where each atom contributes several electrons, many distinct energy bands can form. Two such energy bands can also be separated from each other giving rise to a range of energies where no electronic states are present. Such an energy range is called a band gap in solid state physics and electronics [@kittel; @mermin-ashcroft]. If the maximum energy up to which all quantum states are filled at zero temperature $T=0$, which is known as the Fermi energy of a solid, falls within such a band gap, the solid behaves like an insulator. Such insulators are often termed as the “band insulators". If the Fermi energy is within a band, the solid behaves like a metal. Notice, this theory, known as the band theory, neglects electronic interactions due to which it may fail for certain materials.

Tight binding model {#sec:tightbinding}
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Imagine again building up a one-dimensional crystal lattice by arranging hydrogen-like atoms together along a straight line in an ordered fashion. As we discussed before, when atoms are far apart, they can be treated separately as there is no overlap between their respective eigenstates. Once they come close enough, their wave functions will no longer be orthogonal, they mix up and 