Effects of Disorder in Mg1−xTaxB2 Alloys using Coherent-Potential Approximation

Using Korringa-Kohn-Rostoker coherent-potential approximation in the atomicsphere approximation (KKR-ASA CPA) method for taking into account the effects of disorder, Gaspari-Gyorffy formalism for calculating the electron-phonon coupling constant λ, and Allen-Dynes equation for calculating Tc, we have studied the variation of Tc in Mg1−xTaxB2 alloys as a function of Ta concentration. Our results show that the Tc decreases with the addition of Ta for upto 40at% and remains essentially zero from 60 at% to 80 at% of Ta. We also find TaB2 to be superconducting, albeit at a lower temperature. Our analysis shows that the variation in Tc in Mg1−xTaxB2 is mostly dictated by the changes in the B p density of states with the addition of Ta.. The experimental [1–3] and theoretical [4] efforts aimed at understanding the nature of superconductivity in MgB2 have made substantial progress since the discovery of superconductivity in it [1]. With an enhanced understanding of superconductivity in MgB2, attempts are now being made to understand the changes in the electronic structure and the superconducting properties of MgB2 upon alloying with various elements. Such efforts provide an opportunity to explore the possibility of obtaining MgB2 alloys with improved superconducting properties. The changes in the superconducting properties of MgB2 due to substitution of various elements such as Be, Li, C, Al, Na, Zn, Zr and others have been studied experimentally [3,5]. Some theoretical work has also been reported within the rigid-band model. The main effects of alloying are seen to be (i) a decrease in transition temperature, Tc, with increasing concentration of the alloying elements except for Zn (and possibly Li) where Tc is seen to increase somewhat, (ii) changes in lattice parameters a and c, and (iii) a change in crystal structure. Preprint submitted to Elsevier Preprint 9 March 2008 With a view to understand the changes in the electronic structure and the superconducting properties as well as clarifying the reported superconductivity in TaB2 [6,7], we have carried out an ab initio study of Mg1−xTaxB2 alloys. We have used Korringa-Kohn-Rostoker coherent-potential approximation [15] within the atomic-sphere approximation (KKR-ASA CPA) method for taking into account the effects of disorder, Gaspari-Gyorffy formalism for calculating the electron-phonon coupling constant λ, and Allen-Dynes equation for calculating Tc in Mg1−xTaxB2 alloys as a function of Ta concentration. Such an attempt allows us to examine the possibility of superconductivity in TaB2, given the superconductivity in MgB2. We have analyzed our results in terms of the changes in the total density of states (DOS), in particular the changes in the B p contribution to the total DOS, as a function of Ta concentration. Based on our calculations, described below, we find that inMg1−xTaxB2 alloys (i) the Tc decreases with the addition of Ta for upto 40 at%, remains essentially zero from 60 at% to 80 at%, and then rises to ∼ 1.8K for TaB2, (ii) the Tc for TaB2 is much lower than reported earlier [6], and (iii) the variation in Tc is mostly dictated by the changes in the B p densities of states as more and more Ta are added. Before we describe our results, we outline some of the computational details. The charge self-consistent electronic structure ofMg1−xTaxB2 alloys as a function of x has been calculated using the KKR-ASA CPA method [11]. We have used the CPA rather than a rigid-band model because CPA has been found to reliably describe the effects of disorder in metallic alloys. We parametrized the exchange-correlation potential as suggested by Perdew-Wang [12] within the generalized gradient approximation. The Brillouin zone (BZ) integration was carried out using 1215 k-points in the irreducible part of the BZ. For DOS calculations, we added a small imaginary component of 2 mRy to the energy and used 3887 k-points in the irreducible part of the BZ. The lattice constants for MgB2 and TaB2 were taken from experiments while for other compositions we used the Vegard’s law. The WignerSeitz radii for Mg and Ta were slightly larger than that of B. The sphere overlap, which is crucial in ASA, was less than 10% and the maximum l used was lmax = 3. The electron-phonon coupling constant λ was calculated using Gaspari-Gyorffy [13] formalism with the charge self-consistent potentials of Mg1−xTaxB2 obtained with the KKR-ASA CPA method. Subsequently, the variation of Tc as a function of Ta concentration was calculated using Allen-Dynes equation [14]. The average values of phonon frequencies ωln for TaB2 and MgB2 were taken from Refs. [9] and [10] respectively. For intermediate concentrations, we took ωln to be the concentration-weighted average of MgB2 and TaB2.