In the study of matter, both living and inanimate, the breakthrough discoveries and most scientists' intellectual obsessions often flow from what we call emergent behavior: phenomena not readily predictable from a detailed knowledge of the material subunits alone. We call systems that display emergent behavior complex adaptive matter, and their relevant organizing principles are unique to their scales of length and time. This issue of MRS Bulletin provides an overview of the aggregate of research on complex adaptive matter through a survey of five examples, ranging from intrinsically disordered electron matter in high-temperature superconductors to protein aggregates in amyloid diseases like Alzheimer's. We explain the philosophy and motivation for this research, noting that the study of emergent phenomena complements a globally reductionist scientific approach by seeking to identify, with intellectual precision, the relevant organizing principles governing the behavior. Our authors focus on the character of emergence for their particular systems, the role of materials research approaches to the problems, and the efforts to identify the organizing principles at work.

“Soft” condensed-matter science (also known as colloid chemistry) has revealed the nearly zoological complexity of long-lived structures that can arise from the competing interactions working in concert with thermal fluctuations both near and far from equilibrium. “Hard” condensed-matter science has revealed the stark beauty of elementary excitations shimmering on a placid quantum Fermi sea. The study of strongly correlated electronic states of matter is forcing us to unify these often disparate branches of materials science. Explaining confusing phenomena occurring in high-temperature superconductors and related materials seems to require that long-lived electronic structures be generated largely on their own, but perhaps with a little help from lattice disorder.We will explain the fruitful analogy between such systems and classical colloidal systems such as mayonnaise. Ordered crystalline, striped, or checkerboard phases and striped glasses emerge as candidate forms of highly correlated matter that may explain many puzzling observations of electronic materials.

High-temperature superconductivity in the cuprates emerges when the localized electrons of a Mott insulator become mobile due to carrier doping. Understanding both the electronic ground state and the excited states of these systems are key challenges in physics today. Angle-resolved photoemission spectroscopy (ARPES) and inelastic neutron-scattering (INS) studies have been remarkably successful in mapping the momentum-space characteristics of the cuprate electronic structure. However, since cuprate superconductivity develops from atomically localized electrons and exhibits nanoscale disorder, a pure momentum-space description is unlikely to be sufficient. Instead, simultaneous information on electronic structure at the nanoscale in real space, and throughout momentum space, is required. Here, we describe a combination of novel spectroscopic imaging scanning tunneling microscopy (SI-STM) techniques that we have developed to achieve these apparently contradictory aims, along with the outcome of a series of SI-STM studies of the electronic structure of Bi2Sr2CaCu2O8+x.

We discuss three examples of emergent behavior in correlated electron matter, in which the discovery of scaling of several measured quantities with a single energy scale provides a key clue to a common magnetic origin: the emergence of itinerant (mobile) electronic behavior from the Kondo lattice of localized f electrons found in cerium- and uranium-based heavy fermion materials; the emergence of unconventional superconductivity in the cuprate and “high-temperature” heavy electron Ce- and Pu-based 1-1-5 superconductors; and the emergence of pseudogap behavior in the underdoped and optimally doped cuprate superconductors.We conclude with some speculation on ways in which these novel perspectives might be used to design new materials.

Geometric frustration occurs when a set of degrees of freedom is incompatible with the space it occupies. A purely geometric example is the impossibility of close-packing pentagons in two dimensions. Another simple example is atomic magnetic moments with antiferromagnetic interactions. These moments lower their interaction energy by pointing antiparallel to their neighbors, an arrangement incompatible with the occupation of a crystal lattice of triangular symmetry. Other manifestations of frustration occur in ice, glass, liquid crystals, and correlated metals. Because frustration governs the rules of packing, examples are also found in biological materials, as in the self-assembly of liposomes that form nanotubules. Geometric frustration is essentially “many-body” in nature: the basic concept is trivial on the scale of three particles, but complex and anharmonic for an Avogadro's number of particles. In fact, geometrically frustrated systems are so anharmonic that no general theoretical framework exists to explain their collective behavior. This article will explore the basic concepts of geometric frustration and illustrate these concepts with examples from magnetism, crystal structures, and molecular systems.

Numerous human diseases are associated with conformational change and aggregation of proteins, including Alzheimer's, Parkinson's, prion diseases (such as mad cow disease), familial amyotrophic lateral sclerosis (ALS, or Lou Gehrig's disease), Huntington's, and type II (mature onset) diabetes. In many cases, it has been demonstrated that conformational change and aggregation can occur outside living cells and complex biochemical networks. Hence, approaches from materials and physical science have enhanced our understanding of the role of protein aggregation in these diseases at the molecular and nanoscale levels. In this article, we will review what is known about these protein structures from the perspective of materials science, focusing on the details of emergent oligomeric and nanotube-like structures, their interactions with model lipid bilayers, how the structures relate to observed biological phenomena, and how protein aggregation and amyloid formation can be employed for the good in biology and materials science.