Superconductivity is a phenomenon where electrical resistance drops to exactly zero below a critical temperature. It was discovered in 1911. Some key properties include the Meissner effect where magnetic fields are expelled, and the isotope effect showing the involvement of electron-phonon interaction. Applications include MRI machines, particle accelerators, and SQUID magnetometers. Future applications may include more efficient power grids, electric vehicles, and magnetic refrigeration if issues with alternating current can be addressed.

1. Superconductivity- A quick review
• Experimental Survey
– Occurrence of Superconductivity
– Destruction of Superconductivity by Magnetic Fields
– Meisner Effect
– Heat Capacity
– Energy Gap
– Microwave and Infrared Properties
– Isotope Effect
• High-Temperature Superconductors

2. K.Onnes (1911) :
ρ → 0 as T → TC
Superconductivity :
It is a phenomenon
of exactly
zero electrical
resistance. It was
discovered by
Dutch
physicist Heike
Kamerlingh
Onnes on April 8,
1911

3. Meissner Effect: Expulsion of magnetic
fields occurring in certain materials when cooled below
a characteristic critical temperature.
1. ρ → 0 for T < TC . Persistent
current in ring lasts > 1 yr.
2. NMR: supercurrent decay time >
105
yrs.
3. Meissner effect: superconductor =
perfect diamagnet.
Normal state SuperC state
4. BCS theory: Cooper pairs (k↑, –k↓ ). See App. H & I.

4. Occurrence of Superconductivity
Occurrence:
Metallic elements, alloys, intermetallic compounds,
doped semiconductors, organic metals, …
Range of TC :
90K for YBa2Cu3O7.
.001K for Rh.
Si: TC = 8.3K at P = 165 Kbar

5. Destruction of Superconductivity by Magnetic Fields
Magnetic field destroys superconductivity.
( ) 0C CH T =
C aCH B=
Magnetic impurities lower TC :
10–4
Fe destroys superC of Mo (TC = 0.92K ).
1% Gd lowers TC of La from 5.6K to 0.6K.
Non-magnetic impurities do not affect TC .
in CGS units
( ) ( )
2
0 1C C
C
T
H T H
T
  
 = − ÷
   

6. Meissner Effect
Normal state SuperC state
B = 0 inside superC
For a long thin specimen with long axis // Ha,
H is the same inside & outside the specimen (depolarizing field ~ 0)
4 0a π= + =B H M →
1
4a
M
H π
= −
Caution: A perfect conductor (ρ = 0) may not exhibit Meissner effect.
ρ=E jOhm’s law → 0 0if ρ= =E
1
0
c t
∂
∇× + =
∂
B
E → 0
t
∂
=
∂
B
(B is frozen, not expelled.)
Also, a perfect conductor cannot maintain a permanent eddy current screen
→ B penetrates ~1 cm/hr.

7. Most elements
Alloys / Transition metals with high
ρ. ρ = 0 but B ≠ 0 in vortex state.

8. HC2 ~ 41T for Nb3(Al0.7 Ge0.3).
HC2 ~ 54T for PbMo6S8.
Commercial superconducting magnets of ~1T are readily available.

9. Heat Capacity
S NS S<
→ superC state is more ordered
ΔS ~ 10–4
kB per atom
→ only 10–4
e’s participate in transition.
Al
NC Tγ= N
T
S
T
=
∂
∂ NS Tγ=→

10. Isotope Effect
CM T constα
=Isotope effect:
→ e-phonon interaction involved in superC.
Original BCS:
1/2
C DebyeT Mθ −
µ µ 1
2
α =→
Deviation from α = ½ can be caused by coulomb interaction between e’s.
Absence of isotope effect due to band structure.
( )1/2 FN V
B C Dk T e εγ
ω
π
−
= h

11. Thermodynamics of the Superconducting
Type I superC:
0
aB
adW ×= −∫ BM
adF d= − ×M B
1
4
S aaF Bd B d
π
=
( ) ( )
2
0
8
a
S a S
B
F B F
π
− =
( ) ( )0N aC NF B F=
( ) ( )0 0N SF F F∆ = −
( ) ( )N aC S aCF B F B= ( )
2
0
8
aC
S
B
F
π
= +
2
8
aCB
π
=
C C
N S
T T
dF dF
dT dT
=
→ no latent heat
( 2nd
order transition)
(continuous transition)
4π= +B H M

12. Josephson Superconductor Tunneling
• DC Josephson effect:
DC current when E = B = 0
• AC Josephson effect:
rf oscillation for DC V.
• Macroscopic long-range quantum interference:
B across 2 junctions → interference effects on IS

13. DC Josephson Effect
1
2i T
t
ψ
ψ
∂
=
∂
h h 2
1i T
t
ψ
ψ
∂
=
∂
h h T = transfer frequency
ji
j jn e
θ
ψ =
→ 11 1
1
1
1
2
n
i
t n t t
ψ θ
ψ
∂ ∂ ∂
= + ÷
∂ ∂ ∂ 
2i T ψ= −
2
1
in
i T e
n
δ
= −
22 2
2
2
1
2
n
i
t n t t
ψ θ
ψ
∂ ∂ ∂
= + ÷
∂ ∂ ∂ 
1i T ψ= −
1 1 2
1 1
1
2
n
i i T
n t t
θ ψ
ψ
∂ ∂
+ = −
∂ ∂∴
2 1δ θ θ= −
2 2 1
2 2
1
2
n
i i T
n t t
θ ψ
ψ
∂ ∂
+ = −
∂ ∂
1
2
i
n
i T e
n
δ−
= −
Real
parts:
1 2
1 1
1
sin
2
n n
T
n t n
δ
∂
=
∂
2 1
2 2
1
sin
2
n n
T
n t n
δ
∂
= −
∂
Imaginary
parts:
1 2
1
cos
n
T
t n
θ
δ
∂
= −
∂
2 1
2
cos
n
T
t n
θ
δ
∂
= −
∂
→
1
1 22 sin
n
T n n
t
δ
∂
=
∂
1 2n n
t t
∂ ∂
= −
∂ ∂
2
1 22 sin
n
T n n
t
δ
∂
= −
∂
∴
∴ 1 2
1 2
1 1
cosn n
t n n
δ
δ
 ∂
= − ÷ ÷∂  
1n
J
t
µ
∂
∂ → 0 sinJ J δ= n1 ≈ n2 → DC current up to iC while V = 0.
1 2 0n n δ δ≈ → ≈

14. AC Josephson Effect
11 1
1
1
1
2
n
i
t n t t
ψ θ
ψ
∂ ∂ ∂
= + ÷
∂ ∂ ∂ 
2 1
eV
i T iψ ψ= − +
h
22 2
2
2
1
2
n
i
t n t t
ψ θ
ψ
∂ ∂ ∂
= + ÷
∂ ∂ ∂ 
1 1 2
1 1
1
2
i
n n eV
i i T e i
n t t n
δθ∂ ∂
+ = − +
∂ ∂ h∴
2 12
2 2
1
2
i
n n eV
i i T e i
n t t n
δθ −
∂ ∂
+ = − −
∂ ∂ h
Real
parts:
1 2
1 1
1
sin
2
n n
T
n t n
δ
∂
=
∂
2 1
2 2
1
sin
2
n n
T
n t n
δ
∂
= −
∂
Imaginary
parts:
1 2
1
cos
n eV
T
t n
θ
δ
∂
= − +
∂ h
2 1
2
cos
n eV
T
t n
θ
δ
∂
= − −
∂ h
→
1
1 22 sin
n
T n n
t
δ
∂
=
∂
1 2n n
t t
∂ ∂
= −
∂ ∂
2
1 22 sin
n
T n n
t
δ
∂
= −
∂
∴
∴
0 sinJ J δ=
V across junction:
1
2 1i T eV
t
ψ
ψ ψ
∂
= −
∂
h h 2
1 2i T eV
t
ψ
ψ ψ
∂
= +
∂
h h 2q e= −
1 2
eV
i T iψ ψ= − −
h
1 2
1 2
1 1 2
cos
eV
n n
t n n
δ
δ
 ∂
= − − ÷ ÷∂   h
AC current with
1 2 0
2 eV
n n tδ δ≈ → ≈ −
h
0 0
2
sin
eV
J tδ
 
≈ − ÷
 h
2 eV
ω =
h
483.6 Mhz≈ for V = 1 μV
Precision
measure
of e/

15. High-Temperature Superconductors
TC ceiling for intermetallic compounds = 23K.

16. Applications
Superconducting magnets are some of the most powerful electromagnets used in
• MRI/NMR machines,
• mass spectrometers,
• and the beam-steering magnets used in particle accelerators.
Superconductors are used to build Josephson junctions which are the building blocks
of SQUIDs (superconducting quantum interference devices), the most
sensitive magnetometers known.
SQUIDs are used in scanning SQUID microscopes and magnetoencephalography.
The large resistance change at the transition from the normal- to the
superconducting state is used to build thermometers in
cryogenic micro-calorimeter, photon detectors. The same effect is
used in ultrasensitive bolometers made from superconducting
materials.

17. Promising future applications
• high-performance smart grid,
• electric power transmission,
• transformers,
• power storage devices,
• electric motors (e.g. for vehicle propulsion, as in maglev trains),
• magnetic levitation devices,
• fault current limiters,
•enhancing spintronic devices with superconducting materials,
• and superconducting magnetic refrigeration.

18. Promising future applications
However, superconductivity is sensitive to moving
magnetic fields so applications that use alternating
current (e.g. transformers) will be more difficult to
develop than those that rely upon direct current.
Compared to traditional power lines superconducting
transmission lines are more efficient and require only
a fraction of the space, which would not only lead to
a better environmental performance but could also
improve public acceptance for expansion of the
electric grid.