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PHYS3002: Introduction to Solid State Physics > Lecture 15 > Flashcards

Lecture 15 Flashcards

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1
Q

Give the equation for the entropy of a system

A

S = entropy
∂G = change in Gibbs free energy
∂T = change in temperature

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2
Q

Give the equation for the difference in entropy between the superconducting and the normal to the state

A

∆S = change in entropy
∂G = change in Gibbs free energy
∂T = change in temperature
B = magnetic flux = 0
B_c = critical flux

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3
Q

When does the change in entropy for a system equal 0? Why?

A

At the Curie temperature because the critical field equals 0 at this point.

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4
Q

Why isn’t there any latent heat for the transition from the normal to the superconducting state?

A

Because this transition occurs without a discontinuity in entropy.

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5
Q

Give the equation for the difference in the specific heat at constant volume between the superconducting and the normal

A

∆C_v = change in specific heat
T = temperature
∆S = change in entropy
B_c = magnetic flux

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6
Q

Give the equation for the difference in the specific heat at constant volume between the superconducting and the normal to the state at the Curie temperature

A

∆C_v = change in specific heat
T = temperature
B_c = magnetic flux

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7
Q

Describe the graph of specific heat against temperature for a superconducting and a normal state

A

There is a sharp rise in the specific heat at the Curie temperature of a superconductor due to the onset of ordering of the conduction electrons.

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8
Q

Describe the graph of the resistivity and the specific heat against T/T_c for a superconductor

A
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9
Q

Give the equation for electronic specific heat

A

C_v-el = electronic specific heat
C0 = constant
E_g = bandgap energy ~ (7/2)(k_B)(T_c)
T = temperature

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10
Q

What range is the electronic specific heat equation valid for?

A
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11
Q

The electronic specific heat presents the same behaviour as the number of _______ and _____ in a semiconductor.

A

Electrons
Holes

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12
Q

Describe the graph of electronic specific heat against 1/T

A
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13
Q

Compare the energy bands of a semiconductor to the energy states of a superconductor

A

They are equivalent

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14
Q

How can the energy gap of a semiconductor be measured?

A

By measuring photon absorption

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15
Q

How can the bandgap of a superconductor be measured?

A

By measuring microwave photon absorption (as the bandages are only a few meV).

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16
Q

What does the BCS theory of superconductivity explain?

A
  • Attraction between pairs of electrons.
  • How bound electron ‘Cooper pairs’ can form.
  • How Cooper pairs can form a collective ground state of lower energy than that of the normal electron states.
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17
Q

What are Cooper pairs?

A

Composite bosons made of bound electron pairs. They are formed by attraction between electrons via a lattice.

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18
Q

Describe the interaction between two electrons in free space

A

There is a strong Coulombic repulsion

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19
Q

Why do metals have no net charge?

A

The conduction electrons move through a lattice of positive ions and the charges balance out.

20
Q

Describe how electrons can locally distort a crystal lattice

A
21
Q

Describe how electrons can attract one another in a lattice

A
  • A single electron distorts a crystal lattice by attracting positive ions towards it.
  • The electron then leaves at the Fermi velocity which is faster than the speed of lattice distortion (the speed of sound).
  • This leaves a trail of net positive charge behind the electron which attracts other electrons.
22
Q

What is the approximate value of the Fermi velocity

A
23
Q

What is the approximate value of the speed of sound in a crystal lattice

A
24
Q

Is attraction between electrons in a crystal direct or indirect?

A

Indirect

25
Q

What causes the attraction between electrons in a crystal?

A

Phonon exchange

26
Q

Attraction between electrons via a lattice can produce _____ ________ _____.

A

Bound electron pairs

27
Q

When is Cooper pair production possible?

A
  • If the electron wavevectors are -k and +k.
  • If the modulus of the wavevector is equal to the Fermi wavevector.
  • If the electrons have opposite spin (S = 0 for the pair).
  • If the electrons have zero angular momentum (L = 0).
28
Q

What is the binding energy per electron of a Cooper pair?

A

∆(T)

29
Q

What is the binding energy per pair of a Cooper pair?

A

2∆(T)

30
Q

What is the size of the binding energy of a Cooper pair?

A

~ a few meV

31
Q

Why are Cooper pairs composite bosons?

A

Because they have no net spin

32
Q

The superconducting transition is a form of ____-_______ _________.

A

Bose-Einstein condensation

33
Q

What happens when Cooper pairs condense?

A

They condense into the superconducting ground state below T_c.

34
Q

Cooper pairs are all described by the same _________ ___________.

A

Macroscopic wavefunction

35
Q

How does the binding energy per Cooper pair change with an the number of pairs?

A

The binding energy per Cooper pair increases as the number of pairs increases.

36
Q

Describe a zero supercurrent Cooper pair

A

The electrons have the wavevectors +k and -k. The centre of mass of the pair is at k = 0.

37
Q

Describe a Cooper pair with a supercurrent

A

The centre of mass of the pairs has a wavevector, K alongside the electron wavevectors of +k and -k.

38
Q

Give the equation for the average distance between the electrons in a Cooper pair

A

ζ = BCS coherence length
∆(0) is the energy gap at T = 0

39
Q

What conditions are required for the scattering of a Cooper pair?

A

The reduction of kinetic energy must be greater than or equal to the pair binding energy (2∆).

40
Q

Describe the wavevectors of a Cooper pair with no supercurrent, with a supercurrent, and after scattering

A
41
Q

Give the equation for the current density

A

j = current density
n = density of electrons
q = charge
v = particle velocity

42
Q

Give the equation for the initial total energy of the Cooper pair of electrons before scattering

A

Ei = initial total energy
K = Cooper pair wavevector
k = electron wavevector
m_e = electron mass

43
Q

Give the equation for the final total energy of the two
normal electrons after scattering

A

Ef = final total energy

44
Q

Give the equation for the critical pair velocity of a Cooper pair

A

v_c = critical pair velocity
∆ = binding energy

45
Q

Give the equation for the critical current density of a Cooper pair

A

j_c = critical current density
n = density of electrons
v_c = critical pair velocity
∆ = binding energy

PHYS3002: Introduction to Solid State Physics (21 decks)

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