Density of States - k-space Topologies

k-space Topologies

The density of states is dependent upon the dimensional limits of the object itself. The role dimensions play is evident from the units of DOS (Energy−1Volume−1). In the limit that the system is 2 dimensional a volume becomes an area and in the limit of 1 dimension it becomes a length. It is important to note that the volume being referenced is the volume of k-space, the space enclosed by the constant energy surface of the system derived through a dispersion relation that relates E to k. The dispersion relation for electrons in a solid is given by the electronic band structure. An example of a 3-dimensional k-space is given in Fig. 1. It can be seen that the dimensionality of the system itself will confine the momentum of particles inside the system.