Next-nearest Neighbor Hopping Research Articles

Low-density ferromagnetism in the Hubbard model.

A single-band Hubbard model with nearest and next-nearest neighbour hopping is studied for $d=1$, 2, 3, using both analytical and numerical techniques. In one dimension, saturated ferromagnetism is found above a critical value of $U$ for a band structure with two minima and for small and intermediate densities. This is an extension of a scenario recently proposed by M\"uller--Hartmann. For three dimensions and non-pathological band structures, it is proven that such a scenario does not work.

DMRG study of ferromagnetism in a one-dimensional Hubbard model

The one dimensional Hubbard model with nearest and (negative) next-nearest neighbour hopping has been studied with the density-matrix renormalization group (DMRG) method. A large region of ferromagnetism has been found for finite density and finite on-site interaction.

Theory of spin dynamics in high- Tc superconductors

We analyze the spectrum of magnetic excitations as observed by neutron diffraction and NMR experiments in YBa 2Cu 3O 6+ x , in the frame of the single-band t- t′- J model in which the next-nearest neighbor hopping term has been introduced in order to fit the shape of the Fermi surface revealed in photoemission. Within the slave-boson approach, we have as well examined the d-wave superconducting state, and the singlet-RVB phase appropriate to describe the normal state of heavily doped systems. Our calculations show a smooth evolution of the spectrum from one phase to the other, with the existence of a spindashgap in the frequency dependence of χ″( Q, ω ). The value of the threshold of excitations E G is found to increase with doping, while the characteristictemperature scale T m at which the spindashgap opens, exhibits a regular decrease, reaching T c only in the overdoped regime. These very typical combined variation of E G and T m with doping results of strong-correlation has its effect in the presence of a realistic band structure. We point out the presence of a resonance in the ω-dependence of χ″( Q, ω) in good agreement with the neutron diffraction results obtained at x = 0.92 and x = 1.0. This resonance is interpreted as a dynamical Kohn anomaly of the second kind in the Cooper channel. Finally, we examine the q- dependence of the dynamical susceptibility allowing to study the magnetic correlation length ξ as a function of doping, frequency and temperature.

Spin-gap and magnetic excitations in the cuprate superconductors

We have analysed the spin-excitation spectrum as observed by neutron and NMR experiments in YBa 2 Cu 3 O 6+ z in the frame of a bidimensional t-t′-J model. Next-nearest neighbour hopping term t′ is introduced in order to fit the shape of the Fermi surface revealed by photoemission. Within the slave-boson approach, we study as well the d-wave superconducting state, as the singlet-RVB state which is expected to describe the normal phase of heavily-doped systems. In the superconducting state, d-wave pairing leads to the prediction of a resonance and a gap-structure in the spin-excitation spectrum, in good agrement with neutron diffraction results for ξ = 0.92 and ξ = 1.0. Our calculations show a smooth evolution of the spectrum from one phase to the other: the value of the threshold of excitations E G increases with doping, while the temperature T m at which the spin-gap opens regularly decreases, reaching T C only in the overdoped regime. This very atypical combined variation of E G and T m with doping results of strong-correlation effects in presence of the realistic band-structure considered here.

Spin excitations in high-T c superconductors : discussion of neutron and NMR experiments

The spin excitation spectrum as observed in neutron diffraction and NMR experiments in YBa 2Cu 3O 6+x is theoretically examined on the basis of a bidimensionnal extended t-t'-J model in which next-nearest neighbour hopping term t' is considered in order to fit the shape of the Fermi surface observed in angle-resolved photoemission experiments. We study more specifically the superconducting phase in which d-wave pairing leads to the prediction of a resonance in S(Q o,ω) surimposed to a gap-structure in agreement with the neutron results. We also extend our calculations to the study of the RVB (resonant-valence-bond) singlet state and show that the latter is a good candidate to describe the normal phase above T c of heavily-doped systems.