Using k-space allows us to consider the energy states of a material as a function of momentum, rather than position. This is important because the momentum of electrons in a material is conserved, making it a more accurate representation of the system.
K-space is the reciprocal space of real space, meaning that it represents the periodicity of the material's crystal lattice. In the calculation of density of states, we use k-space to consider the energy levels of electrons within this periodic structure.
No, it is not possible to accurately calculate the density of states using real space. This is because real space does not take into account the periodicity and symmetry of a material's crystal structure, which are crucial factors in determining the energy levels of electrons.
The Brillouin zone is a representation of the allowed momentum states of electrons in a material. In the calculation of density of states, we use the Brillouin zone to consider the energy levels of electrons at different points in k-space.
One limitation of using k-space is that it assumes a perfect, idealized crystal structure. In reality, most materials have defects and imperfections which can affect the energy levels of electrons. Additionally, k-space calculations can become complex and time-consuming for highly disordered systems.