Band structure of ${\mathrm{MgB}}_2$ with different lattice constants

We report a detailed study of the electronic structure of the ${\mathrm{MgB}}_2$ with different lattice constants by using the full-potential linearized augmented plane-wave method. It is found that the lattice parameters have great effect on the $\sigma$ band of boron. Our results indicate that increasing the lattice constant along the c axis will increase the density of states at the Fermi level, shift the $\sigma$ band upward, and increase the hole number in the $\sigma$ band. So, the superconducting transition temperature $T_c$ will be raised correspondingly. Changing the lattice constant along a axis has the opposite effect to that of the c axis. Our result is in agreement with the experiment. A possible way of searching for higher $T_c$ superconductor has been indicated, i.e., making ${\mathrm{MgB}}_2$ to have longer c axis and shorter $a,b$ axis by doping.