# Calculation of the Fermi Arc

Can I ask two questions, regarding the Fermi Arc?

Suppose there are only three atoms in the bulk Weyl Semimetal system and the Fermi Arc of the system is within the x-y plane. If there is only one orbital on each atom; then, the Hamiltonian for the bulk Weyl Semimetal is a $$6\times6$$ matrix, which is written below. $$\begin{matrix} \space&1st\space atom\uparrow&2nd\space atom\uparrow&3rd\space atom\uparrow&1st\space atom\downarrow&2nd\space atom\downarrow&3rd\space atom\downarrow\\ 1st\space atom\uparrow&M_{11}&M_{12}&M_{13}&M_{14}&M_{15}&M_{16}\\ 2nd\space atom\uparrow&M_{21}&M_{22}&M_{23}&M_{24}&M_{25}&M_{26}\\ 3rd\space atom\uparrow&M_{31}&M_{32}&M_{33}&M_{34}&M_{35}&M_{36}\\ 1st\space atom\downarrow&M_{41}&M_{42}&M_{43}&M_{44}&M_{45}&M_{46}\\ 2nd\space atom\downarrow&M_{51}&M_{52}&M_{53}&M_{54}&M_{55}&M_{56}\\ 3rd\space atom\downarrow&M_{61}&M_{62}&M_{63}&M_{64}&M_{65}&M_{66}\\ \end{matrix}$$

1. How to build up the surface green function with this bulk Hamiltonian?
2. How to compute the Fermi Arc of the Weyl Semimetal? I mean how to find each point on the Fermi Arc and plot them? What is the criterion on finding the Fermi Arc?

Would anyone please give me some suggestions on the solution?

Thank you very much in advance.

Kind regards,

Kieran