Tutorial 4 the bcs theory of superconductivity june 1, 2015 in the lectures you saw a phenomenological analysis of superconductors. The second order phase transition at t c ginzburg and landau, 1950. Electronic structure, bcs beschreibung des supraleitenden zustands. A microscopic theory of superconductivity was developed in 1957 by john bardeen, leon cooper and j. Historically, this approach has been very successful. London and london derived a phenomenological theory of superconductivity which correctly describes the meissner e ect. What links here related changes upload file special pages permanent link page information. In 1957, more than 40 years after the discovery of superconductivity, three physicists, bardeen, cooper and schrieffer, finally found the correct explanation to superconductivity in metals.
Consider two electrons that interact with each other via an attractive potential vr 1 r. A floquet bcs gap equation is derived which calls for a numerical solution and does not permit closed analytic results. Bcs theory of superconductivity the properties of type i superconductors were modeled successfully by the efforts of john bardeen, leon cooper, and robert schrieffer in what is commonly called the bcs theory. Bcs theory applies directly to superconductors such as nb3ge tc 23k in which the electrons are bound together by their interaction with the vibrations of the underlying lattice. The timetested bcs theory of superconductivity is generally accepted to be the correct theory of conventional superconductivity by physicists and, by extension, by the world at large. Bcs theory bcs theory of superconductor was put forward by bardeen, cooper and schrieffer in 1957 and hence named as bcs theory. The reader will master london theory and the pippard equations, and go on to understand type i and type ii superconductors their thermodynamics, magnetic properties, vortex dynamics, current transport, cooper pairs and the. Topology and geometry for physics, the fundamentals of density functional theory, the particle world of condensed matter, theory of superconductivity. Levy, magnetism and superconductivity springer, 2000 1. Schrieffer their surname initials providing the designation bcs to explain the behaviour of superconducting materials.
Bcs wave function, energy gap and quasiparticle states. In a superconductor, the majority of these electrons merge in order to form a large collective wave. Superconductivity and bcs theory max planck institute. Find materials for this course in the pages linked along the left. As we have seen, phonons mediate an attraction between electrons. In this macroscopic quantum state, the electrons form. Furthermore, bcs theory has proven unable to predict any new superconducting compounds. The main point of the bcs theory is that the attractive electronelectron interaction mediated by the phonons gives rise to cooper pairs, i. Much of the physics involved in the bcs theory can be discussed in the context of a simple quantum mechanics problem.
The bcs theory is, in its simplest form, actually contradictory to our crude macroscopic view expressed earlier. Eremin, maxplanck institut fur physik komplexer systeme, dresden, germany. Verify that the link points to the correct file and location. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. A key conceptual element in this theory is the pairing of electrons close to the fermi level into cooper pairs through interaction with the crystal lattice. Apr 16, 2017 this video lecture will explain the bcs theory of superconductivity.
Hence it predicts that superconductivity and high transition temperatures will occur in materials with strong electronphonon interaction as evidenced eg by large temperature dependence of the normal. Superconductivity and the bcs theory mapping ignorance. Theory of superconductivity advanced books classics. In the first part, a general equation for the superconductivity is. This theory could explain the effects such as zero resistivity, meissner effect, isotopic effect etc.
In typical type i superconductors, this force is due to coulomb attraction between the electron and the crystal lattice. The microscopic theory of superconductivity is an excellent example of a steady seventy years progress towards this goal which is still further going on. A general theory of superconductivity with points of view differing from those of the bcs theory is presented in two parts. The authors of the bcs theory, as it is known, received the nobel prize for their work in 1972. The scmaglev superconducting maglev formerly called the mlu is a magnetic levitation maglev railway system. Landaus theory of second order phase transition formulated in 1950, before bcs masterpiece of physical intuition grounded in thermodynamics even after bcs it still is very fruitful in analyzing the behavior of superconductors and is still one of the most widely used theory of superconductivity. The band theory of metals has been subjected to experimental tests many times and is now the accepted model of the behaviour of conductors and insulators. Superconductivity and bcs theory introduction electronphonon interaction, cooper pairs bcs wave function, energy gap and quasiparticle states predictions of the bcs theory limits of the bcs gap equation. A primer, microscopic theory of superconductivity, the essentials of dft and fplo, high tc superconductors. Bcs theory is unable to predict new superconductors because it assumes that superconductivity is associated with the electronphonon interaction. The discussion of cooper pairs, the foundation for bcs theory, though not difficult to read, is easier to understand after going through gordon bayms discussion of this topic in lectures on quantum mechanics lecture notes and supplements in physics. Here we will discuss a new ground state of the interacting electron gas.
The theory is also used in nuclear physics to describe the pairing. We will then calculate and study interesting quantities of the superconducting system, and nally describe how the results predicted by the bcs theory fare against experimental evidence obtained about superconductors. This book proposes a thorough introduction for a varied audience. In this work, we aim to obtain a rather general and explicit analytical result to illustrate the drivinginduced elevation of the critical temperature of a normal superconductor by extending the conventional bcs theory. Introduction in these lectures i want to give an introduction into the physical principles of superconductivity and its fascinating properties. The bcs theory makes a crucial assumption at the beginning. But it has to be modified when it comes to superconductivity. With the discovery of materials that went superconducting at temperatures above the theoretical limit imposed by bcs theory see history, there was and still is much debate as to what the mechanism of superconduction in these compounds might be one explanation involves the use of holes within the superconductor many high t c superconductors are. Lecture notes on superconductivity a work in progress. We start with a general hamiltonian that describes manyfermion system interacting via a spinindependent. In particular, you saw that given some empirical results, many additional predictions can be made using the ginzburglandau formalism. Prior to this, there was ginzburglandau theory, suggested in 1950, which was a macroscopic theory.
Electron lattice interaction via lattice deformation. The central feature of the bcs theory is that two electrons in the superconductor are able to form a bound pair called a cooper pair if they somehow experience an attractive interaction between. It envisions resistancefree conduction of coupled pairs of electrons called cooper pairs. Click download or read online button to get new theory of superconductivity book now. Free superconductivity books download ebooks online. We will look at features of superconductors before the discovery of the bcs theory, and examine the assumptions and methods used to develop the theory. Fernandes here we will discuss a new ground state of the interacting electron gas. Bcs theory of superconductivity hyperphysics concepts. John schieffers book was written for solid state physicists with more than just a casual interest in superconductivity. Concepts of fermi liquid theory and instability of the normal state.
M2icfp 20172018 the bcs theory of superconductivity bardeen. The bcs theory has been used to successfully explain the following experi mental results. Superconductivity and the bcs theory syed ali raza. The bcs theory of superconductivity has successfully described the measured properties of type i superconductors. Bcs theory of superconductivity john bardeen leon neil cooper john robert schrieffer of the prize of the prize of the prize usa usa usa university of illinois urbana, il, usa brown university providence, ri, usa university of pennsylvania philadelphia, pa, usa b. The reduction of the energy gap as you approach the critical temperature can be taken as an indication that the charge carriers have some sort of collective nature. This theory is remarkable enough that it is interesting to look at the chain of ideas which led to it. Each of these electrons is relatively independent and follows its own path independent of other electrons. As discussed earlier, superconductivity arises because electrons do not interact destructively with atoms in the crystal lattice of the material.
This paper suggests the possibility that bcs theory itself as the theory of conventional superconductivity may require a fundamental overhaul. The theory describes superconductivity as a microscopic effect caused by a condensation of cooper pairs. More detailed accounts can be found in the excellent text books by w. The contrasting behavior of nmr relaxation rate with ultrasound absorption is explained in a natural manner by the pair nature of bcs wave function, providing proof of this central concept of the bcs theory. Bcs theory or bardeencooperschrieffer theory is the first microscopic theory of. Robert schrieffer, which is known as the bcs theory. Electronic structure, bcsbeschreibung des supraleitenden zustands. In 1957, bardeen, cooper and schrieffer bcs proposed a theory that explained the microscopic origins of superconductivity, and could quantitatively predict the properties of superconductors. The superconducting properties of small specimens 9. New theory of superconductivity download ebook pdf, epub. In this section, we will see how superconductivity emerges in an electron gas with attraction the theory. For comparison, the resistivity of copper at room temperature is.
The remaining four chapters are devoted to the simplest phenomenological weak coupling theory of superconductivity on a microscopic level, the bcs theory, which provided the. We will then calculate and study interesting quantities of the su. Bcs theory finite temperatures the model hamiltonian bogoliubovvalatintransformation calculation of the condensation energy bcs theory having seen that the fermi sea is unstable against the formation of a bound cooper pair when the net interaction is attractive, we must then expect pairs to condense until an equilibrium point is reached. I outline an alternative to conventional bcs theory proposed to apply to all superconductors, conventional. The theory of superconductivity introduced by ginzburg and landau is a macroscopic theory, and the bcs theory is a suitable limit to it at the microscopic scale. The second essential observation was that superconductors not only prevent a magnetic. The main idea of the bcs theory relies on the quantum nature of electrons. E physics 460 f 2000 lect 23 26 superconducting transition tc bcs prediction. Theory of superconductivity problem set 10 exercise 12 diagonalization of the bcs hamiltonian. This video lecture will explain the bcs theory of superconductivity.
The bcs theory says that electrons do actually interact with the atoms, but constructively. In a theoretical model that has since been called bcs, after their initials, they proposed the following explanation. Bcs theory, in physics, a comprehensive theory developed in 1957 by the american physicists john bardeen, leon n. Free superconductivity books download ebooks online textbooks. Bcs theory or bardeencooperschrieffer theory named after john bardeen, leon cooper, and john robert schrieffer is the first microscopic theory of superconductivity since heike kamerlingh onness 1911 discovery. Phonon mediated attractive interaction and the cooper pairs. Lecture notes applied superconductivity electrical. By the di nition of magnetic work the rst law of thermodynamics for a magnetic material becomes. Brief introduction to superconductivity pdf 69p covered topics are discovery and first insights, the physics of the cooper pairs, bcs theory of superconductivity, characteristics of the superconducting state, the strong coupling theory, hightc superconducting materials, crystal structures, superconducting properties, models on the mechanism. These lectures attempt at a concise description of what has been achieved so far in this direction.
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