Conventional Shubnikov-de Haas (SdH) theory (Landau quantisation in the
metallic regime)
2 ) sinh(
2 )
exp(
) ,
( 2 *
* 2
eB T m k
eB T m k
C B T
B
B B
SdH
h h
π π µ
π
= −
∆ρ
)]
1 (
0
cos[
xx
= ρ + ∆ ρ π ν −
ρ
SdH(1)
Landau quantisation modulates the DOS without inducing a QH liquid
DOS
E
ω c
h
Picture for conventional SdH oscillations
Introducing positive magnetoresistance (PMR) background
2 2
xy xx
xx
xx ρ + ρ
= ρ σ
e2
h
xy ν
ρ =
0 as
0
and
0
both σxx → ρxx → T →
Quantum Hall Conductor
•
ρxx, or more precisely, σxx increases with increasing T•
Activated behaviour: σxx exp(-∆/2kBT), where ∆is the mobility gap
∝
