Superconductivity Of Metals And Alloys

P. G. De Gennes

• Publisher: CRC Press
• Year: 2018
• ISBN:
  9780429976667
• Edition: 1
• Topic: Sciences physiques
• Subtopic: Physique

Drawn from the author's introductory course at the University of Orsay, Superconductivity of Metals and Alloys is intended to explain the basic knowledge of superconductivity for both experimentalists and theoreticians. These notes begin with an elementary discussion of magnetic properties of Type I and Type II superconductors. The microscopic theory is then built up in the Bogolubov language of self-consistent fields. This text provides the classic, fundamental basis for any work in the field of superconductivity.

1

FUNDAMENTAL PROPERTIES

1–1 A NEW CONDENSED STATE

We take a piece of tin and cool it down; at a temperature T₀ = 3.7°K we find a specific heat anomaly (Fig. 1-1a). Below T₀ the tin is in a new thermodynamical state. What has happened?

It is not a change in the crystallographic structure, as far as x rays can tell. It is not a ferromagnetic, or antiferromagnetic, transition. (It can be seen by magnetic scattering of neutrons, that tin carries no magnetic moment on an atomic scale.) The striking new property is that the tin has zero electrical resistance. (For instance, a current induced in a tin ring has been observed to persist over times > 1 year.) We say that tin, in this particular phase, is a superconductor, and we call the permanent current a supercurrent.

A large number of metals and alloys are superconductors, with critical temperatures T₀ ranging from less than 1°K to 18°K. Even some heavily doped semiconductors have been found to be superconductors.

Historically, the first superconductor (mercury) was discovered by Kammerling Onnes in 1911.

The free energy F_S in the superconducting phase can be derived from the specific heat data and is represented on Fig. 1-1b (solid line). The dotted line gives the corresponding curve F_n for the normal metal. The difference ${({\text{F}}_{\text{S}}-{\text{F}}_{\text{n}})}_{\text{T}}=0$ is called the condensation energy. It is not of order k_BT₀ per electron; it is, in fact, much smaller, of order ${({\text{k}}_{\text{B}}{\text{T}}_0)}^2/{\text{E}}_{\text{F}}$ (where E_F is the Fermi energy of the conduction electrons in the normal metal). Typically E_F ~ 1 eV and k_BT₀ ~ 10⁻³ eV. Only a fraction ${\text{k}}_{\text{B}}{\text{T}}_0/{\text{E}}_{\text{F}}(~{10}^{-3})$ of the metallic electrons have their energy significantly modified by the condensation process.

Figure 1-1

(a) The electronic specific heat C of a superconductor (in zero magnetic field) as a function of temperature (qualitative plot). Above T₀ (in the normal phase) ${\text{C}}_{(}{}_{\text{per}\text{atom})}~{\text{k}}_{\text{B}}^2\text{T}/{\text{E}}_{\text{F}}$ where E_F is the Fermi energy. At the transition point T₀, C has a discontinuity. At ≪ T₀, C is roughly exponential C ~ exp (− 1.76 T₀/T). (b) Free energy of the superconducting phase (F_S) and of the normal phase (F_n) versus temperature. The two curves meet (with the same slope) at the transition point T = T₀. At T = 0 the difference F_n – F_S is of order ${({\text{k}}_{\text{B}}{\text{T}}_0)}^2/{\text{E}}_{\text{F}}$ per atom.

1–2 DIAMAGNETISM

The London Equation

We now extend our energy considerations to situations where there are supercurrents j_S (r) and associated magnetic fields h(r) in the sample.¹ We see that in the limit where all fields, currents, and so on, are weak and have a slow variation in space the condition of minimum free energy leads to a simple relation between fields and currents (F. and H. London, 1935).

We consider a pure metal with a parabolic conduction band; the electrons have an effective mass m. The free energy now has the following form:

$\mathcal{F}={\displaystyle \int {\text{F}}_{\text{S}}}\text{d}r+{\text{E}}_{\text{kin}}+{\text{E}}_{\text{mag}}$

(1-1)

where F_S is the energy of the electrons in the condensed state at rest and E_kin is the kinetic energy associated with the permanent currents. Let us call v(r) the drift velocity of the electrons at point r. It is related to the current density j_S by

${\text{n}}_{\text{S}}\text{e}v(r)={\text{j}}_{\text{S}}(r)$

(1-2)

(where e is the electron charge, and n_S the number of superconducting electrons per cm³). Then w...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Chapter 1 Fundamental Properties
• Chapter 2 Magnetic Properties of First Kind Superconductors
• Chapter 3 Magnetic Properties of Second Kind Superconductors
• Chapter 4 Description of the Condensed State
• Chapter 5 The Self-Consistent Field Method
• Chapter 6 Phenomenological Landau-Ginsburg Equations
• Chapter 7 Microscopic Analysis of the Landau-Ginsburg Equations
• Chapter 8 Effects of Strong Magnetic Fields and of Magnetic Impurities
• Index