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Example 2D square lattice with s and p orbitals

We next consider a slightly more complex case, the two-dimensional square lattice with one atom per unit cell. We assume that there are four atomic orbitals per atom, one s -type and three p-type px, Py, Pz). We work again within the orthogonal basis of orbitals and nearest neighbor interactions only, as described by the equations of Table 4.1. The overlap matrix elements in this case are [Pg.129]

There are a number of different on-site and hopping matrix elements that are generated from all the possible combinations of / m(r) and (f i(r) in Eq. (4.22), [Pg.129]

The hopping matrix elements are shown schematically in Fig. 4.3. By the symmetry of the atomic orbitals we can deduce  [Pg.130]

Having defined all these matrix elements, we can calculate the matrix elements between crystal states that enter in the secular equation we find for our example [Pg.131]

With these we can now construct the hamiltonian matrix for each value of k, and obtain the eigenvalues and eigenfunctions by diagonalizing the secular equation. [Pg.131]


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Orbital s orbitals

Orbitals p orbital

P orbital

P orbitals

S orbitals

Square lattice

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