# k B = JK 1 = ev K 1 m p = kg m n = kg a 1 = h 2 /m 0 e 2 = m

## Full text

(1)

### Physical Constants

Units

Angstrom 1 ˚A = 1010m (∼size of an atom)

Fermi 1 fm = 1015m (∼size of a nucleus)

Electron-volt 1 eV = 1.60218×10−19J←→11 600 K Magnetic induction tesla (1 gauss←→10−4tesla)

Fundamental Constants

Planck constant h=6.6261×1034J s

¯

h=h/2π=1.05457×1034J s Speed of light c=299 792 458 m s1

Vacuum permeability μ0=4π×107H m1 (ε0μ0c2=1)

Boltzmann constant kB=1.38066×10−23J K−1=8.6174×10−5eV K−1 Avogadro number NA=6.0221×1023

Electron charge e=1.60218×10−19C Electron mass m0=9.1094×10−31kg

Proton mass mp=1.67262×10−27kg

Neutron mass mn=1.67493×10−27kg

Fine structure constant α=e2/hc¯ =1/137.036 (dimensionless)

Classical electron radius re=e2/m0c2=2.818×1015m Compton wavelength λc=h/m0c=2.426×1012m of the electron

Bohr radius a1= ¯h2/m0e2=0.52918×1010m Hydrogen ionisation energy EI=m0e4/2h¯2=α2m0c2/2=13.6057 eV Bohr magneton μB=qeh¯/2m0= −9.2740×10−24J T−1

= −5.7884×105eV T−1 Nuclear magneton μN=qh¯/2mp=5.0508×1027J T−1

=3.1525×108eV T1

H. Alloul,Introduction to the Physics of Electrons in Solids, Graduate Texts in Physics, DOI 10.1007/978-3-642-13565-1, cSpringer-Verlag Berlin Heidelberg 2011

593

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(3)

EulerFunction

=

0

xt1exdx=

=

!

/

=√

π

RiemannζFunction

ζ

=

n=1

nt

### with some specific values

t 2 3 4

ζ π2/6 1.202 π4/90

Integrals of the Fermi–Dirac Function

f

=

ex+

df/dx=

2

0

f

=

0 −

/dx)x dx=

t>

0

f

t1dx=

0

xt1

ex+

dx=

0

xt

2

dx=

−21t

### )(t)ζ (t), which yields some specific values

595

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596 Appendix B Some Useful Functions and Relations

0

f

=

0

x2

2

dx=

ζ

=π2

0

f

2dx=

0

x3

2

dx=

ζ

0

f

3dx=

0

x4

2

dx=

ζ

=

π4

Bessel Functions

α

x2d2y

dx2+xdy

dx+

2α2

=

α) or

α

### The Bessel functions

of the first kind Jn

n

x

x→ ∞

Jn

=

π

π

0

xsinu)du

Jn

=(−1)nJn

n

x

J0

x2

Jn

n!

x

n

x→ ∞

Jn

πx 1

2

x

π

eixsinφ=

n=−∞

Jn

inφ

### The

modified Bessel functions of orderα

x2d2y

dx2+xdy

dx

2+α2

=

### 0.

(5)

Appendix B Some Useful Functions and Relations 597

Kn

### (x),with integer

n, are solutions which diverge

x

### 0, and vanish exponentially for

x→ ∞. Their integral representation is

Kn

=

inπ

−∞

nt)dt

Kn

=Kn

x

K0

≈ −

Kn

x

n

x→ ∞

Kn

πx 1

2

d

dx

xnKn

= −xnKn−1

dK0/dx= −K1= −K1

(6)
(7)

### Standard Notation

A(T,μ) Grand canonical potential

M Atomic mass

I Electric current

T Temperature

U Internal energy

V Potential difference

Z Atomic number

ZG(T,μ) Grand partition function

e Electron charge

h Planck constant (=2πh)¯

kB Boltzmann constant

s Electron spin (s=1/2)

Φ Flux of magnetic induction around a contour (C)

β Reciprocal ofkBT

χ,χ˜ Magnetic susceptibility (χ˜=μ0χ)

δ(x) Dirac delta

δij Kronecker delta

γ Gyromagnetic ratio

μ Chemical potential

μB Bohr magneton

A Vector potential

Ba Applied magnetic induction (=μ0Ha)

F Force

Ha Applied magnetic field

M Magnetisation

j Electric current density

k Wave vector

pi Momentum ofith electron vi Velocity ofith electron

μ Atomic magnetic moment

599

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(9)

### Specific Notation

ak0,k1 Atomic form factor [=f(k1k0)]

BJ(x) Brillouin function with total angular momentumJ as a function ofx=gJμ0μBHa/kBT

Ce(T) Specific heat •electronic

Cn •in normal metal state

Cs •in superconducting state

Cv •at constant volume

D Coefficient characterising magnetic anisotropy energy per ion (seeK) D(E) Density of states•of energyEper atom and per spin direction Dd(E) •of a free electron gas inddimensions

Ds(E) •excited in the superconducting state

DΩ(E) •of energyEper unit volume

Dχ •at the Fermi level obtained by the Pauli susecptibility Dc •at the Fermi level obtained by the specific heat Dc(E−Ec) •of the conduction band of a semiconductor Dv(E−Ec) •of the valence band of a semiconductor E1,E2,...En Atomic energy levels

Ev Atomic energy level of a valence electron

Ek Electronic energy of state with quasi-momentumk(single band)

EF Fermi energy

EZ Energy of Zeeman coupling between magnetisation and magnetic field

Ed Demagnetisation energy

Ean Anisotropy energy as a function of orientation ofM(seeHA) Ewall Energy of a Bloch wall per area of primitive cell

Ec Energy at minimum of conduction band (semiconductor) Ev Energy at maximum of valence band (semiconductor) Ec Condensation energy in superconducting state Eg Semiconductor band gap (=EcEv)

Eh Energy of hole

Gs(T,Ha) Gibbs free energy•of superconducting state

Gn(T,Ha) •of normal metal

Gsf(T,Ha) •of superconducting film

Gms(T,Ha) •of mixed state

601

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602 Appendix D Specific Notation Hc,Hc(T) Critical thermodynamic field of a superconductor

Hc Critical field of thin superconducting film Hc1 Lower critical field for type II superconductor Hc2 Upper critical field for type II superconductor

ˆ

HrfZ Hamiltonian for Zeeman coupling with a radiofrequency field ˆ

HA Magnetic anisotropy Hamiltonain, e.g.,HA=D

R(SzR)2

HK Anisotropy field

Hd Demagnetising field

Ic Critical current of a Josephson junction

J Total angular momentum of an atomic state (J=L+S) JNN Current in tunnel junction•between two normal metals

JNS •between normal metal and superconductor

J Exchange interaction•between two spinsS1andS2

J0 •interatomic

K Magnetic anisotropy coefficient= −NDS2= −DM20/Ng2μ20

L Spatial dimensions of a macroscopic crystal L Latent heat at normal–superconducting transition

L Lorenz number

L T,M(r)

Ginzburg–Landau functional L(T,Mz) Landau function

M0(T) Spontaneous magnetisation of ferromagnet Ms Magnetisation at saturation

Malt Alternating magnetisation in antiferromagnet with two sublattices Ne Number of electrons in solid

Nn Number of atomic nuclei in solid

N Demagnetisation tensor

Pi Momentum ofith atomic nucleus RW Wilson ratio relatingχPandCein metal Ss Entropy •of superconducting state

Sn •of normal state

S(k) Structure factor (primitive cell) Tc Critical temperature of superconductor

TC Curie temperature

TN N´eel temperature

T1 Relaxation time •spin lattice

T2 •spin–spin

ˆ

TRi Operator effecting translation of crystal lattice byRi

U(r) Magnetic potential

V(r1r2) Interaction between two electrons atr1andr2

Vat Atomic potential

VK Fourier component of periodic potential for vectorKof reciprocal lattice Vc(r) Coulomb potential

Vk Fourier component of attractive potentialV(r1r2) between two electrons due to electron–phonon interaction

(11)

Appendix D Specific Notation 603 V0 Interaction between electrons due to electron–phonon coupling

in point interaction limit

a Distance between nearest neighbour atoms c Specific heat capacity per particle

d Width of tunnel barrier

f(E) Fermi population factor

gJ Land´e factor of electron in ground state with total angular momentumJ

jen Energy flux

Mean free path •of particle

e •of electron

(me)αβ Effective electron mass tensor [(mh)αβfor hole]

me Effective mass •of electron (isotropic case)

m •of charge

m(t) Magnetic response to pulse excitation att=0 n Band index (band structure of solid) norne Number density•of conduction electrons

np •of Bravais lattice points

ns •of electrons condensed in superconductor

nh •of holes in semiconductor

q Electric charge of pair in superconductor (q= −2e) t1 Hopping integral •between nearest neighbours

tn, •between sitesnand

un,k(r) Coefficient of eik·rin Bloch functionψn,k(r) v Volume of primitive cell in crystal

vF Electron velocity at Fermi level z Number of nearest neighbours of atom

k Width •of wave packet in quasi-momentum space

r •of wave packet in real space

Δ Supeconducting band gap

Ω Volume of solid

Φ0 Flux quantum (=h/2e)

Φ Fluxoid (quantised quantity in superconductor) α Optical absorption coefficient

α Exponent for isotopic effect

α=a/λ whereais thickness of superconducting film αn Overlap integral between atomic sitesandn

χ(ω) Real part of alternating magnetic susceptibility (dispersion) χ(ω) Imaginary part of alternating magnetic susceptibility (absorption) χd Diamagnetic susceptibility

χn(r) Atomic wave function •leveln

χv(r) •valence state

χP Pauli susceptibility of metal

δ Binding energy of Cooper pair

ε Dielectric constant of semiconductor

(12)

604 Appendix D Specific Notation εk Energy of an electronic plane wave eigenstate (h¯2k2/2m0)

ε(k) Spin wave dispersion relation

|φ(r)|2=φ2 Density of superconducting pairs (=ns/2)

γ Linear term in electronic specific heat of metal (Ce=γT)

κ Thermal conductivity

κ=λ/ξ Ratio of penetration depth to coherence length λ,λ(T) Penetration depth

λ0 •at zero temperature

λL •London

λ Spin–orbit coupling coefficient (λl·s) λ Molecular field coefficient

μe Electron mobility

ωc Cyclotron angular frequency of charge in magnetic field

ωD Debye angular frequency

ωL Larmor angular frequency

ψnk(r) Bloch function with band indexnand quasi-momentumk ρ(r) Electronic density atr

σ,σe,σh Electron or hole conductivity σ(ω) Alternating conductivity of a metal σs(ω) Alternating conductivity of a superconductor T Transmission coefficient of a tunneling barrier τ Relaxation time due to wall mobility in a ferromagnet

τe Relaxation time of electron velocity distribution and electron collision rate θ(r) Phase of wave functionψ(r) (superconductor)

θD Debye temperature characterising phonon spectrum in solid ξ Coherence length in the superconducting state

ζ Thickness of Bloch wall

Beff Effective magnetic induction at a site in a magnetic compound J Total angular momentum for one ion

Hd Demagnetising field

K Vector in reciprocal lattice Rl Vector in real lattice

|R Excited state of Heisenberg model: single site atR has spin reversed with respect to ferromagnetic ground state

|Ri,χ0(r−Ri) Atomic state and wave function for a nucleus atRi a1,a2,a3 Vectors specifying unit cell•of real lattice a1,a2,a3 •of reciprocal lattice beff Effective field in rotating frame at magnetic resonance

E Electric field

jc Critical current density of a superconductor

jh Hole current density

¯

hk Quasi-momentum or crystal momentum

k0 Incident wave vector

k1 Scattered wave vector

kh Quasi-momentum of hole

(13)

Appendix D Specific Notation 605 δk Displacement of Fermi surface in quasi-momentum space

under effect of a force

|k Eigenstate of Heisenberg model corresponding to a spin wave of wave vectork m Magnetisation in the rotating frame

vn,k Average velocity of electron in Bloch stateψn,k

ve Drift velocity of conduction electrons

vh Hole velocity

vg Group velocity of wave packet

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### Quantum Mechanics and Statistical Physics

1. Balian, R.: From Microphysics to Macrophysics, Vols. I and II. Springer-Verlag, Berlin, Heidelberg, New York, NY (1991)

2. Basdevant, J.L., Dalibard, J.: Quantum Mechanics. Springer-Verlag, Berlin, Heidelberg (2002) 3. Georges, A., M´ezard, M.: Introduction ´a la th´eorie statistique des champs. Cours de l’Ecole

Polytechnique, Palaiseau, France

### Solid State Physics

4. Ashcroft, N.W., Mermin, N.D.: Solid State Physics. Saunders College Publishing, Philadel- phia, PA (1976)

5. Dugdale, J.S.: The Electronic Properties of Metals and Alloys. Edward Arnold, London (1977) 6. Ibach, H., Luth, H.: Solid State Physics. Springer-Verlag, Berlin, Heidelberg, New York, NY

(1995)

7. Kittel, C.: Introduction to Solid State Physics, 7th edn., Wiley, New York, NY (1996) 8. Olsen, J.L.: Electron Transport in Metals. Interscience, New York, NY (1962)

9. Voos, M., Drouhin, H.J., Dr´evillon, B.: Semi-conducteurs et composants. Cours de l’Ecole Polytechnique, Palaiseau, France

10. Ziman, J.M.: Electrons and Phonons. Oxford University Press, Oxford (1960)

### Superconductivity and Magnetism

11. Abragam, A.: Principles of Nuclear Magnetism. Oxford University Press, Oxford (1994) 12. Becker, R., D¨oring, W.: Ferromagnetismus. Springer, Berlin (1939)

13. Chikamuzi, S.: Physics of Ferromagnetism. Clarendon Press, Oxford (1997) 14. Cullity, B.D.: Introduction to Magnetic Materials. Wesley, Reading, MA (1972)

15. Evetts, J.: Concise Encyclopedia of Magnetic and Superconducting Materials. Pergamon Press, Oxford (1992)

16. L´evy, L.P.: Magnetism and Superconductivity. Springer-Verlag, Berlin, Heidelberg, New York, NY (2000)

17. Orlando, T.P., Devlin, K.A.: Foundations of Applied Superconductivity. Addison Wesley, Reading, MA (1991)

607

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608 References 18. Rose-Innes, A.C., Rhoderick, E.H.: Introduction to Superconductivity. International Series in

Solid State Physics, Pergamon Press, Oxford (1978)

19. Tilley, D.R., Tilley, J.: Superfluidity and Superconductivity. Graduate Students Series in Physics, Institute of Physics Publishing, London (1990)

20. Tinkham, M.: Introduction to Superconductivity. McGraw-Hill Inc, New York, NY (1996)

### Subatomic Physics

21. Roug´e, A.: Introduction `a ła Physique Subatomique. Editions de l’Ecole Polytechnique, Palaiseau, France

(17)
(18)

H

Li

Na

K

Rb

Cs Ba *La Hf Ta W Re Os Ir

Fr Ra Ac

Ce

Th Pa U Np Pu Am

Pr Nd Pm Sm Eu

Sr Y Zr

Be

Mg

Ca Sc Ti V

Nb Mo Tc Ru Rh

Cr Mn Fe Co

HEX

HEX

HEX

HEX HEX CC CC CUB CC HEX

FCC

FCC HEX

HEX

HEX HEX

CC CC

10.8 3.41 9.04 1.46

480 390

380 359

FCC 1

3

11

19

37

55 56 57 72 73 74 75 76 77

87 88 89

58

90 91 92 93 94 95

59 60 61 62 63

139

4.69 10.9

100 210 188 150

152 157 166 107

Europium Samarium

Promethium Neodymium

Praseodymium

38 39 40 41 42 43 44 45

2.91 8.4 2.1 4.06 3.3 4.6

350 382

351 380

275 61.6

3.64 10.1

256 250

147 45.7

20 21 22 23 24 25 26 27

385 5.0

16.6

400 420 130

Iron Cobalt

127 2.9

230

Calcium Scandium 0.4 Titanium

7.8 Technetium 0.5 Ruthenium Rhodium 5.35 Vanadium

9.25 Niobium 0.92 denum Molyb-

Chromium Manganese 1.97

2.43

3.53 2.72 10.1 2.4 5.84 1.22 2.4 2.35 3.15

225 310 416 400 430

132

4.9 0.13 Hafnium 4.4 Tantalum 0.015Tungsten 1.7Rhenium 0.65Osmium 0.14Iridium 110 42.3

Barium

Lanth- anum 50

56 21.5

18.4 24.6 100

Potassium

Rubidium

Cesium

* Lanthanides

† Actinides

Cerium

1.37 Thorium 1.3 Protactinium 1.1 Uranium 0.08 Neptunium Plutonium Americium Strontium Yttrium 0.5 Zirconium

12

1.46 1.34

318 82.3 150 37.7

Sodium Magnesium [Ar]3s

[Ar]4s

[Kr]5s

[Xe]6s

[Xe]7s [Xe]7s2 [Xe]7s26d

[Xe]4f26s2

[Rn]6d27s2 [Rn]5f26d7s2 [Rn]5f36d7s2 [Rn]5f46d7s2 [Rn]5f67s2 [Rn]5f77s2 [Xe]4f36s2 [Xe]4f46s2 [Xe]4f56s2 [Xe]4f66s2 [Xe]4f76s2 [Kr]5s2

[Xe]6s2 [Xe]5d6s2 [Xe]4f145d26s2[Xe]4f145d36s2[Xe]4f145d46s2[Xe]4f145d56s2[Xe]4f145d66s2 [Xe]4f145d9 [Kr]4d5s2 [Kr]4d25s2 [Kr]4d45s [Kr]4d55s [Kr]4d65s [Kr]4d75s [Kr]4d85s [Ar]4s2 [Ar]3d4s2 [Ar]3d24s2 [Ar]3d34s2 [Ar]3d54s [Ar]3d54s2 [Ar]3d64s2 [Ar]3d74s2 4

CC

CC

CC

CC

CC

CC FCC

FCC

FCC TET ORT ORT MCL

HEX HEX ROM CC

CC CC CC

FCC HEX

HEX HEX

HEX

1.76 0.21

1000 166 0.03 Beryllium 400 55.1

Lithium

[He]2s [He]2s2

[Ar]3s2 110

1s Hydrogen

– –

## Periodic Table of the Elements

Translated with the agreement of the author from the french edition of ref (16):

“Magnétisme et Supraconductivité” by L. Lévy, Savoirs Actuels, InterEditions, CNRS Editions (1997).

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Rn

86

Xe

54

[Kr]4d105s2p6

55

Ar

18 FCC

[Ar]3s2p6

63

Ne

10

63 46

[He]2s2p6

He

HEX 2

26 1s2

Sommerfeld constant (mJ/mole2) Z

Debye temperature (K) Tc (K)

Crystal Structure Symbol

Fermi temperature (× 1000 K) Configuration

Helium

F

MCL 9

[He]2s2p5

O

CUB 8

[He]2s2p4

79

N

HEX 7

[He]2s2p3

1800

C

DIA 6

[He]2s2p2 1250

B

TET 5

[He]2s2p

Br

35

[Ar]3d104s2p5

ORT

Se

34

[Ar]3d104s2p4

HEX FCC

Cl

17

[Ar]3s2p5

ORT

S

16

[Ar]3s2p4

ORT

P

15

[Ar]3s2p3

CUB

Si

14

[Ar]3s2p2

DIA FCC

625

Al

13

[Ar]3s2p 1.26

394 136

Neon Fluorine Oxygen

Nitrogen Carbon

Chlorine Sulfur

Bromine Selenium

Phosphorus Silicon

Boron

Argon

Kr

36

[Ar]3d104s2p6

85

Krypton

Iodine Tellurium

Antimony Xenon

FCC

Arsenic

Californium

Curium Berkelium Nobelium

Nickel Copper

Bk

97

[Rn]5f76d27s2

Cm

96

[Rn]5f76d7s2 _

_ _

_

Cf

98

[Rn]5f96d7s2 _

_

Einsteinium

Es

99 _

_

Fermium

Fm

100 _

_

Mendelevium

Md

101 _

_

No

102 _

_

Lawrencium Lutetium

Lr

103 _

_ 150

As

33

[Ar]3d104s2p3

ROM

285 Germanium

Ge

32

[Ar]3d104s2p2

DIA

360 1.08 Gallium 1.18 Aluminum

Ga

31 [Ar]3d104s2p 0.62

120 ORT

240 0.9 Zinc

Zn

30 [Ar]3d10 0.6

110 HEX

234

Cu

29 [Ar]3d104s 0.67 315 81.6

Ni

28 FCC

FCC FCC

FCC FCC

FCC [Ar]3d84s2

_ 375 _

At

85

4f145d106s2p5

Po

84

4f145d106s2p4

I

53

[Kr]4d105s2p5

ORT FCC

FCC

FCC

Te

52

[Kr]4d105s2p4

HEX

Polonium CUB

Bi

83 4f145d106s2p3 0.084 115

Bismuth ROM

Pb

82 4f145d106s2p2 3.14

120 110

Tl

81 4f145d106s2p 2.83

88 94.6

139

Sb

51

[Kr]4d105s2p3 0.63

127 ROM

200

Sn

50

[Kr]4d105s2p2 1.84

118 TET

HEX FCC

170 3.75 Tin

In

49 [Kr]4d105s2p 1.8

100 TET

129 3.4 Indium

Cd

48 [Kr]4d105s2 0.63

86.8 HEX

Ag

47

[Kr]4d105s2 0.66

63.8 215

Pd

46 [Kr]4d10 10 275 _

1.37 Thallium

Hg

80 [Xe]4f145d106s2 2.2

96 82.6

ROM

4.16 Mercury Gold

Silver

Platinum

Au

79 [Xe]4f145d106s 0.7

100 64.2

Pt

78 [Xe]4f145d96s 6.68

170 230

Gd

64

176 [Xe]4f75d6s2 _

_ HEX

Terbium

Tb

65

188 [Xe]4f96s2 _

_ HEX

Dysprosium

Dy

66

186 [Xe]4f106s2 _

_ HEX

Holmium

Ho

67

191 [Xe]4f116s2 _

_ HEX

Erbium

Er

68

195 [Xe]4f126s2 _

_ HEX

Thulium

Tm

69

200 [Xe]4f136s2 _

_ HEX

Ytterbium

Yb

70

118 [Xe]4f146s2 _

_

Lu

71

207 [Xe]4f145d6s2 10.22

_ HEX

Al

13 CFC

[Ar]3s2p 1.29

394 136

1.18 Aluminium

(20)
(21)

### Index

A

Absorption,209,321,328 Acceptor,126

Alkaline earth metals,204 Allowed energy band,15 Alloy,33

Alloys, electronic energy and stability of,391 Alternating magnetisation,252

Aluminium, Reflectance of,373 Angle-resolved photoemission

spectroscopy,89 Antiferromagnetic Solid,563

Antiferromagnetic Transition,564 Preliminaries Case,563

Susceptibility,565 Antiferromagnetism,252,341 Atomic force microscopy,310 Atomic vibration,118

Atom with partially filled shell,237 Avogadro number,593

B

Band gap,62,67,76,84,215 Band structure,15

extended zone,57 restricted zone,57 BCS theory,215 Binding energy,213 Bitter method,288,307,308 Bloch function,13,14,54,111 Bloch’s law,350

Bloch theorem,13,53 Bloch wall,283,285,322,324

energy of formation,287 thickness,287

Body-centered cubic lattice,29 Bohr magneton,593

Bohr radius,593 Boltzmann constant,593 Bose condensation,222 Boson,222,349

Bragg diffraction,24,37,39 Bragg peak,41,43 Bragg plane,39,59,66 Bravais lattice,26,28,38 Brillouin function,244 Brillouin zone,66,221 C

Causality,321 Chemical shift,340 Coercive field,289

Coherence length,185,207,222 Collision,103

Collision time,118 Compton wavelength,593 Condensation energy,210,215 Conduction band,77,115 Constant energy surface,69 Contact interaction,340 Conventional cell,28,30,31 Cooper pair,161,213 Critical current,324 Critical exponents,357 Critical field,150,178,183,186

lowerHc1,191 upperHc2,192

Critical temperature,147,217,259 Cryogenics,204

Crystal lattice,26,28,38 Crystallography,205 Crystal momentum,16,56 Cubic lattice,29,32

Cuprate superconductor,33,65,259

613

(22)

614 Index Curie paramagnetism,235,244

Curie temperature,251,353 Curie–Weiss law,353 Cyclotron Resonance,441

Electron State,441 Metals,444 Silicon,442 D

Debye frequency,220 Debye temperature,119 Debye–Waller Factor,367 Defect,116,119

Demagnetisation energy,282,284 Demagnetising field,279,298,303,328 Density functional theory,7

Density of states,17,71,86,235 Diamagnetism,177,234 Diffraction,35

Bragg,37

Dipole interaction,244,277,337 Disorder,44

Dispersion,321,328 Dissipation,320 Donor level,125 Drude model,102 E

Easy magnetisation axis,272 Effective mass,114 Elastic collision,119

Electrical conductivity,103,108 Electron,593

nearly free,56,61,66 Electron microscopy,308 Electron mobility,103

Electron–phonon interaction,206,220,221 Energy bands,20

Entropy,179 EPR,331

Ewald construction,40 Exchange anisotropy,273 Exchange constant,246 Exchange energy,285 Exchange Hamiltonian,246 Exchange interaction,245,354 Excited state,208,216 F

Faraday effect,307 Fermi–Dirac statistics,108 Fermi energy,73,108

Fermi sphere,73,108 Ferrimagnetism,252,255,322 Ferrites,304

Ferromagnetic resonance,325,329 Ferromagnetism,236,249,340

hard,290 soft,290

Field effect (doping),126,130 Fine structure constant,593 First Brillouin zone,16,57,59,65 Flux quantum,160,161,192 Fluxoid,159

Form factor, atomic,43 Fourier transform,336 Free energy,178,184 Free precession,335 Fullerene,33,260 G

Gap,220 Gauge,159

Giant Magneto-Resistance,264 Glass,33

Graphene,29,78,126,130 Group velocity,108,111 Gyromagnetic ratio,324 H

Hall effect,126,306 Hall voltage,297 Hartree approximation,7 Hartree–Fock approximation,7 Heisenberg model,247 Helium,4

High Temperature Superconductors,223,259, 261,306,309

High Temperature superconductors,32,65,89 Hole,121

Hopping integral,10 Hubbard model,256 Hund rules,240 Hydrogen atom,236 Hyperfine interaction,340 Hysteresimeter,304

Hysteresis cycle,276,289,304 I

Impurity,116,119 Insulator,75

Insulator–Metal Transition,419 Alkali Elements and Hydrogen,423 Hydrogen-Like Orbitals,419

Insulator–Metal Transition in Si–P,423 Interactions Between Electrons,420

(23)

Index 615 Interface,188

Interface energy,188 Intermediate state,303 Ising model,359 Isotope effect,206,220 J

Josephson effect,165,217

Josephson Effects in Zero Magnetic Field,481 Josephson Junction in a Microwave Field,

483

Model Josephson Junction,481 Realistic Josephson Junction,481 Josephson Junction in a Magnetic Field,491

Current Distribution,492 Josephson Plasma Resonance,495 Screening of,493

Joule effect,118 K

Kerr effect,307

Kramers–Kronig relations,321,334 L

La2CuO4,557 Landau function,355 Landau theory,354 Land´e factor,240,324,333 Lanthanide,204

Larmor frequency,297,324,339 Larmor resonance,150 Latent heat,179 Lattice planes,27 Levitation,155 Linear atomic chain,11 Linear response,320 Liquid vortex phase,306 Little–Parks Experiment,469 London equations,152,156 Lorentz microscopy,309 Lorenz number,107,111 M

Magnesium Diboride,541

Atomic and Electronic Structure,541 Superconductivity,543

Magnetic anisotropy,272,285,330 Magnetic domain,283

rotation of,289

Magnetic force microscopy,311 Magnetic hysteresis,273,275,289 Magnetic pole,278

Magnetic potential,278 Magnetic susceptibility,300

complex,320

Magnetisation,299 remanent,289 rotation of,274 of superconductors,301 Magnetocrystalline anisotropy,272 Magneto-optical effects,308 Magnetoresistance,297,306 Magnon,348,351

Matthiessen’s law,118 Maxwell equations,156

Mean field approximation,251,352,359 Mean free path,106

Meissner effect,154,177 Metal,75,341

Microstructure,323 Miller indices,38 Mixed state,185,188,306 Molecular field,249 Monovalent metal,221

Monovalent Metals, Optical Response of,399 M¨ossbauer effect,341

Mott–Hubbard insulator,256 Multielectron atoms,237 Muon,339

N NbSe2,531

Near-field microscopy,310 N´eel state,252

N´eel temperature,252 Neutron,205,593 NMR,331,339

high resolution,334 Noble metals,204 Nuclear magneton,593 Nuclear spin,333 O

Ohm’s law,103,156 One-dimensional system,5 Optical absorption,84 Order parameter,356 Orientational disorder,34 Overlap integral,19 P

Paramagnetic insulator,257

Pauli exclusion principle,107,213,238,245 Pauli paramagnetism,178

Pauli spin paramagnetism,235 Pauli susceptibility,341

Penetration depth,156,182,185,192,339 Periodic boundary conditions,12 Perovskite structure,32

(24)

616 Index Persistent current,149,156

Phase transition,352,354 Phonon,118

Phonons in Solids,453 Debye Model,453 Detection of,455 Einstein Model,453 Resistivity,457

Thermodynamic Properties,456 Photoemission,88

Planck constant,593 Plastic crystal,34 Potential, atomic,6 Pressure,204,205 Primitive cell,26 Proton,593

Pseudogap phase,259 Pulse response,321 Q

Quasi-momentum,16 R

Rayleigh regime,289 Reciprocal lattice,35,38,43 Reflectivity,209

Relaxation time,103,336 Renormalisation group,359 Rotating frame,326 Rydberg constant,593 S

Scanning tunneling microscopy,85,87 Semi-classical approximation,108 Semiconductor,31,76,77,204

doped,123 Semi-metals,204 Singlet state,238 Slater determinant,8 Solid solution,33 Specific heat,81,179 Spin echo,337

Spin lattice relaxation time,325 Spin–orbit interaction,240 Spin singlet,213

Spin wave,348,351

Spontaneous magnetisation,235 SQUID,166,217,299 Structural defect,302 Structure factor,42 Superconductivity,147,177 Superexchange interaction,252

Superfluidity,222 Susceptibility, Pauli,82 Symmetry axes,n-fold,28 Symmetry breaking,248 T

Thermal conductivity,105 Thermodynamic potential,178 Thin Film,579

Non-uniform Situations,581,583 Uniform Magnetisation,580 Thin film,181

Thin Films and Magneto-Optic Applications, 573

Tight-binding approximation,63,64,68 Transfer integral,10

Transition metals,204,221 Transverse relaxation,338 Triplet state,239

TTF-TCNQ Compounds,405 Dimerised Chain,407,413 Isolated Chains,405 Observations,406 Peierls Transition,409,416 Tunnel effect,85,217 Two-fluid model,157 Type I superconductor,188 Type II Superconductor,511 Type II superconductor,188 V

V3Si,523 Vacancy,120 Valence band,77

Van der Waals interaction,222 Vortex,192

Vortex pinning,198 W

Wave packet,108 Wigner–Seitz cell,27 Wilson ratio,83 X

X ray,35,205 Y

YBa2Cu3O7, Band Structure,377 Chain and Plane,380

Isolated Copper–Oxygen Chain,378 Isolated Copper–Oxygen Plane,379 Realistic Models,381

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