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Chapter 10: Q21CQ (page 467)

What is Cooper pair, and what role does it play in superconductivity?

Short Answer

Expert verified

Cooper pairs are a pair of electrons at states slightly above Fermi energy and attract each other mediated via photons.

Step by step solution

01

Significance of cooper pair

Hundreds of nanometers, three orders of magnitude bigger than the lattice spacing, are thought to be the range over which electron pairs are coupling, according to the behaviour of superconductors. These linked electrons, known as Cooper pairs, can assume the characteristics of a boson and condense into the ground state.

02

Step 2:

Cooper pairs have the same momentum and are more ordered. They are at lower energy state then the normal electrons in superconductors.

03

Step 3:

At lower temperature, random vibration of the positive ions cannot scatter electrons if they are in the form of cooper pairs.

Hence, cooper pair forms when there is superconductivity. When they are broken the superconductivity also disappears.

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Most popular questions from this chapter

why is covalent bonding directional, while ionic bonding is not?

Question: When electrons cross from the n-type to the p-type to equalize the Fermi energy on both sides in an unbiased diode they leave the n-type side with an excess of positive charge and give the p-type side an excess of negative. Charge layers oppose one another on either side of the depletion zone, producing. in essence, a capacitor which harbors the so-called built-in electric

field. The crossing of the electrons to equalize the Fermi energy produces the dogleg in the bands of roughly Egap , and the corresponding potential differerence

is Egap /e. The depletion zone in a typical diode is wide, and the band gap is 1.0 eV. How large is the built-in electric field?

Describe the similarities and differences between Type-I and Type-II superconductors.

Question: The Fermi velocity VF is defined byEF=12mvF2 , where is the fermi energy. The Fermi energy for silver is 5.5eV.(a) Calculate the Fermi velocity.(b) what would be the wavelength of an electron with this velocity. (c)How does this compare with the lattice spacing of 0.41 nm? Does the order of magnitude makes sence?

As a crude approximation, an impurity pentavalent atom in a (tetravalent) silicon lattice can be treated as a one-electron atom, in which the extra electron orbits a net positive charge of 1. Because this "atom" is not in free space, however, the permitivity of free space, ε0. must be replaced by κε0, whereκ is the dielectric constant of the surrounding material. The hydrogen atom ground-state energies would thus become

E=−me42(4πκε0)2ℏ21n2=−13.6eVκ2n2

Given κ=12for silicon, how much energy is needed to free a donor electron in its ground state? (Actually. the effective mass of the donor electron is less than , so this prediction is somewhat high.)
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