Chemical structure generation and analysis package following proper spacegroup symmetry.

This contruction of monochalcogenide structure describes each layer as an intermediate structure between h-BN, a flat graphene-like layer, and black phosphorus. As the ratio between the two in-plane lattice parameters decrease, Se atoms are pushed out of plane creating truss-like scaffold with Ge atoms as the tip of trigonal pyramids pointing up and down alternately. Geometric relations for Se scaffolding are presented here:

,

with a, b = lattice vector size along $\hat{a}, \hat{b}$ and scaffold height,

$h = \frac{\sqrt{3 - (b/a)^{2}}}{2} a$,

Ge position is defined relative to Se positions using rigid rotation approximation.

continuing

To build a bulk GeSe with lattice vectors (a,b,c) with the armchair direction along $a$ and out of plane along direction $c$ with spacegroup 31 symmetry enforcement. atoms = unit_cell(a, b, c, orientation ='ac', use_symm=True) To build a monolayer GeSe with lattice vectors (a,b,c) with the armchair direction along $c$ and out of plane direction along $a$ with spacegroup 62 symmetry enforcement. atoms = unit_cell_bulk(a, b, c, orientation ='ca', use_symm=True)

Measure MXM tilt angle with the armchair direction along $a$ and out of plane along direction $c$ as defined in 10.1103/PhysRevB.97.024110: theta_deg = tilt_angle(atoms, proj = 'ac', thres=0.9, absolute=True)