1
Theory of Solids HW10 Solution
By Qifeng Shan
Ashcroft and Mermin’s book
143
If there is any nonuniformity of the magnetic field over the sample of metal used in a de
Haasvan Alphen experiment, then the structure in
g
(
ε
) will reflect this variation.
Different regions will have maxima in
g
(
ε
) at different field strengths, and the
susceptibility, which sums contributions from all regions, may lose its oscillatory
structure. To avoid this, any spatial variation
δ
H
in the field must lead to a variation
δ
ε
v
that is small compared with
ε
v
+1
ε
v
for the extremal orbits. Using the fact that
ǝ
A
(
ε
,
k
z
)
/
ǝ
H
from (14.13) for an extremal orbit. Deduce from this that to preserve the oscillatory
structure the field inhomogeneity must satisfy
A
A
H
H
,
(14.25)
where
Δ
A
is given in (14.12).
Solution
:
From Eq. (14.13), we have
A
v
k
k
A
z
z
v
,
(1)
And from (14,12),
Δ
A
.
2
c
eH
A
(2)
At extrmal orbits, the first derivative for
A
with respect to
H
vanishes:
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 Fall '09
 Shan
 Solid State Physics, Magnetic Field, Velocity, Fermat's theorem, Qifeng Shan Ashcroft

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