-dimensional extended t-J model

“…Results of band-structure calculations [24,25] and experimental analysis [26] show that T c is enhanced by the next-nearest neighbor hopping t t ¢/ , and the highest T c,max for different monolayer hole doped cuprates strongly correlates with t t ¢/ . However, this contradicts with previous results [27,28] of exact calculations that for the hole doped systems, introducing t¢ into the t J -model will suppress pairing.…”

Fidelity and superconductivity in two-dimensionalt−Jmodels

“…II, several authors have discussed the importance of introducing long-range hopping in microscopic Hubbard and t-J-like models in order to capture many of the features observed in high-temperature superconductors. 35,36,[38][39][40][41] Here, we briefly discuss how a finite next-nearest-neighbor hopping affects the results discussed above for the plain t-J model.…”

“…It has been discussed is several works that longer-range hoppings are needed to reproduce the Fermi surface and electron-hole asymmetries for different cuprate superconductors. [35][36][37][38][39][40][41] Here we will briefly discuss the effect of the next-nearest-neighbor hopping…”

d -wave bond-order charge excitations in electron-doped cuprates

“…Various approximations to the t-J [22,23,21] and the strong coupling Hubbard [24] model show that the models have a strong tendency toward phase separation, especially for parameters appropriate for electron-doped cuprates. The phase separation, however, can be an artifact caused by neglecting the long-range Coulomb interaction.…”