3. Static magnetoconductivity tensor. For the drift velocity theory of m(dv/dt +v/t) = −e(E + B ×v/c), with B = B2, show that the static current density can be written in matrix form as 0- In the high magnetic field limit %0 1+ (@T)² 1 @ T 0 @T>>1, show that σ. = yx -00 T 1 0 1+ (@T)² nec B 0 0 xy Ex E E₂
3. Static magnetoconductivity tensor. For the drift velocity theory of m(dv/dt +v/t) = −e(E + B ×v/c), with B = B2, show that the static current density can be written in matrix form as 0- In the high magnetic field limit %0 1+ (@T)² 1 @ T 0 @T>>1, show that σ. = yx -00 T 1 0 1+ (@T)² nec B 0 0 xy Ex E E₂
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Transcribed Image Text:3. Static magnetoconductivity tensor. For the drift velocity theory of
m(dv/dt +v/t) = −e(E + B ×v/c), with B = B2, show that the static current density
can be written in matrix form as
0--
In the high magnetic field limit
%0
1+ (@T)²
1
@ T
0
-00 t
1
0
σ =
yx
@T>>1, show that
0
0
1+ (@_T)²
nec
B
xy
Ex
E
E₂
In this limit=0, to order 1/7. The quantity o
conductivity.
yx
called the Hall
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Step 1: Starting with equation of motion of electron in the crystal
VIEWStep 2: Expression for drift velocity along each direction Vx , Vy & Vz
VIEWStep 3: Relation between current density & drift velocity & Expression of current density along x direction
VIEWStep 4: Expression of current density along y & z direction & then final result
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