A layering model for superconductivity in the borocarbides

Abstract

We propose a superlattice model to describe superconductivity in layered materials, such as the borocarbide families with the chemical formulae RT2B2C and RT BC, with R being (essentially) a rare earth, and T a transition metal. We assume a single band in which electrons feel a local attractive interaction (negative Hubbard-U ) on sites representing the T B layers, while U = 0 on sites representing the RC layers; the multi-band structure is taken into account minimally through a band offset ε. The one-dimensional model is studied numerically through the calculation of the charge gap, the Drude weight, and of the pairing correlation function. A comparison with the available information on the nature of the electronic ground state (metallic or superconducting) indicates that the model provides a systematic parametrization of the whole borocarbide family.The study of Nickel borocarbides (BCs), with the general formula R Ni 2 B 2 C, has given rise to a wealth of interesting information [1,2,3,4]. Superconductivity has been found for R = Sc, Y, Ce, Dy, Ho, Er, Tm, Lu, and Th, but not for R = La, Pr, Nd, Sm, Yb, U, Gd, and Tb. In addition to the 'high' critical temperature for some compounds -T c > 15 K for R = Sc, Y and Lu -, the other aspect which has drawn attention to these materials is the coexistence, for R = Dy, Ho, Er, and Tm, of superconductivity and magnetic ordering of the 4f localized moments. Structurally, the BCs are characterized by a stacking of alternating RC sheets and Ni 2 B 2 layers[3], with both its band structure [5,6] and the near isotropic resistivity [4] being consistent with three-dimensional behaviour.From the microscopic point of view, superconductivity in these materials is mediated by phonons, as evidenced by specific heat [7] and isotope effect [8] measurements. It would then appear natural to relate the suppression of superconductivity, as R and the transition metal (T ) are varied, in terms of the BCS parameters, Θ D , N (E F ), and V (respectively, the Debye temperature, the density of states at the Fermi level, and some measure of the electron-phonon coupling strength):Since resistivity measurements indicate that V does not vary much with R in R Ni 2 B 2 C [9], one is left primarily with Θ D and N (E F ). While Θ D generally increases as R goes from Lu to La, measurements of the Sommerfeld coefficient, γ ∝ N (E F ), lead to γ Lu ∼ 2γ La in the Ni series. However, as the transition metal is varied, this simple parametrization no longer accounts for the trend of experimental data in an unambiguous way. Indeed, LaPt 2 B 2 C is a superconductor [and, for this Pt series, so are the compounds with R = Pr, Y [4], and, possibly [10], Nd], even though it has a smaller N (E F ) than non-superconducting LaNi 2 B 2 C: γ = 5 and 8 mJ/mol K 2 , respectively [11]. Another important piece of information is provided by studies of a closely related phase, R NiBC [3, 12, 13]. The structural difference between R Ni 2 B 2 C and R NiBC is the number of R C layers between the Ni 2 B 2 stacks: one in the fo...

Pairing correlations in the two-layer attractive Hubbard model

“…That is, the suppression of superconductivity caused by the appearance of a degenerate charge density wave phase at n = 1 is eliminated. Paiva et al [35] explored a one-dimensional model of borocarbides in which U < 0 and U = 0 sites alternate. Superconductivity is found to be possible only above a critical density.…”

Critical temperature for the two-dimensional attractive Hubbard model

“…10 The attractive Hubbard model with a periodic modulation of U has been used to interpret superconductivity in layered structures. 11 A basic concern has run through many of these calculations, in particular, those based on quantum Monte Carlo ͑QMC͒ simulations. In two dimensions, there is a consensus that the early QMC phase diagram 12,13 -in the space of critical temperature T c , electronic density ͗n͘, and magnitude of the on-site attraction ͉U͉-is qualitatively correct.…”

Effects of nanoscale spatial inhomogeneity in strongly correlated systems

“…Figure 1 and Table I represent superlattices in which only the on-site interaction is spatially modulated, which is the case most studied in the literature. [9][10][11][12][13][14][15][16][17] Many important features of superlattice structures are already apparent in this type of model. However, in a real system it is impossible to modulate the on-site interaction without simultaneously modulating the on-site potential as well, i.e., without creating inequivalent sites.…”

“…All this calls into question the common practice to employ the homogeneous Hubbard model to model spatially inhomogeneous many-body systems, and demands a reconsideration of the role of nanoscale spatial inhomogeneity in strongly correlated systems. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] This work was supported by FAPESP and CNPq. *Electronic address: capelle@if.sc.usp.br 27 Note that one cannot use the Hohenberg-Kohn theorem to argue that the potential that produces the same density distribution in both systems must be the same one that yields the same groundstate energy.…”