53 Superconductivity Kevin A. Delin 53.1 Introduction Terry P. Orlando 53.2 General Electromagnetic Properties Massachusetts Institute of 53.3 Superconducting Electronics 53.4 Types of Superconductors 53.1 Introduction The fundamental idea behind all of a superconductor's unique properties is that superconductivity is a quantum mechanical phenomenon on a macroscopic scale created when the motions of individual electrons are corre- lated. According to the theory developed by John Bardeen, Leon Cooper, and Robert Schrieffer(BCS theory) nis correlation takes place when two electrons couple to form a Cooper pair For our purposes, we may therefore consider the electrical charge carriers in a superconductor to be Cooper pairs(or more colloquially, superelec rons)with a mass m* and charge twice those of normal electrons. The average distance between the two electrons in a Cooper pair is known as the coherence length, s. Both the coherence length and the binding energy of two electrons in a Cooper pair, 24, depend upon the particular superconducting material. Typically, the coherence length is many times larger than the interatomic spacing of a solid, and so we should not think of Cooper pairs as tightly bound electron molecules. Instead, there are many other electrons between those of a specific Cooper pair allowing for the paired electrons to change partners on a time scale of h/(2A)where h Planck's constant If we prevent the Cooper pairs from forming by ensuring that all the electrons are at an energy greater than the binding energy, we can destroy the superconducting phenomenon. This can be accomplished, for example, with thermal energy. In fact, according to the BCS theory, the critical temperature, T. associated with this 2△ ≈3.5 kaT where kg is Boltzmanns constant. For low critical temperature(conventional)superconductors, 24 is typically on the order of 1 meV, and we see that these materials must be kept below temperatures of about 10 K to exhibit their unique behavior. High critical temperature superconductors, in contrast, will superconduct up to temperatures of about 100 K, which is attractive from a practical view because the materials can be coole cheaply using liquid nitrogen. Other types of depairing energy are kinetic, resulting in a critical current density J e, and magnetic, resulting in a critical field He. To summarize, a superconductor must be maintained under the appropriate temperature, electrical current density, and magnetic field conditions to exhibit its speci properties. An example of this phase space is shown in Fig. 53.1 c 2000 by CRC Press LLC© 2000 by CRC Press LLC 53 Superconductivity 53.1 Introduction 53.2 General Electromagnetic Properties 53.3 Superconducting Electronics 53.4 Types of Superconductors 53.1 Introduction The fundamental idea behind all of a superconductor’s unique properties is thatsuperconductivity is a quantum mechanical phenomenon on a macroscopic scale created when the motions of individual electrons are corre￾lated. According to the theory developed by John Bardeen, Leon Cooper, and Robert Schrieffer (BCS theory), this correlation takes place when two electrons couple to form a Cooper pair. For our purposes, we may therefore consider the electrical charge carriers in a superconductor to be Cooper pairs (or more colloquially, superelec￾trons) with a mass m* and charge q* twice those of normal electrons. The average distance between the two electrons in a Cooper pair is known as the coherence length, j. Both the coherence length and the binding energy of two electrons in a Cooper pair, 2D, depend upon the particular superconducting material. Typically, the coherence length is many times larger than the interatomic spacing of a solid, and so we should not think of Cooper pairs as tightly bound electron molecules. Instead, there are many other electrons between those of a specific Cooper pair allowing for the paired electrons to change partners on a time scale of h/(2D) where h is Planck’s constant. If we prevent the Cooper pairs from forming by ensuring that all the electrons are at an energy greater than the binding energy, we can destroy the superconducting phenomenon. This can be accomplished, for example, with thermal energy. In fact, according to the BCS theory, the critical temperature, Tc , associated with this energy is (53.1) where kB is Boltzmann’s constant. For low critical temperature (conventional) superconductors, 2D is typically on the order of 1 meV, and we see that these materials must be kept below temperatures of about 10 K to exhibit their unique behavior. High critical temperature superconductors, in contrast, will superconduct up to temperatures of about 100 K, which is attractive from a practical view because the materials can be cooled cheaply using liquid nitrogen. Other types of depairing energy are kinetic, resulting in a critical current density Jc , and magnetic, resulting in a critical field Hc. To summarize, a superconductor must be maintained under the appropriate temperature, electrical current density, and magnetic field conditions to exhibit its special properties. An example of this phase space is shown in Fig. 53.1. 2 3 5 D k TB c ª . Kevin A. Delin Jet Propulsion Laboratory Terry P. Orlando Massachusetts Institute of Technology