Solid State Behavior

**Chapter 1**

**Abstract**

*Roberto Raúl Deza*

resonant crystal structures.

**1. Introduction**

**3**

spatiotemporal synchronization

(which do flow but at least at geological timescales).

ordered structure" explains easily those properties.<sup>1</sup>

Issues in Solid-State Physics

In the first sections, we bring into the present context some of our past contributions on the influence of quantum correlations on the formation of tightly bound solids. We discuss the effects of the overlap between neighbor orbitals in diverse situations of interest—involving both bulk and surface states—and call the reader's attention to an exact tight-binding calculation which allows gauging the errors introduced by the underlying hypotheses of the usual tight-binding approximation. We round up this part by reviewing a quantum Monte Carlo method specific for strongly correlated fermion systems. In the last section, we explore some nonequilibrium routes to (not necessarily tightly bound) solid state: we discuss spatiotemporal pattern formation in arrays of FitzHugh-Nagumo (FHN) neurons, akin to

**Keywords:** quantum correlations, band structure, tight-binding approach,

neighbor orbital overlap, fermion Monte Carlo, non-equilibrium pattern formation,

Since childhood, we all have an intuition of what a solid is. However, most properties we intuitively assign to solids come in a vast range. Diamonds—and some metals—are hard, and ordinary glasses are brittle; but vulcanized rubber is neither, and it is a solid too. Perhaps the best characterization is this: *at our human timescales, a solid does not flow*. That is why this category includes glasses and ice

Regarding their structure, a huge class of solids are *crystalline*. This is so to such extent that *solid state* came to be synonymous of crystalline structure, and the more comprehensive category of *condensed matter* (which admittedly includes condensed fluids or liquids) came into fashion. The name *crystal* was assigned in the late antiquity to precious and semiprecious stones that outstood for their transparency and diaphaneity. In fact, the modern meaning of the term as "an almost perfectly

Many solids we interact with—metals, stones, etc.—are random assemblies of grains, held together by strong adhesion forces. Like those of sand, quartz, or salt, those grains are very likely to be themselves crystals (which as said do not imply they are perfect: they may contain lots of impurities and defects). But there are two particular aspects of crystals we are concerned with here. The first is that

<sup>1</sup> For isolators like these, the bandgap is too large for visible light to be absorbed by creating electronhole pairs. Moreover, the absence of charge carriers rules out light scattering. Impurities provide localized midgap states, which favor two-step electron-hole pair creation by visible light.
