Geometry functions and methods

g.get_hamiltonian()

Generate the tight-binding Hamiltonian of the geometry. By default it has first-neighbor hopping \(t=1\) and is spinful. See Building a Hamiltonian.

Optional arguments

• tij=None: the hoppings. None is first-neighbor hopping \(t=1\). A list gives the 1st, 2nd, 3rd... neighbor hoppings, for example [1.0,0.2]. It can also be a function of the two positions that returns the hopping between them, or a specialhopping.HoppingGenerator
• has_spin=True: include the spin degree of freedom
• is_sparse=False: store the matrices as sparse matrices, for large unit cells
• non_hermitian=False: build a non-Hermitian Hamiltonian (see Non-Hermitian Hamiltonians)
• is_multicell=False: include hoppings to unit cells beyond the first neighbor cells
• nc=2: how many neighbor cells are included when is_multicell=True

A misspelled keyword raises TypeError with the list of accepted ones.

Returns the Hamiltonian

g.remove()

Return a copy of the geometry with some sites removed. Use it to make a vacancy or an antidot in a flake or in a supercell, before building the Hamiltonian (see Operators for an example).

Arguments

• i=0: the sites to remove: one index of g.r, a list of indices, or a function of the position, which removes every site where it returns True

Returns a new geometry; g is not changed

g.get_supercell()

Generate a supercell

Arguments

• nsuper: size of the supercell. A number or a tuple multiplies the lattice vectors. A 3x3 integer matrix \(M\) gives a general supercell, with lattice vectors \(\mathbf a'_i=\sum_j M_{ij}\mathbf a_j\) (see Band unfolding)

Optional arguments

• store_primal=False: keep the primitive geometry inside the supercell. It is needed to unfold the bands with operator="unfold" (see Band unfolding)

For a 2D geometry, a non-integer nsuper gives a supercell whose area is nsuper\(^2\) times the primitive one, so np.sqrt(3) gives the \(\sqrt3\times\sqrt3\) cell.

Returns a new geometry

g.get_unfolded_kpath()

Return the k-path of the primitive cell, written in the reduced coordinates of the supercell. This is the path along which an unfolded band structure is computed (see Band unfolding). The same method exists as h.get_unfolded_kpath(). The supercell must be built with store_primal=True.

Arguments

• kpath=None: as in g.get_kpath(), a list of k-points or a list of high-symmetry labels, both read in the primitive cell
• g0=None: the primitive geometry, if the supercell does not contain it
• nk: number of k-points along the path

Returns an array of k-points, one per row, to give as kpath= to h.get_bands() or h.get_kdos_bands()