ABSTRACT
From quantum mechanics, we know that properties of materials at the atomic scale di er from those of their macroscopic counterparts. One of the properties is the electrical conductance, which is discussed in detail in this chapter. For macroscopic conductors, Ohm’s law holds and states that the conductance of the conductor is inversely proportional to its length. Intuitively, we can understand Ohm’s law if we consider electrons as particles, which, on their way from one electrode to the other, su er scattering in the conductor. However, intuition fails if dimensions reach the Fermi wavelength of electrons. Electrons are now transported ballistically through the microscopic conductor and the character of conductance changes conceptually. Currently, many experimental and theoretical investigations are devoted to an understanding of how electrons are transported through atoms, atomic wires, and molecules. e reason for this increased interest may be found in the ongoing miniaturization in the microelectronic industry. Although we are far from replacing silicon technology by the socalled molecular electronics, it is important to unravel the quantum properties of conductors with nanometer dimensions and to discover new challenges, which must be faced upon reducing the size.
