15.2 Magnetic Fields
445
Fig. 15.18 Hall resistivity ρ xy and longitudinal resistivity ρ xx for a modulation-doped GaAs/(Al,Ga)As heterostructure
(n = 4 × 10 11 cm −2 , μ = 8.6 × 10 4 cm 2 /Vs) at 50 mK as a function of magnetic field (10 kG=1 T). The numbers refer
to the quantum number and spin polarization of the Landau level involved. The inset shows schematically the Hall bar
geometry, V L (V H ) denotes the longitudinal (Hall) voltage drop. Reprinted with permission from [1459], ©1982 APS
ρ xy =
−σ xy
σ 2
xx + σ 2
xy
→ −
B
n e
.
(15.41c)
15.2.8.1 Integer QHE
Experiments yield strong deviations from the linear behavior of the transverse resistivity ρ xy ∝ B
(15.41c) for large magnetic fields at low temperatures for samples with high carrier mobility, i.e.
ω c τ 1 (Fig. 15.18). In Fig. 15.19a, b, Hall bars are shown for 2DEGs in silicon metal-oxidesemiconductor field-effect transistor (Si-MOSFET) electron inversion layers and at GaAs/(Al,Ga)As
heterostructures, respectively.
The Hall resistivity exhibits extended Hall plateaus with resistivity values that are given by
1
ρ xy
= ν
e
2
h
,
(15.42)