Electronic Bands and Fermi Surfaces

The bands for anti$-$ferromagnetic superconductor $C{a}_{4}A{l}_2{O}_{6}F{e}_{2}A{s}_2$ having $6-$electrons are given in figure.

Near the Fermi energy $(E=0)$ the states consist mainly of Fe$-3$d $d(xy),d(yz),d(xz),d(3z^2-r^2),d(x^2-y^2)$ and

As$-4p$ orbitals. They are color$-$coded $($lighter for $x\frac{z}{y}z$ states and darker for $x^2-y^2$ states$).$

a$.$ Circle the crossing points at the Fermi energy on band plot for $(k_x,k_y,0)=(+-,+-,0).$

b$.$ ONLY for the $k_z=0$ plane, i$.$e$.,(k_x,k_y,0),$ mark those points for $(k_x,k_y)=(+-,+-)$ in the BZ square

provided and then sketch the Fermi surface $($connect the points known to define the surfaces$).$

c$.$ Label curves in the bands at crossing points with $a$#$1=(x\frac{z}{x}z)$ or $a$#$2=(x^2-y^2)$ character, noting

that is possible, depending on direction in $k-$space, for an arc along to vary in character.

d$.$ For any pockets found, state whether they are "hole" or "electron" pockets?

$x\frac{Z}{Y}Z$

$x^2-Y^2$