What are 'superlattices' and 'artificial atoms'? An introductory book to nanotechnology (Nanotechnology: An Introduction
by Jeremy Ramsden) states the following:

Stacking objects with nanoscale sizes in one, two or three dimensions
  (yielding nanoplates, nanofibers and nanoparticles with, respectively,
  confinement of carriers in two, one or zero dimensions) creates a new
  class of superlattices or artificial atoms.

My question is: What are superlattices and artificial atoms here, and why does it create a "new class" of superlattices or artifical atoms?
By the way, I am taking an introduction to nanoscience but only have a very rudimentary knowledge of quantum mechanics.
 A: A superlattice is a periodic arrangement of different materials to make up a composite with different properties than could be achieved with either material on its own. 
As your book notes, this can happen in one, two and three dimensions. This means that the material can be periodic along a single axis (forming a periodic arrangement of layers), two independent axes (forming a bunch of periodically stacked wires, with no periodicity along the wires' axis) or on all three dimensions (forming a three-dimensional lattice of nano-scale particles).
They are called superlattices (as opposed to regular lattices) because they are most often made out of metals or dielectrics that themselves have a crystalline structure. Thus, the periodic array of materials is superposed on the internal lattice structure of the materials themselves:

Image source

"Artificial atom" is a common name for quantum dots, which are usually small islands of semiconductor enclosed within a larger volume of some other semiconductor. 

Image source
These are normally chosen so that electrons have a lower energy in the island than on the surrounding semiconductor, which means that at low temperatures you can trap electrons there. Moreover, with careful engineering, you can get these to behave essentially like single-particle confined quantum systems, with the same sort of features (like quantization of energy into a small discrete set of possible states) that atoms show, though on different scales. (For example, the fact that the length scales are much longer means that the quantized energy levels are generally much lower.)

Both of these classes of objects can show rather different behaviour to their 'normal' versions: superlattices can be a lot more varied than normal crystal lattices (so you get things like hyperbolic metamaterials), and similarly quantum dots allow us to engineer some of the properties of the confined quantum system (as opposed to atoms, where we just have the ones Nature gave us and very few ways to change them). This is probably what Ramsden means by a 'new class' of lattices and confined quantum systems.
