Electronic properties of 1D LaB$_{6}$ rods*

Metal hexa-borides have varieties of interesting properties and were utilized frequently in technological applications: e.g. LaB$_{6}$ is known to have extremely low work function, thus is used as one of the most popular electron emitter. Our project is initiated by the experimental findings that LaB$_{6}$ nano-rods generated stronger electric current than in the bulk case. Thus we focus on the band structure calculations of quasi-1D nano-rods with various widths and breadths for the purpose of studying the relationship between work function and rod shapes. Our samples consist of up to ten unit cells, i.e. n\textbf{\textit{a}} X m\textbf{\textit{b}} (\textbf{\textit{a}} and \textbf{\textit{b}} are lattice vectors and n X m $\le $ 10). To accomplish our calculations, we applied GGA density functional theory with all electron and relativistic effect included.