Assignment Number #1 for PYL-703: Electronic Properties of Materials
Q1. Starting from Drude’s equation, derive the frequency dependence of conductivity 𝜎(𝜔).
Consider that the electrons are in electric field of 𝐸̅ (𝜔).
𝑑𝑝̅
𝑝̅ (𝑡)
= 𝑓 ̅(𝑡) −
𝑑𝑡
𝜏
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 𝐸𝐹 and the Fermi temperature is 𝑇𝐹 .
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 𝑎.
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?