Chap 11 Superconductivity

1
Chap 11 Superconductivity
11. 1 Experimental Facts 1) For some materials
at low enough temperatures (TltTc), there is no
D.C. resistance gt Superconducting state
r
r
phonon
impurity
T
T
Tc
Normal metal
Superconductor
Pb Tc 7.2K Nb Tc 9.3 K Nb3Sn 18.1
K Nb3AlGe 20 K
LaCu2O4 40 K YBCuO 90 K
High Temperature Superconductor
Conventional Superconductor
2
ii) Meissner Effect Perfect Diamagnet
Inside a superconductor , BH4pM0
magnetic flux is expelled from the
superconducting materials
B0
Perfect Conductor
Superconductor
T gt Tc
T gt Tc
T ltTc
T ltTc
3
-4pM
B
super
super
normal
normal
Hc
Hc
Hc Critical Field
3) Specific Heat
C
normal metal
super
T
Tc
4

• At Tc, there is discontinuity in Cv
• Decay exponentially at low T
• i) Ordering at low temperature 2nd order phase
  transition
• ii) Energy gap of order D in the superconducting
  state

4) Tunneling
Insulator
Superconductor
Normal
V
Vc
5
5) Isotope Effect
MaTcConstant
Phonon involvement of the superconductivity Mech
anism
11.2 London Equation Electrodynamics in
Superconductors
i) Perfect Conductor
6
Change of magnetic flux density do not penetrate
far below the surface Perfect Conductor
Ba
2) London Equation Superconductor
7
Surface Current
Ba
Magnetic field cannot penetrate
Meissener Effect
11.3 BCS Theory
1. Electron-Phonon Interaction give rise the
Effective attractive interaction between
electrons near the Fermi Surface
e-
e-
8
Frohlich
k1
k2
phonon
k1
k2
2. Due to this attractive interaction, two
electrons with opposite momentum and spin k gt
-k gt form a bound state Cooper pair
This pair has spin zero (singlet state)
9
Coherent length x
Superconducting to normal boundary size Size of a
cooper pair 10-4 cm macroscopic
3. Superconducting transition temperature/Gap/Crit
ical field
In the superconducting ground state, all
electrons form these Cooper pair, with resultant
energy gap D
5. Specific Heat
10
5. Flux quantization Magnetic flux through a
superconductor ring is quantized and the
effective unit of charge is 2e rather than e.
---gtCooper pairs
B
11
11.4 Type II Superconductor
1957 Abrikosov
Type II
Coherence length lt Penetration depth
Type I
Type II
Hc1
Hc2
Hc
Type II Between Hc1 and Hc2, it is
electrically superconductor, but shows incomplete
Meissner effect
l
l
x
x
sup
nor
sup
nor
Type I
Type II
12
Mixed state between Hc1 and Hc2
The magnetic flux penetrate not in laminar
domains but in a regular array of flux tubes
carrying a quantum of flux ?0hc/2e Vortex phase
(Schubnikov Phase)
11.5 Tunneling and the Josephson Effect

• Single electron tunneling

D
EF
N
S
Thin insulator 50Å
13
I
TgtTc
T0
eV0D/2
V
V0

• Tunneling of Cooper pairs Josephson Effect 1962

Thin insulator 10Å
Sup
Sup
Thin insulator introduce phase shift in their
quantum wave function

• DC Josephson Effect A DC current flows across
  the junction in the absence of any electric or
  magnetic field.

• AC Josephson Effect A DC Voltage applied
  across the junction causes rf current oscillation
  across the junction

14
D.C.
A
A.C.
A
n 484000 V GHz
1 milivolt---gt 484 GHz
microwave