In the high-Tc cuprates, the nanoscale electronic state is important for understanding their com- plex physical properties and unconventional superconducting mechanism. In this work, numerical exact diagonalization method has been used to study the effect of diagonal hopping t' and near- est-neighbor Coulomb interaction V on the electron pair binding energy, spin and charge gaps and corresponding crossover temperatures in the square Hubbard clusters. The calculated results show that t' extends the regime of U in which electron, spin and charge pairings are formed, and corresponding crossover temperature increased. On the contrary, V exhibits opposite effects com- pared to t'. When V approaches to the energy scale of effective attraction induced by U, electron pairing is completely destroyed. Our findings demonstrate that t' can help the formation of super- conducting state, while V will suppress the superconductivity.
In the high-Tc cuprates, the nanoscale electronic state is important for understanding their com- plex physical properties and unconventional superconducting mechanism. In this work, numerical exact diagonalization method has been used to study the effect of diagonal hopping t' and near- est-neighbor Coulomb interaction V on the electron pair binding energy, spin and charge gaps and corresponding crossover temperatures in the square Hubbard clusters. The calculated results show that t' extends the regime of U in which electron, spin and charge pairings are formed, and corresponding crossover temperature increased. On the contrary, V exhibits opposite effects com- pared to t'. When V approaches to the energy scale of effective attraction induced by U, electron pairing is completely destroyed. Our findings demonstrate that t' can help the formation of super- conducting state, while V will suppress the superconductivity.
铜氧化物高温超导体中纳米尺度的电子态对理解这类材料的复杂物理特性和非常规超导机理具有重要的意义。本文采用数值精确对角化方法研究了纳米尺度四方哈伯德团簇中对角跃迁t'和近邻库仑相互作用V对电子对束缚能、自旋和电荷能隙及其对应跨越温度的物理影响。研究结果表明对角跃迁t'有效地扩展了电子配对、自旋和电荷配对的哈伯德U参数区间，升高了它们对应的跨越温度；与此相反，近邻库仑相互作用V显著地缩小了电子配对、自旋和电荷配对的哈伯德U参数区间，并降低了它们对应的跨越温度。当V与哈伯德U产生的有效电子吸引相互作用能量尺度相当时，在整个U值区间不能形成稳定的电子配对态。我们的研究结果说明t'有利于形成电子配对的超导态，而V将抑制超导态的形成。 In the high-Tc cuprates, the nanoscale electronic state is important for understanding their com-plex physical properties and unconventional superconducting mechanism. In this work, numerical exact diagonalization method has been used to study the effect of diagonal hopping t' and nearest-neighbor Coulomb interaction V on the electron pair binding energy, spin and charge gaps and corresponding crossover temperatures in the square Hubbard clusters. The calculated results show that t' extends the regime of U in which electron, spin and charge pairings are formed, and corresponding crossover temperature increased. On the contrary, V exhibits opposite effects com- pared to t'. When V approaches to the energy scale of effective attraction induced by U, electron pairing is completely destroyed. Our findings demonstrate that t' can help the formation of superconducting state, while V will suppress the superconductivity.
We examine the influence of hole doping on superconducting pairing symmetries in the two-dimensional Hubbard model extended by next-nearest-neighbor hopping, nearest-neighbor Coulomb interaction, correlated hopping, exchange interaction and pair-hopping processes. Using Lanczos exact diagonalization supported by projector quantum Monte Carlo method, we calculate superconducting correlation functions corresponding to s-wave, extended s-wave, and d-wave pairing over a broad range of electron concentrations and interaction parameters. We find that hole doping acts as an efficient control parameter of superconducting pairing symmetry, giving rise to robust crossovers between the dominant pairing correlations. While extended s-wave pairing dominates throughout most of the overdoped regime, reducing the hole concentration progressively enhances d-wave correlations over large regions of the ground-state diagram. The critical doping associated with these crossovers depends strongly on the underlying interaction mechanism. In particular, correlated hopping and next-nearest-neighbor hopping substantially modify the location of the pairing-symmetry boundaries, whereas the local Hubbard interaction exhibits a comparatively weaker effect. In contrast to all other interaction channels, a finite nearest-neighbor Coulomb interaction additionally stabilizes conventional s-wave state over a sizeable region of parameter space. Our results demonstrate that superconducting pairing symmetry in the extended Hubbard model is governed by a subtle interplay between carrier concentration and nonlocal electronic interactions.
The emergence of superconductivity (SC) in lattice models, such as the attractive Hubbard one, has renewed interest since the realization of cold-atom experiments. However, reducing the temperature in these experiments is a bottleneck; therefore, investigating how to increase the energy scale for SC is crucial to cold atoms. In view of this, we examine the effects of next-nearest-neighbor hoppings (t′) on the pairing properties of the attractive Hubbard model in a square lattice. To this end, we analyze the model through unbiased Quantum Monte Carlo simulations for fixed density n=0.87, and perform finite-size scaling analysis to the thermodynamic limit. As our main result, we notice that the existence of further hopping channels leads to an enhancement of the pairing correlations, which, in turn, increases the ground-state order parameter Δ. Finally, at finite temperatures, for t′/t≠0, this enhancement of pairing correlations leads to an increase in the critical temperature Tc. That is, the fine-tuning of second-neighbor hoppings increases the energy scales for SC, and may be a route by which cold-atom experiments can achieve such a phase and to help us further understand the nature of this phenomenon.
The influence of the next-nearest-neighbor (NNN) antiferromagnetic interaction J ’has been examined within t-t'-J-J ’model in an exact technique. An 8-site square cluster is chosen as the representative of the system. The effect of the next-nearest-neighbor (NNN) antiferromagnetic interaction on various ground state properties such as electron-electron correlation, spin-spin correlation, effective hopping amplitude etc. has been studied. Temperature variation of the susceptibility shows that J ’suppresses short range antiferromagnetic order. Applying periodic boundary conditions, the calculations have been extended beyond the 8-site limit.
Motivated by significant discrepancies between experimental observations of electron-doped cuprates and numerical results of the Hubbard model, we investigate the role of nearest-neighbor (NN) electron interactions V by studying the t−U−V model on square lattices. Upon doping δ= 0.153, by using constrained path quantum Monte Carlo (CPQMC) method, we find that NN electron attraction V can notably drive an exotic p-wave spin-triplet pairing, while the NN electron repulsion V will suppress the dx2−y2-wave (d-wave) pairing and triggers the dxy-wave pairing. Especially in the intermediate coupling regime, as NN repulsion increases, the intensity of dxy-wave pairing also increases, further suppressing the presence of d-wave pairing, which may help explain the notable suppression of d-wave pairing in electron-doped cuprate superconductors. Besides the pairing phase, we also find that the NN electron attraction V has no significant effect on spin density wave (SDW) and charge density wave (CDW), but repulsion V significantly enhanced CDW and suppressed SDW. Our study suggests the t−U−V Hubbard model can serve as the minimal model to capture the essential physics of the electron-doped cuprates.
The attractive Hubbard model plays a paradigmatic role in the study of superconductivity (superfluidity) and has become directly realizable in ultracold atom experiments on optical lattices. However, the critical temperatures, Tc's, remain lower than the lowest temperatures currently achievable in experiments. Here, we explore a possible route to enhance Tc by introducing an additional next-nearest-neighbor (NNN) hopping, t′, in a two-dimensional square lattice. We perform sign-problem-free determinant quantum Monte Carlo simulations to compute response functions such as pairing correlation functions, superfluid density, and uniform spin susceptibility. Our results show that a judicious choice of t′ can increase Tc by up to 50% compared to the case with only nearest-neighbor hopping. In contrast, the preformed pairs temperature scale, named pairing temperature, Tp, decreases with increasing ∣t′/t∣, which should represent a reduction of the pseudogap region, favoring a more BCS-like behavior at intermediate coupling. We further analyze the interacting density of states to characterize the transition from a pseudogap regime to a fully gapped superconducting state. These findings suggest that NNN hopping could be a viable route to increase Tc to values closer to experimentally accessible temperature scales.