Question: Example 9.12: Debye frequency in a superconductor Considering the cubic metal lattice of a superconductor with neighbouring ion separation d at temperature T = 0,

Example 9.12: Debye frequency in a superconductor Considering the cubic metal lattice of a superconductor with neighbouring ion separation d at temperature T = 0, show that the Debye frequency is given by

ωD =

2√2

(meMaBd3)1/2 2√2

√meM√nd2

, (9.48)

where me is the mass of the electron, M that of an ion, aB the Bohr radius, and d naB, n an integer.

[Hint: Equate the oscillator potential of the ion to the energy of attraction between electron and ion, and express e2 in terms of aB, giving e2 2/med ].

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