Superconductivity and related macroscopic quantum phenomena John H. Miller, Jr., from the University of Houston, Dept. of Physics and Texas Center for Superconductivity, walks us through superconductivity and related macroscopic quantum phenomena. Quantum behavior applies not only to microscopic but also to macroscopic systems. Spin-½ particles, fermions, obey the Pauli Exclusion Principle, whereby no two can occupy the same quantum state. By contrast, many integer-spin particles, bosons, can condense into a single macroscopic state. In a superconductor (1), below its critical temperature or Tc , electrons condense into an electronic superfluid that flows with no resistance. For electrons (spin- ½) to condense, they must form pairs. There is one problem, however. Electrons normally repel each other.
Superconductivity and related macroscopic quantum phenomena John H. Miller, Jr., from the University of Houston, Dept. of Physics and Texas Center for Superconductivity, walks us through superconductivity and related macroscopic quantum phenomena. Quantum behavior applies not only to microscopic but also to macroscopic systems. Spin-½ particles, fermions, obey the Pauli Exclusion Principle, whereby no two can occupy the same quantum state. By contrast, many integer-spin particles, bosons, can condense into a single macroscopic state. In a superconductor (1), below its critical temperature or Tc , electrons condense into an electronic superfluid that flows with no resistance. For electrons (spin- ½) to condense, they must form pairs. There is one problem, however. Electrons normally repel each other.
As we all know, single microscopic particles such as electrons or atoms do not behave according to the familiar classical (Newtonian) physics which describes the everyday world, but rather according to the prescriptions of quantum mechanics, the outcome is often bizarre and counterintuitive. When a macroscopic number of such particles (say ∼ 10) is assembled under conditions where the effects of quantum mechanics are important, the results can be even more spectacular; they include macroscopic phenomena such as superfluidity and superconductivity, which are completely impossible to explain in classical terms. Most, though not all of these exotic phenomena, are a result of a phenomenon which I shall refer to generically as “quantum condensation,” in which a macroscopic number of particles or pairs of particles—a nonzero fraction of all particles present—occupy a single quantum state; this phenomenon is traditionally referred to as Bose-Einstein condensation (BEC) when it occurs in a system of bosons such as liquid He, and as Cooper pairing when it occurs, for pairs of particles, in a system of fermions such as the electrons in a superconducting metal. As a result of quantum condensation, the characteristically quantum-mechanical behavior which we are used to seeing at the level of single electrons is as it were amplified by the cooperation of condensed particles and can manifest itself at the macroscopic level. The present essay is intended as a general introduction to the subject of quantum condensation and its consequences, as manifested in a variety of physical systems. I will try to review the fundamental physical ideas, usually without de-
Collective quantum phenomena and their applications John H. Miller, Jr., University of Houston (UH), from the Dept. of Physics and Texas Center for Superconductivity, explains collective quantum phenomena and their applications. The evidence supporting the quantum behavior of electrons, as well as every other known particle in the universe, is overwhelming. On the centennial anniversary of Max Planck’s seminal paper on energy quantization (1), Kleppner and Jackiw pointed out, “Quantum theory is the most precisely tested and most successful theory in the history of science”. (2)
We have seen in Chapter 3 , that as temperature is increased quantum statistics, both Bose-Einstein or Fermi-Dirac, tend to classical. High temperatures blur out quantum effects in a system, which can be safely described in classical terms. In this chapter, we will consider some systems which manifest quantum properties at macroscopic level, but at very low temperatures. We recall that helium is the only substance which remains liquid at low temperature, down to absolute zero (see Chapter 6 ), a phenomenon related to the quantum behavior of its constituent atoms. Liquid helium was instrumental to the discovery that some metals are able to sustain an electrical current for long periods of time without any driving force. This phenomenon is named superconductivity, and is also a macroscopic manifestation of the quantum behavior of the electrons in metals. Later on it was discovered that liquid helium itself shows a similar property, named superfluidity, consisting in its ability to flow through a capillary without viscosity. Hence, a persistent flow of liquid can be maintained without any driving force. While the quantum agents of superconductivity are electrons, which are spin- 1/2 fermions, those of superfluidity are 4 He atoms, which are spin- 0 bosons. There are other systems able to display similar behavior as liquid 3 He, atomic nuclei and nuclear matter. In fact, superfluidity and superconductivity are new phases of matter related to the bosonic character of 4 He atoms or of pairs of fermions (either electrons, 3 He atoms or nucleons), the same as Bose-Einstein condensation in ultracold atomic gases. The temperatures where these new phases manifest range from 165 K for superconductivity down to a few nano-Kelvin for Bose-Einstein condensation.
A system composed of particles, whose quantum mechanical zero point energy is large compared to their interaction energy, does not solidify even at absolute zero temperature and remains a so-called quantum liquid. Typical examples of such systems are conduction electrons in metals and liquid helium. Many conductors undergo a phase transition at their critical temperature T c and become superconducting below it. Similarly, liquid 4 He under its vapour pressure becomes a superfluid at T c = 2.17 K ( T λ is often used instead of T c ), and liquid 3 He at T c = 0.9 mK. Although the phenomena are called superconductivity for a charged system like conduction electrons, and superfluidity for a neutral system like liquid helium, they are characterised by the same basic property that the wave nature of the particles manifests itself on a macroscopic scale, as we shall see below. Phenomena The most important factor in determining the properties of a quantum liquid is the statistics of the constituent particles. Liquid 3 He becomes a typical Fermi liquid below 0.1 K and a superfluid below a few mK, in contrast with the bosonic liquid 4 He mentioned above. The two superfluids are quite different both phenomenologically and microscopically. Table 1.1 shows systems which exhibit, or are predicted to exhibit (in brackets), superconductivity or superfluidity. In the case of fermion systems pair formation is responsible for the phenomena so that their properties differ according to the pairing type.
Bose-Einstein condensation, superfluidity, and superconductivity are quantum mechanics made visible. They mark the boundary between the classical and the quantum worlds, and they show the macroscopic role of quantum mechanics in condensed matter. This book presents these phenomena in terms of particles, their positions, and their momenta, giving a concrete visualisation and description that is not possible with traditional wave functions. A single approach that bridges the classical-quantum divide provides new insight into the role of particle interactions in condensation, the nature of collisions in superfluid flow, and the physical form of Cooper pairs in high-temperature superconductors. High-temperature superconductivity is explored with quantum statistical mechanics, which links it to Bose-Einstein condensation. Identifying a new mechanism for Cooper pairing, this explains the differences between the low- and high-temperature superconducting regimes and the role of the molecular structure of the conductor. The new perspective offered by this book on Bose-Einstein condensation, superfluidity, and high-temperature superconductivity gives particle-based explanations as well as mathematical and computational methods for these macroscopic quantum phenomena so that readers understand the role of particle interactions and structure in the physics of these phenomena. This book will appeal to undergraduate and graduate students, lecturers, academics, and scientific researchers in the fields of Bose-Einstein condensation and condensates, superfluidity, and superconductivity. It will also be of interest to those working with thermodynamics, statistical mechanics, statistical physics, quantum mechanics, molecular dynamics, materials science, condensed matter physics, and theoretical chemistry. Key Features: · Explores Bose-Einstein condensation with new evidence for multiple condensed states and novel Monte Carlo simulations for interacting bosons · Establishes the thermodynamic nature of condensed bosons from an analysis of fountain pressure measurements, including that they carry energy and entropy, and the thermodynamic principle of superfluid flow · Derives equations of motion for condensed bosons, and performs molecular dynamics simulations of the viscosity with molecular trajectories that give rise to superfluidity · Identifies the mechanism for electron pairing in high-temperature superconductivity
Abstract Starting from first principles, this book introduces the closely related phenomena of Bose condensation and Cooper pairing, in which a very large number of single particles or pairs of particles are forced to behave in exactly the same way. Their consequences in condensed matter systems are also explored. Eschewing advanced formal methods, the book uses simple concepts and arguments to account for the various qualitatively new phenomena which occur in Bose-condensed and Cooper-paired systems, including but not limited to the spectacular macroscopic phenomena of superconductivity and superfluidity. The physical systems discussed include liquid 4-He, the BEC alkali gases, “classical” superconductors, superfluid 3-He, “exotic” superconductors, and the recently stabilized Fermi alkali gases.