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Section 1: Introduction

The term emergent behavior refers to the collective phenomena observed in macroscopic systems that are distinct from their microscopic constituents. It is brought about by the interaction of the microscopic constituents with one another and with their environment. Whereas the Standard Model of particle physics described in Units 1 and 2 has enjoyed great success by building up systems of particles and interactions from the ground up, nearly all complex and beautiful phenomena observed in the laboratory or in nature defy this type of reductionist explanation. Life is perhaps the ultimate example. In this unit, we explore the physics of emergent phenomena and learn a different approach to problem solving that helps scientists understand these systems.

New experimental probes, such as angle-resolved photoemission spectroscopy (ARPES) enable us to study emergent behavior in quantum matter at an unprecedented level of detail. ARPES is an experimental technique to observe the distribution of the electrons (more precisely, the density of single-particle electronic excitations) in the reciprocal space of solids.

Figure 1: New experimental probes, such as angle-resolved photoemission spectroscopy (ARPES) enable us to study emergent behavior in quantum matter at an unprecedented level of detail. ARPES is an experimental technique to observe the distribution of the electrons (more precisely, the density of single-particle electronic excitations) in the reciprocal space of solids.

Source: © Wikimedia Commons, Public Domain. Author: Saiht, 15 June 2009. More info

Understanding emergent behavior requires a change of focus. Instead of adopting the traditional reductionist approach that begins by identifying the individual constituents and interactions of a system and then uses them as the basic building blocks for creating a model of a system's behavior, we must focus on identifying the origins of the emergent collective behavior characteristic of the system. Thus, in creating models of quantum matter, we use the organizing principles and concepts responsible for emergent quantum behavior as our basic building blocks. These new building blocks, the collective organizing principles, represent gateways to emergence.

Certain aspects of emergent behavior are considered "protected," in the sense that they are insensitive to the details of the underlying microscopic physical processes.

Much of this unit deals with the phenomenon of superconductivity, where electrical current can flow with absolutely no resistance whatsoever. Unraveling the mystery of how electrons (which experience a repulsive electrical interaction) can cooperate and produce coherent collective phenomena is a detective story that is still being written.

To build a little intuition about the subtle interactions that give rise to superconductivity (and the related phenomenon of superfluidity), and to set the stage for what follows, imagine two electrically charged bowling balls placed on a spring mattress. They experience a repulsive electrostatic interaction, but the indentation in the mattress made by one of the bowling balls can influence the other one, producing a net attractive force between them. This is crudely analogous to the direct interactions between electrons and their coupling to the excitations of the crystal lattice of a superconducting metal: an attractive interaction between electrons can result if the interaction between each electron and the excitations of the embedding lattice is strong enough to overcome the electrostatic repulsion and this interaction can give rise to the pairing condensate that characterizes the superconducting state.

Another concept that will arise in this unit is the notion of a "quasiparticle." The concept of a quasiparticle arises in a simplifying framework that ascribes the combined properties of an electron and its modified surroundings into a "virtual" equivalent composite object that we can treat as if it were a single particle. This allows us to use the theoretical toolkit that was built up for the analysis of single particles.

As shown in the figure, dimensionality can influence dramatically the behavior of quasiparticles in metals.

Figure 2: As shown in the figure, dimensionality can influence dramatically the behavior of quasiparticles in metals.

Source: © Joseph Sulpizio and David Goldhaber-Gordon, Stanford University. More info

As we will see below, both the superfluid state of 3He and the superconducting states of metals come about because of quasiparticle pairing processes that transform a collection of fermions (the nuclei in the case of superfluid 3He, and electrons in the case of superconductivity) into a collective, coherent single quantum state, the superfluid condensate. This exhibits the macroscopic quantum mechanical effects of a superfluid flowing with no dissipation, and of the flow of electrical current with literally zero resistance, in a superconductor.

Understanding the subtle interactions that give rise to the pairing of fermions requires looking at the fluids and materials in a different way.

Our change in focus means, in general, that instead of following the motion of single particles in a material, we will focus on the behavior of the material as a whole—for example, the density fluctuations found in bulk matter. A simple example of a density fluctuation is a sound wave traveling through a medium such as air, water, or a solid crystal. Just as light can equally well be described as fluctuations of the electromagnetic field whose quantized particles are called "photons," the collective density fluctuations in crystalline solids can be described by quantized particles called phonons. Analogously to the particle interactions described in Unit 2, the electronic density fluctuations can couple to phonons and other fields, and the interaction between the density wave and various fields can represent both the influence of particle interactions and the external probes used to measure systems' behavior. We will also be interested in the spin fluctuations of fermions, which are particles with half-integer spin.

This unit will introduce the frontiers of research in the study of emergent behavior in quantum matter and call attention to the applicability of some key organizing principles to other subfields in physics. Sections 2 through 5 present what we might call "old wine in a new bottle"—an emergent perspective on subject matter described in many existing texts on quantum matter, while the last three sections highlight the frontiers of research in the field.

In the two sections devoted to superconductivity, I have gone to some length to sketch the immediate emergent developments that led up to the historic paper in which Bardeen, Cooper, and Schrieffer described their microscopic theory known as BCS. I have done so, in part, because I can write about these from personal experience. But I also believe that learning how a major problem in physics was finally solved after 45 years of trying might help nonscientists and would-be scientists appreciate the complex process of discovery and provide encouragement for young researchers seeking to solve some of the most challenging problems that our community faces today.