Physics 573: Problem set 5
-
Adapt the discussion of classical charge motion (chapter 1 in AM,
chapter 6 in Kittel) to fill in
the details for the conductivity tensor in the presence of crossed
(constant) electric and magnetic fields.
-
A tetragonal crystal has conductivities in the base (square plane)
σxx = σyy,
and also σxy = 0.
Show that the current in this plane is parallel to the electric field in
the plane. Discuss the same question for electric fields that are out
of the xy plane.
-
A certain partially compensated semiconductor has both electrons and
holes. The electrons have density n and relaxation time
τn, and the holes have density p and
relaxation time
τp. What is the high field value of the Hall
conductance σxy?
- A simple tight-binding model can be made
from Coulomb interaction between an electron and two ions (at
r = 0, and r = R) that each have
e.g. a hydrogen-like 1s atomic orbital.
(a) Evaluate the overlap
integral between the ions, and
(b) estimate the width of the band for a cubic crystal of such
atoms if the cube
edge is equal to twice the Bohr radius.
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