Assignment Number #1 for PYL-703: Electronic Properties of Materials Q1. Starting from Drude’s equation, derive the frequency dependence of conductivity π(π). Consider that the electrons are in electric field of πΈΜ (π). ππΜ πΜ (π‘) = π Μ (π‘) − ππ‘ π Q2. The atom He3 has spin ½ and is a fermion. The density of liquid He3 is 0.081 g/cm3 near absolute zero. Calculate the Fermi energy πΈπΉ and the Fermi temperature is ππΉ . Q3. Outline the basic difference between Drude’s model and Sommerfeld’s model. Q4. Show that the specific heat for free electrons obtained from Sommerfeld model is linear in temperature. Q5. Calculate density of states for free electrons in two-dimension as per Sommerfeld model. Q6. Draw electronic band structure for electrons in a periodic lattice. Note: Show the diagrams in extended zone scheme and reduced zone scheme. Assume that the lattice is one-dimensional with the lattice spacing of π. Q7. Comment on the origin of bandgaps for free electrons in a periodic potential. Q8. What would be the shape of Fermi surface for a cubic metal?