The document discusses superconductivity, a phenomenon in certain materials at low temperatures that exhibits zero electrical resistance and the Meissner effect. It covers key concepts such as types of superconductors, flux quantization, and the London equations, along with applications like SQUID devices and MRI. The document highlights important theoretical frameworks, including BCS theory and energy gaps associated with superconductivity.

1. Superconductivity
IBRAHIM ABD ELHAMID AHMED
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2. Main Items
 Introduction.
 Superconductivity.
 Meissner effect.
 Flux Quantization.
 Types of Superconductors.
 London Equations.
 BCS Theory.
 London Penetration Depth
 Applications of Super conductors.
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3. Introduction:
• In 1911 H. Kamerlingh Ohnes found that mercury lost
all electrical resistance
when cooled to the temperature
of liquid helium (4.2 K)and reached
the superconducting state.
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4. Superconductivity
• Superconductivity is a phenomenon occurring in certain
materials generally at very low temperatures ,
characterized by nearly zero electrical resistance and
expulsion of the magnetic field .
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5. Response Of Magnetic Field
(Meissner effect)
• So superconductivity material acts as an ideal
diamagnetic
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6. Response Of Magnetic Field
• When the applied field is increased to critical field
(𝐻 𝐶), the superconductivity is destroyed.
• The critical field (𝐻 𝐶) is a function of temperature.
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7. Response Of Magnetic Field
• This variation is empirically found to be represented by
the expression:
𝐻𝑐 𝑇 = 𝐻𝑐(0) 1 −
𝑇
𝑇𝑐
2
• Where 𝐻 𝐶(0) is the maximum value of the field
at 𝑇=0K. 𝐻 𝐶(0) And 𝑇𝑐 are constants of the material.
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8. Flux Quantization
• when a superconducting ring is placed in a magnetic
field and the field is removed, flux lines are trapped and
are maintained by a persistent current.
ɸ =
𝑛ℎ
2𝑒
= 𝑛ɸ0
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9. Types of Super conductors
• Type I (soft superconductors)
• Examples: Al , Zn ,Hg and Sn .
• Type II (hard
superconductors)
• Examples: Ta ,V ,and Nb.
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10. London Equations
• Maxwell's equation:
𝛻 × 𝐸 =
−𝑑𝐵
𝑑𝑡
• The first London equation:
𝑑𝐽 𝑆
𝑑𝑡
=
𝑛 𝑠 𝑒2
𝑚
𝐸
• The second London equation:
𝛻 × 𝐽𝑠 = −
𝑛 𝑠 𝑒2
𝑚
𝐵
Where:
𝐽𝑠 : Current density of superelectron & 𝑛 𝑠: Superelectron
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11. Energy Gap
• The exponential behavior of the electronic specific heat
in superconducting state implies the presence of an
energy gap.
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12. BCS Theory
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13. London Penetration Depth
• According to the London equation, the flux does not
suddenly drops to zero at the surface but decreases
exponentially.
• the magnetic field B decreases exponentially from its
external value to zero, according to the expression:
𝐵 𝑥 = 𝐵0 𝑒
−𝑥
𝝺
• Penetration depth varies with temperature according to
the empirical expression:
𝛌 𝑇 = 𝛌0 1 −
𝑇
𝑇𝑐
2
−1
2
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14. London Penetration Depth
• λ increases with the increase of 𝑇 and becomes infinite
at T = 𝑇𝑐
• 𝑤 =
𝑛 𝑠
𝑛0
Where w is called
order parameter
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15. Applications of Superconductors
 SQUID:
• SQUID stands for Superconducting Quantum
Interference Device.
 MRI:
• MRI stands for magnetic resonance imaging.
 Maglev train
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16. Thank you
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