Low-dimensional materials (LDMs) are a new class of materials, which have one or more physical dimension(s) constrained to the nanometer scale. This constraint implies that the electrons within them are confined to less than three dimensions, a property that imparts such materials with new and unusual properties, as well as new opportunities for novel engineering applications. The properties of low-dimensional materials are substantially different from those of their bulk counterparts, and their understanding requires the application of fundamental chemical engineering concepts. In studying such materials, the central focus has been on understanding their physical and chemical properties, and their potential technological applications. Examples of LDMs include two-dimensional (2-D) nanosheets, one-dimensional nanowires, nanotubes and nanorods (1-D), and zero-dimensional quantum dots (0-D), all of which showcase a whole new range of properties when compared to their three-dimensional (3-D) bulk equivalents, with the change in properties arising from quantum confinement and/or surface and interfacial effects. Quantum confinement effects appear when the confining dimension(s) is (are) on the order of the wavelength of the electron wave function. This implies that when electrons or holes (the absence of electrons) are moving, their mean free path is larger than the dimension of the quantum structure, which typically happens at the nanoscale. In general, solids have a defined spectrum of allowable electronic states, called the electronic density of states (DOS). The nanoscale confinement in LDMs brings about a transition from a continuous to a discontinuous DOS which results in a whole new set of physical, optical and chemical properties. 2-5 Electrical conductivity is typically expected to be lower for LDMs than for their bulk equivalents due to scattering from, e.g., wire boundaries, edge effects, and quantization of conductivity. Thinking about a nanowire: the thinner the wire is, the smaller the number of channels available for the transport of electrons.
6As dimensions of electronics keep getting smaller it is likely to encounter ballistic transport of electrons, meaning there is negligible resistivity in the medium due to scattering. It can be observed when the mean free path of the electron is much bigger than the dimensions of the medium it travels through. This phenomenon occurs at the nanoscale and is, thus, more likely to be observed in LDMs than in their bulk equivalents. InAs nanowires with a diameter of 50 nm have shown ballistic transport over a length scale of about 200 nm at room-temperature.7 However, it is generally hard to observe ballistic conduction in nanowires at roomtemperature due to edge effects: the dangling bonds present defects and act as scattering sites for the electrons.Thermal energy is another area where LDMs exhibit unique properties. The energy is stored and transmitted in nanostructures using electrons and particularly phononsquantized units of solid lattice vibration. Like electr...