Download Williams Thesis - Center for Quantum Devices

-10
S XY (kΩ) 13
VB ( V )
40
S XY (kΩ)
12
(a)
8
4
-20
-5
0 B = 8T
V =-20V
-4 B
0
4
V1
(b)
μd
Region 1
VT ( V )
I
μs
V2
6
Region 2
VT ( V )
8
-4
8 (c)
VB =-20V
S XY (kΩ) 10
(d)
S XY
6
B(T)
2 kΩ
4
2
0
1
2
3
4
5
VT ( V )
6 3
4
5
VT ( V )
6
Figure 6.3: (a) Sxy (Vtg ) at B=8T shows well developed QH platueas of 2, 6 and 10 e2 /h
in the unipolar regime. The resistance is lower in the p-n regime (for values of Vtg on
the right of the dashed red line), a result of edge state transport in Region 2. A peak in
resistance (indicated by the black arrow) develops on the bipolar side. Inset: This peak
(yellow line indicated by the black arrow) is reduced in magnitude as Vbg approaches the
CNP (Vbg =40V) of Region 1. (b) Schematic of the edge states present in the two regions
of the device. When the edge states propagate as shown, the voltage difference between V1
and V2 is reduced. (c) Sxy (Vtg , B) for B between 0 and 8T. In addition to this reduction
in resistance, a peak forms that moves linearly in the (Vtg ,B) space. (d) horizontal cuts
corresponding to the colored lines in Fig. 6.3(c) show a gradual evolution (black dashed
line) of the zero B-field peak to the resistance peak in the QH regime.
resistance from ρxx . This case is unlikely as the contribution from ρxx in the p-p regime
is not as large as this peak observed in the p-n regime. The reduction of resistance and
peak disappear as the CNP of Region 1 is approached [inset of Fig. 6.3(a)]. Sxy (Vtg , B)
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