Condensed Matter Physics - Band Theory of Solids : Nearly Free Electron Approximation

The Nearly Free Electron Approximation is a method used in solid state physics to describe the behavior of electrons in a crystalline lattice. It lies between the two extremes of the free electron model and the tight binding model. This model acknowledges the periodic potential of the crystal lattice,but assumes that the potential is weak and causes only small perturbation to the electron’s free motion. The Bloch Theorem applies,ensuring that the electron wave functions are of Bloch form. Energy band gaps arise at the Brillouin zone boundaries due to the interference of electron wave functions with the periodic lattice potential, results in the splitting of energy levels into different bands. The model is particularly useful for understanding the formation of energy bands and gaps in materials where the electron-lattice interaction is weak,such as simple metals.