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

Appendix A

Physical Constants

Units

Angstrom 1 ˚A = 10⁻¹⁰m (∼size of an atom)

Fermi 1 fm = 10⁻¹⁵m (∼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=6.6261×10⁻³⁴J s

¯

h=h/2π=1.05457×10⁻³⁴J s Speed of light c=299 792 458 m s⁻¹

Vacuum permeability μ0=4π×10⁻⁷H m⁻¹ (ε0μ0c²=1)

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

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

Proton mass m_p=1.67262×10⁻²⁷kg

Neutron mass m_n=1.67493×10⁻²⁷kg

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

Classical electron radius r_e=e²/m₀c²=2.818×10⁻¹⁵m Compton wavelength λc=h/m₀c=2.426×10⁻¹²m of the electron

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

= −5.7884×10⁻⁵eV T⁻¹ Nuclear magneton μN=qh¯/2m_p=5.0508×10⁻²⁷J T⁻¹

=3.1525×10⁻⁸eV T⁻¹

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

Appendix B

Some Useful Functions and Relations

EulerFunction

(t)

=

_∞

0

x^t−1e^−xdx=

(t

−

1)

(t

−

1)

=

(t

−

1)

!

(1

/

2)

=√

π

.

RiemannζFunction

ζ

(t)

=

∞

n=1

1

n^t

with some specific values

t 2 3 4

ζ π²/6 1.202 π⁴/90

Integrals of the Fermi–Dirac Function

f

(x)

=

1

e^x+

1 and

−df/dx=

1 4 cosh

²

(x/2)

_∞

0

f

(x)dx

=

_∞

0 −

(df

/dx)x dx=

ln 2.

For

t>

1

_∞

0

f

(x)x

^t−1dx=

_∞

0

x^t−1

e^x+

1

dx=

1 4t

_∞

0

x^t

cosh

²

(x/2)

dx=

(1

−2^1−t

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

595

596 Appendix B Some Useful Functions and Relations

_∞

0

f

(x)xdx

=

1 8

_∞

0

x²

cosh

²

(x/2)

dx=

1

2

ζ

(2)

=π²

12 ,

_∞

0

f

(x)x

²dx=

1 12

_∞

0

x³

cosh

²

(x/2)

dx=

3

2

ζ

(3)

≈

3

2 1.202

≈

1.8,

_∞

0

f

(x)x

³dx=

1 16

_∞

0

x⁴

cosh

²

(x/2)

dx=

21

4

ζ

(4)

=

7 120

π⁴

.

Bessel Functions

The Bessel functions of order

α

are solutions of the differential equation

x²d²y

dx²+xdy

dx+

(x

²−α²

)y

=

0.

They are important to solve Laplace’s equation in cylindrical (for integer

α) or

spherical (half-integer

α

) coordinates.

The Bessel functions

of the first kind Jn

(x) with integer

n

are solutions which are constant for

x→

0 and are oscillating decreasing functions for

x→ ∞

. They have an integral form given by

Jn

(x)

=

1

π

_π

0

cos(nu

−xsinu)du

with

J₋n

(x)

=(−1)ⁿJn

(x).

For

n≥

0, they can be expanded for small

x

into

J0

(x)

≈

1

−x²

4 and

Jn

(x)

≈

1

n!

x

2

n

. The asymptotic form for

x→ ∞

is

Jn

(x)

≈

2

πx ¹

2

cos

x−nπ

2

−π

4

.

Sinusoidal functions of sinusoidal functions can be developed into series of Bessel functions using

e^ixsinφ= ^∞

n=−∞

Jn

(x)e

^inφ

.

The

modified Bessel functions of orderα

are solutions of the differential equation

x²d²y

dx²+xdy

dx−

(x

²+α²

)y

=

0.

Appendix B Some Useful Functions and Relations 597

The modified Bessel functions

Kn

(x),with integer

n, are solutions which diverge

for

x→

0, and vanish exponentially for

x→ ∞. Their integral representation is

given by

Kn

(x)

=

1 2 exp

inπ

2

∞

−∞

exp(−ix sht

−nt)dt

, with

K₋n

(x)

=Kn

(x).

Their expansion for small

x

is

K0

(x)

≈ −

lnx and

Kn

(x)

≈

1 2n!

2

x

n

. Their asymptotic forms for

x→ ∞

are

Kn

(x)

≈

2

πx ¹

2

exp(−x).

These functions are related to one another through

d

dx

xⁿKn

(x)

= −xⁿKn−1

(x), which gives as an example

dK0/dx= −K₋1= −K1

.

Appendix C

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

Z_G(T,μ) Grand partition function

e Electron charge

h Planck constant (=2πh)¯

k_B Boltzmann constant

s Electron spin (s=1/2)

Φ Flux of magnetic induction around a contour (C)

β Reciprocal ofk_BT

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

B_a Applied magnetic induction (=μ0H_a)

F Force

H_a Applied magnetic field

M Magnetisation

j Electric current density

k Wave vector

p_i Momentum ofith electron v_i Velocity ofith electron

μ Atomic magnetic moment

599

Appendix D

Specific Notation

a_k0,k1 Atomic form factor [=f(k1−k₀)]

B_J(x) Brillouin function with total angular momentumJ as a function ofx=g_Jμ0μBH_a/k_BT

C_e(T) Specific heat •electronic

C_n •in normal metal state

C_s •in superconducting state

C_v •at constant volume

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

D_s(E) •excited in the superconducting state

D_Ω(E) •of energyEper unit volume

D_χ •at the Fermi level obtained by the Pauli susecptibility D_c •at the Fermi level obtained by the specific heat D_c(E−E_c) •of the conduction band of a semiconductor D_v(E−E_c) •of the valence band of a semiconductor E₁,E2,...E_n Atomic energy levels

E_v Atomic energy level of a valence electron

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

E_F Fermi energy

E_Z Energy of Zeeman coupling between magnetisation and magnetic field

E_d Demagnetisation energy

E_an Anisotropy energy as a function of orientation ofM(seeH_A) E_wall Energy of a Bloch wall per area of primitive cell

E_c Energy at minimum of conduction band (semiconductor) E_v Energy at maximum of valence band (semiconductor) E_c Condensation energy in superconducting state E_g Semiconductor band gap (=E_c−E_v)

E_h Energy of hole

G_s(T,H_a) Gibbs free energy•of superconducting state

G_n(T,H_a) •of normal metal

G_sf(T,H_a) •of superconducting film

G_ms(T,Ha) •of mixed state

601

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

H_c Critical field of thin superconducting film H_c1 Lower critical field for type II superconductor H_c2 Upper critical field for type II superconductor

ˆ

H^rf_Z Hamiltonian for Zeeman coupling with a radiofrequency field ˆ

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

R(S^z_R)²

H_K Anisotropy field

H_d Demagnetising field

I_c Critical current of a Josephson junction

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

J_NS •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 M_s Magnetisation at saturation

M_alt Alternating magnetisation in antiferromagnet with two sublattices N_e Number of electrons in solid

N_n Number of atomic nuclei in solid

N Demagnetisation tensor

P_i Momentum ofith atomic nucleus R_W Wilson ratio relatingχPandC_ein metal S_s Entropy •of superconducting state

S_n •of normal state

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

T_C Curie temperature

T_N N´eel temperature

T₁ Relaxation time •spin lattice

T₂ •spin–spin

ˆ

T_Ri Operator effecting translation of crystal lattice byR_i

U(r) Magnetic potential

V(r1−r₂) Interaction between two electrons atr₁andr₂

V_at Atomic potential

V_K Fourier component of periodic potential for vectorKof reciprocal lattice V_c(r) Coulomb potential

V_k Fourier component of attractive potentialV(r1−r₂) between two electrons due to electron–phonon interaction

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

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

j_en Energy flux

k_F Fermi wave vector for free electron gas

Mean free path •of particle

e •of electron

(me)_αβ Effective electron mass tensor [(mh)_αβfor hole]

m_e 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) norn_e Number density•of conduction electrons

n_p •of Bravais lattice points

n_s •of electrons condensed in superconductor

n_h •of holes in semiconductor

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

t_n, •between sitesnand

u_n,k(r) Coefficient of e^ik·rin Bloch functionψn,k(r) v Volume of primitive cell in crystal

v_F 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 α−n 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

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 (=n_s/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

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

H_d Demagnetising field

K Vector in reciprocal lattice R_l Vector in real lattice

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

|R_i,χ0(r−R_i) Atomic state and wave function for a nucleus atR_i a₁,a₂,a₃ Vectors specifying unit cell•of real lattice a^∗₁,a^∗₂,a^∗₃ •of reciprocal lattice b_eff Effective field in rotating frame at magnetic resonance

E Electric field

j_c Critical current density of a superconductor

j_h Hole current density

¯

hk Quasi-momentum or crystal momentum

k₀ Incident wave vector

k₁ Scattered wave vector

k_h Quasi-momentum of hole

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

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

v_e Drift velocity of conduction electrons

v_h Hole velocity

v_g Group velocity of wave packet

References

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

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

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

Francium Radium Actinium

* 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).

Rn

86

4f¹⁴5d¹⁰6s²p⁶ Radon Astatine

– – –

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

7.23 Lead

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

120 0.56 Cadmium Palladium

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

Gadolinium

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

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

lowerH_c1,191 upperH_c2,192

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

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

Face-centered cubic lattice,30,34,43,59,69 Faraday balance,300

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

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

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