In this chapter we will temporarily leave the arena of many-body physics and second quantization and, at least superficially, return to single-particle quantum mechanics. By establishing the path integral approach for ordinary quantum mechanics, we will set the stage for the introduction of functional field integral methods for many-body theories explored in the next chapter. We will see that the path integral not only represents a gateway to higher-dimensional functional integral methods but, when viewed from an appropriate perspective, already represents a field theoretical approach in its own right. Exploiting this connection, various techniques and concepts of field theory, namely stationary phase analyses of functional integrals, the Euclidean formulation of field theory, instanton techniques, and the role of topological concepts in field theory, will be motivated and introduced in this chapter.

In the preceding chapters we encountered a wide range of long-range orders, or, to put it more technically, different types of mean-fields. Reflecting the feature of (average) translational invariance, the large majority of these mean-fields turned out to be spatially homogeneous. However, there have also been a number of exceptions: under certain conditions, mean-field configurations with long-range, spatial textures are likely to form. One mechanism driving the formation of inhomogeneities is the perpetual competition of energy and entropy: being in conflict with the (average) translational invariance of extended systems, a spatially non-uniform mean-field is energetically costly. On the other hand, this very “disadvantage” implies a state of lowered degree of order, or higher entropy. (Remember, for example, instanton formation in the quantum double well: although energetically unfavorable, once it has been created it can occur at any “time,” which brings about a huge entropic factor.) It then depends on the spatio-temporal extension of the system whether or not an entropic proliferation of mean-field textures is favorable.

In this chapter, the concept of path integration will be extended from quantum mechanics to quantum field theory. Our starting point will be from a situation very much analogous to that outlined at the beginning of the previous chapter. Just as there are two different approaches to quantum mechanics, quantum field theory can also be formulated in two different ways: the formalism of canonically quantized field operators, and functional integration. As to the former, although much of the technology needed to efficiently implement this framework – essentially Feynman diagrams – originated in high-energy physics, it was with the development of condensed matter physics through the 1950s, 1960s, and 1970s that this approach was driven to unprecedented sophistication. The reason is that, almost as a rule, problems in condensed matter investigated at that time necessitated perturbative summations to infinite order in the non-trivial content of the theory (typically interactions).

In the previous chapters we have introduced important elements of the theory of quantum many-body systems. Perhaps most importantly, we have learned how to map the basic microscopic representations of many-body systems onto effective low-energy models. However, to actually test the power of these theories, we need to understand how they can be related to experiment. This will be the principal subject of the present chapter.

Modern condensed matter physics benefits from a plethora of sophisticated and highly refined techniques of experimental analysis including the following: electric and thermal transport; neutron, electron, Raman, and X-ray scattering; calorimetric measurements; induction experiments; and many more (for a short glossary of prominent experimental techniques, see Section 7.1.2 below). While a comprehensive discussion of modern experimental condensed matter would reach well beyond the scope of the present text, it is certainly profitable to attempt an identification of some structures common to most experimental work in many-body physics.

After having discussed many aspects related to MOMs in the previous chapters, from the synthesis of the building blocks, the molecules, to the assembling of such molecules in the solid state in the form of single crystals and thin films, this last chapter is devoted to the physical properties of MOMs based on selected examples. The reader should be aware that this selection, being personal and thus inevitably partial, does not cover the plethora of examples that can be found in the literature. I assume the risk of overlooking some important works. In order to apologize in advance for not including several important investigations I reproduce the wise comment from M. Faraday written in 1859 but of surprising actuality (Faraday, 1859):

Broadly speaking, crystalline molecular organic materials (MOMs) are soft solids with a 3D periodic distribution of organic molecules exhibiting weak intermolecular forces, their cohesion being essentially mediated by dipolar (permanent or fluctuating charges), hydrogen bonding and π–π interactions. The molecules involved in the formation of such materials may be of a purely organic nature (e.g., metal-free) or based on hybrid organic–inorganic combinations (e.g., organo-metallic with transition metals). Solids can be built from molecules of a single species or binary or ternary combinations, and inorganic molecules can also be introduced forming hybrid organic–inorganic materials. Such regular solids are often seen by chemists as supramolecular entities, the solid as a macromolecule, in spite of their discrete character, while physicists tend to think in terms of a weakly interacting ordered gas, with cohesion energies larger than about 0.2 eV per molecule the typical energies of noble gas crystals. Although describing the same objects, the terminology used by chemists and physicists is usually distinct and scientific discussions are not always fully synthesized, hindering the desired effective flow of ideas. One of the objectives of this book is to bring both scientific communities to a common neutral playground to better understand the inherently interdisciplinary, rich, complex and exciting field of crystalline MOMs, which involves both experimental and theoretical chemists and physicists and material scientists.

Stating that molecules constitute the most important part of MOMs seems superfluous since they are indeed their fundamental building blocks. However, since most of the attention and glory has been devoted to the properties of MOMs, from both the scientific and technological points of view, the first and indispensable step in the chain that leads to MOMs, that is the synthesis of the constituent molecules without which MOMs cannot be built, has somehow been ignored. For a layman in the domain of synthesis of organic molecules (and this is my case) it is certainly easy to fall under the wrong impression that almost any molecule can be synthesized, given the seemingly countless number of available molecules that can be found in the literature. However, the creation of new molecules is, as expected, a complex matter and we will see a revealing example in the following section, where it will become evident that only a limited number of linear acenes have been prepared.

As soon as the number of MLs increases, or equivalently, when we leave the realm of 2D heterostructures and enter our more familiar 3D space, the deposited materials tend to recover their intrinsic bulk properties, as already discussed in the previous chapter for CuPc, reducing the influence of the interface. For these increasingly thicker deposits the morphology becomes a relevant issue because films generally exhibit physical boundaries (steps, grains, etc.), so relevant that sometimes the physical properties of the films depend mostly on the particular morphology, rather than on their intrinsic properties. Some examples on this significant point will be given in Section 6.4. In fact, long-range ordered films as well as single crystals become thermodynamically stable only in the presence of perturbations such as defects and boundaries. The surface morphology depends not only on the nature of the intermolecular interactions but also on the selected experimental conditions. This situation is crucial. Depending on the chosen points or trajectories in the parameter hyperspace the morphology may substantially vary. Hence, when exploring the growth for a particular system the actual experimental conditions have to be described as accurately as possible.

The present chapter is devoted to several aspects of the growth of thin films of MOMs, such as growth modes, micrometre- and nanometre-scale morpohologies, control of orientation, polymorphism, etc., without pretending to be a classical canonical treatise of crystal growth.

We discussed in Section 1.1 the complexity that a rather simple molecule such as N2 can manifest when it is made to form 2D and 3D periodic and non-periodic structures. This system was used to introduce the myriad molecules that we have been studying throughout this book and now it will help us to conclude. Given that solid nitrogen becomes semiconducting at the elevated pressure of 240 GPa, we can ask ourselves if, from the practical point of view, solid nitrogen is of any use. It is clear that it is hard to find technological applications in these extreme conditions, unless somebody dreams of making business on distant planets or stars. However, the important point is the scientific knowledge that is acquired working with almost any system, no matter how difficult it is. Unfortunately, many scientists fancy themselves as pseudo-technologists mainly because of the desperate search for financial funding. This means that the fabulous science behind the studied systems is not fully explored and that the claims for incredible applications usually remain as claims. Science and technology should go hand in hand, but scientists should have enough free rein to explore the unknown. The results always come.

Sometimes, among the MOMs community one gets the feeling that this field is losing strength, with many scientists getting bored of obtaining and characterizing similar materials with similar properties and hurrying to publish the results. I do not share this opinion. In fact, and I hope I have made it clear in this book, only a few systems out of an incredibly large number are well known, though not completely characterized.

This chapter is devoted to interfaces involving small organic molecules. We start with the ideal 0D case of a single molecule on an inorganic surface. The simple theoretical arguments from R. Hoffmann based on MOs will be discussed and complemented with experiments making use of STMs, demonstrating the incredible capabilities of this technique, which permits not only the chemical identification of such isolated molecules through the determination of their vibrational spectrum but the possibility of directly imaging the MOs in real-space. The 0D case will be followed by examples of the formation of small 2D aggregates, allowing molecule–molecule lateral interactions. Finally, the 2D case where molecules form ordered compact layers on top of the substrate surfaces within the ML regime will be analysed.

A ML can be simply defined as a one-molecule thick 2D film, but the molecular surface density has to be defined for each molecule–substrate system because it depends on the shape, size and relative orientation of the molecules. To clarify this point let us consider the examples of PTCDA and C60 on the Ag(111) surface. The surface density of the substrate is 1.4 × 1015 atoms cm−2, which is usually defined as 1 ML as a reference limit. The surface density of the (102) plane of PTCDA, the cleavage plane, is 8.4 × 1013 and 8.3 × 1013 cm−2 (molecules cm−2) for the monoclinic α and β polymorphs, respectively.

Table A.1 shows the symmetry operations of the point groups more commonly used in the book. The notation for the symmetry operations is the following:

1. E identity transformation

2. Cn proper rotation of 2π/n radians (n ∈ ℕ): the axis for which n is greatest is termed the principal axis

3. Sn improper rotation of 2π/n radians (n ∈ ℕ): improper rotations are regular rotations followed by a reflection in the plane perpendicular to the axis of rotation

4. i inversion operator (equivalent to S2)

5. σ mirror plane

6. σh horizontal reflection plane: perpendicular to the principal rotation axis

7. σv vertical reflection plane: contains the principal rotation axis

8. σd diagonal or dihedral reflection plane: bisects two C2 axes