Show that for the superconducting transition in the absence of magnetic field, there is a discontinuity in the specific heat of a superconductor at Tc which can be written as:
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A metallic element has a density of , a lattice constant of
and an atomic weight
. Calculate the number of atoms per unit cell of this element and predict its lattice crystal structure.
For the energy dispersion relation:
calculate the inverse mass tensor.
In Sommerfeld free electron theory, show that at a temperature T
(i) and (ii)
A metallic crystal has an fcc lattice with a lattice constant . Explain whether the following planes are allowed or forbidden for X-ray diffraction:
(100), (111), (210), (220)
Calculate the X-ray diffraction angles for the allowed planes. Assume that diffraction occurs in the first order and the X-ray wavelength is .
Calculate the energy dispersion for s-band in the bcc lattice for the tight binding approximation.
Note: For the central atom located at (0,0,0) in the bcc unit cell, the nearest neighbours are located at , where a is the lattice constant.
Explain the significance of the pseudogap phase in cuprates.
The susceptibility of is
and its density is
. Calculate its total polarisability. Assume that the mass number for
is 32.