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This Page Intentionally Left Blank

Chapter 9

Characteristic Parameters

Charles R Poole, Jr.

Department of Physics and Institute of Superconductivity,

University of South Carolina, Columbia, South Carolina

John E Zasadzinski and Roberta K. Zasadzinski

Physics Department, lllinois Institute of Technology, Chicago, lllinois

Philip B. Allen

Department of

Physics

and Astronomg~ State University of New York~

Stony Brook, New York

A. Introduction

434

Relationships between Parameters 434

Coherence Lengths and Penetration Depths

References for Sections A-C 442

Superconducting Gap Parameters 445

References for Section D 447

Critical Magnetic Fields 448

References for Section E 458

Critical Currents 473

References for Section F 473

Electron-Phonon Coupling Constants 478

a. Theoretical Background 478

b. Commentary on 2 Values 483

Acknowledgements 488

References for Section G 488

438

ISBN: 0-12-561460-8

$30.00

HANDBOOK OF SUPERCONDUCTIVITY

All rights of reproduction in any form reserved.

433

434 Chapter 9: Characteristic Parameters

Introduction

The main purpose of the present chapter is to present tabulations of data for the

important parameters of superconductors, such as coherence length ~, penetration

depth 2, energy gap Eg = 2A, critical fields B c, Bcl and Bc2 , critical current

density Jc, and electron-phonon coupling constant 2. Characteristic temperatures

T c are tabulated in Chap. 5 Tables 5-1 to 5-40. These various quantities are related

to each other through simple phonon BCS and high kappa (K = 2/~) expressions.

These will be reviewed in the next section, and then we will proceed to provide

various tabulations in succeeding sections. The materials will tend to appear in

the tables in the order: elements, binary compounds and alloys, Laves phases

(AB2), Chevrel compounds, A15 compounds (A3B), miscellaneous materials,

heavy electrons (heavy fermions), perovskites, borocarbides, organics, (buckmin-

ster)fullerenes, then lanthanum, yttrium-type, bismuth, thallium, and mercury-

type cuprates. When more than one reference is given for table entries the values

may be composites or averages. Values from Poole

et al.

(1988, 1995) are

generally averages.

Relationships between Parameters

In Section D of Chapter 4 we summarized the pedictions of the simple, isotropic,

phonon mediated BCS theory that are good approximations for many Type II

superconducting materials, and in Sections C and D of Chapter 12 we review the

high-K expressions for vortices that relate the various critical fields to the

characteristic lengths r and 2. In our earlier work [Poole

et al.

1995, Chap. 10,

Sect. 18] we defined an "ideal Type II superconductor" as a material, all of whose

parameters satisfy these simple relationships. Therefore if any two of the

characteristic parameters of a Type II superconductor are specified, then the

remainder can be estimated. We will assume that the transition temperature T c and

the Ginzburg-Landau parameter K are known and show how to calculate the

remaining properties for an isotropic superconductor, where MKS units are, of

course, used throughout this section.

The energy gap is given by the BCS relation

Eg = 3.528kB Tc .

(1)

The upper critical field Be2 can be equated to the Pauli limiting field (para-

magnetic limit or Clogston-Chandrasekhar limit) given by

Be2 -- Bpaul i - Eg/2~/2~B, (2)

B. Relationships between Parameters 435

and applying Eq. (1) we obtain

Bc2 = 1.83 T c.

(3)

The high-to vortex expression from Eq. (12-9),

Bc2 -- 27r~2,

(4)

where 00 =

h/2e

is the quantum of flux, provides the coherence length

-- (Oo/2rcBc2) 1/2,

(5)

and from the definition ~c = 2/~ of the Ginzburg-Landau parameter ~c, we obtain

the penetration depth 2:

2 = tc~. (6)

Equations (12-8) and (12-10), respectively, which are

O 0 ln~c

Be1- 47r22

(7)

(I) 0

Bc 2x/2~z2~ ' (8)

provide the thermodynamic and lower critical fields

Br -- Bc2/~/2~c

(9)

Bcl - B c In K/~/2~c. (1 O)

The critical current density Jc at 0 K is close to the depairing current density,

estimated from Eq. (12-13),

d~ = o~Bo/#os

(11)

where ~ ,~ 1. A better approximation to the upper limit of Jc is given by the

Ginzburg-Landau expression

Jcmax

2(1

t)l 3/2

10B

4~z2/.t 0

(12)

where t =

T/T c.

The "ideal" relationships of Eqs. (1)-(10) are fairly good first

approximations to the experimentally determined values of many typical Type II

superconductors. In contrast to this most measured supercurrent densities are far

less than the theoretical limiting values (11) and (12).