This chapter deals with the concept of nanomaterials, especially basic quantum mechanics and solid-state physics. It is now a well-established fact that the dynamics of materials in nano-regime cannot be described by simple Newtonian mechanics, and, therefore, one should opt for quantum mechanics. Thus, the focus of this chapter will be on basic quantum mechanics and solid-state physics in order to gain an understanding of the system's transport properties. A few characteristic phenomena of nanomaterials like the density of state, quantum confinement, excitonic radius, etc., will also be discussed in detail. To acquaint the reader with the Fermi energy and related properties, efforts will be made to provide a fundamental concept of statistical physics, specifically the Fermi-Dirac statistics. The authors have focused their efforts exclusively on dealing with different length scales, namely Ballistic transport and the associated Landauer-Buttiker formula of quantum transport in nanomaterials. Also, the relationship between exciton radius and quantum confinement and optical properties of nanomaterial has also been explained in detail. The concept of tunnelling, which is the foundation of quantum transport, has been explained, and an effort has been made to acquaint the reader with quantum conductance and Coulomb blockade.
Keywords: Ballistic transport, Crystallography, Density of state, Exciton, Quantum confinement.
