Detailed electronic structure studies on superconductingMgB2and related compounds

Abstract

In order to understand the unexpected superconducting behavior of ${\mathrm{MgB}}_2$ we have made electronic structure calculations for ${\mathrm{MgB}}_2$ and closely related systems. Our calculated Debye temperature from the elastic properties indicate that the average phonon frequency is very large in ${\mathrm{MgB}}_2$ compared with other superconducting intermetallics and its exceptionally higher $T_c$ can be explained through a BCS mechanism only if phonon softening occurs or the phonon modes are highly anisotropic. We identified a doubly degenerate quasi-two-dimensional key-energy band in the vicinity of $E_F$ along the $\Gamma –A$ direction of BZ (having equal amount of B $p_x$ and $p_y$ character) which plays an important role in deciding the superconducting behavior. Based on this result, we have searched for a similar electronic feature in isoelectronic compounds such as ${\mathrm{BeB}}_2,$ ${\mathrm{CaB}}_2,$ ${\mathrm{SrB}}_2,$ LiBC, and ${\mathrm{MgB}}_2{\mathrm{C}}_2$ and found that hole doped LiBC and ${\mathrm{MgB}}_2{\mathrm{C}}_2$ are potential superconducting materials. We have found that $E_F$ in the closely related compound ${\mathrm{MgB}}_4$ is lying in a pseudogap with a negligibly small density of states at $E_F,$ which is not favorable for superconductivity. There are contradictory experimental results regarding the anisotropy in the elastic properties of ${\mathrm{MgB}}_2$ ranging from isotropic to moderately anisotropic to highly anisotropic. In order to settle this issue we have calculated the single-crystal elastic constants for ${\mathrm{MgB}}_2$ by the accurate full-potential method and derived the directional-dependent linear compressibility, Young’s modulus, shear modulus, and relevant elastic properties from these results. We have observed large anisotropy in the elastic properties consistent with recent high-pressure findings. Our calculated polarized optical dielectric tensor shows highly anisotropic behavior even though it possesses isotropic transport property. ${\mathrm{MgB}}_2$ possesses a mixed bonding character and this has been verified from density of states, charge density, and crystal orbital Hamiltonian population analyses.