The band structure of MgB₂ with different lattice constants

We report a detailed study of the electronic structure of the MgB$_{2}$ with different lattice constants by using the full-potential linearized augmented plane wave(FPLAPW) method. It is found that the lattice parameters have great effect on the $\sigma$ band of Boron. Our results indicate that increasing lattice constant along the {\it c} axis will increase the density of states(DOS) at the Fermi level, making the $\sigma$ band upward shift, and increasing hole number in the $\sigma$ band. So, the superconducting transition temperature T$_{c}$ will be raised correspondingly. Changing the lattice constant along {\it a} axis has an opposite effect to that of along {\it c} axis. Our result is in agreement with experiment. A possible way of searching for higher T$_{c}$ superconductor has been indicated, i.e., making MgB$_{2}$ to have longer {\it c} axis and shorter {\it a, b} axis by doping.