Tunneling between edge states in the quantum Hall regime limited by a mesoscopic island:
A current-plateau phenomenon
Z. H. Liu, G. Nachtwei, J. Groß, R. R. Gerhardts, J. Weis, K. von Klitzing, and K. Eberl
Max-Planck-Institut fu ¨r Festko ¨rperforschung, Heisenbergstraße 1, D-70569 Stuttgart, Germany
Received 23 March 1998
Well-developed current plateaus have been observed in the I - V characteristics of Corbino devices in the
quantum Hall regime, if a striplike island of mesoscopic dimensions is located between two trench fingers
which are etched radially between the central and outer Ohmic contacts. The trenches are 100 nm wide and
define, together with the island, two constrictions of 550–700-nm width. The current plateaus are due to a
limitation of the tunneling rate by the filling of nonequilibrium states around the island. The evolution of the
current plateaus with the filling factor is qualitatively explained by quasielastic inter-Landau-level tunneling.
The latter mechanism determines the onset of the tunneling-current plateau, which extends until the complete
local breakdown of the quantum Hall regime around the island is reached. We investigated this tunneling
phenomenon as a function of the temperature in the range from 23 mK to 2.1 K, and for various sizes of the
island, ranging from 100250 nm
2
to 100 nm8 m. The plateaus were better pronounced, the lower the
temperature and the smaller the island was. To explain the observed tunneling-current plateaus, we suggest a
picture including the properties of the edge states near the trenches and around the island and the incom-
pressible quantum Hall region in between them. S0163-18299804731-6
I. INTRODUCTION
In two-dimensional electron systems 2DES with lateral
confinement, edge channels form near the boundaries in
quantizing magnetic fields.
1
These edge channels can domi-
nate the electronic transport
2
and provide a possible explana-
tion for the quantum Hall effect QHE,
3,4
and a variety of
related phenomena for an overview, see Ref. 5. Therefore,
tunneling between edge states was extensively investigated
both theoretically and experimentally see also Ref. 5.
Recently, tunneling between edge states of a device which
contains an antidot in the middle of a mesoscopic constric-
tion was investigated.
6–8
At very low excitations, Aharonov-
Bohm AB oscillations were observable in the
conductivity.
6–8
We have patterned a similar structure on a Corbino de-
vice, and investigated the current-voltage characteristics in
the QH regime. No tunneling current was observable at small
source-drain voltages. This is due to the formation of incom-
pressible regions insulating barriers between the compress-
ible edge states near the trenches and around the island in
between at integer filling factors.
9
At higher voltages, we
observed well-developed current steps in the I - V character-
istics of such an arrangement, which we attribute to a limi-
tation of the tunneling current by the charging of nonequilib-
rium states around the island.
The main differences of our study from the experiments
of Refs. 6–8 on similar constrictions are the size of the ob-
ject in between the two trenches longer in our case and the
mode of operation, which works far from equilibrium by the
application of high local electric fields instead of aiming on
the AB effect. To realize this mode of operation, the con-
striction had to be wide enough to provide a stable QH cur-
rent path at lower voltages, but small enough to allow tun-
neling at higher voltages. Thus the tunneling is effectively
suppressed up to rather large source-drain voltages, and the
onset of current flow is far beyond the range where the AB
effect is observable.
II. SAMPLES
All devices were fabricated from two Ga
1 -x
Al
x
As/GaAs
heterostructures containing a 2DES, with different densities
n
s
and mobilities
H
( n
s
=2.210
11
cm
-2
,
H
=8.010
5
cm
2
/V s for sample I; and n
s
=3.110
11
cm
-2
,
H
=1.3
10
5
cm
2
/V s for the three samples of sample set II. Figure
1 shows the scheme of the device: in a Corbino ring with a
channel width of 75 m, two trench fingers with a width of
about 100 nm in the narrowest region are etched radially
between the central and outer Ohmic contacts, defining a
small constriction with widths of 1.5 m sample I, 1.2 m
samples IIa and IIc, and 2.1 m sample IIb. An oval
antidot with a size of 100300 nm
2
sample I is etched in
the center of the constriction, with the long direction perpen-
dicular to the trench fingers Fig. 1. The island of the
samples of set II have a width of 100 nm and variable
lengths of 250 nm sample IIa,1 m sample IIb, and 8
m sample IIc, oriented either along sample IIb or per-
pendicular samples IIa and IIc to the trench finger direc-
tion. The whole pattern was prepared by electron-beam li-
thography, followed by reactive ion etching. The etching was
performed to a depth of about 100 nm to ensure a complete
removing of the 2DES the Si doping layer was located at 60
nm below the cap layer in the pattern region. In the QH
regime, this arrangement represents a tunneling device: the
compressible strips surrounding the two trench fingers, being
either in contact with the central or outer Ohmic contacts of
the Corbino ring, form the source and the drain contact. The
island provides electronic states which are isolated from the
PHYSICAL REVIEW B 15 AUGUST 1998-I VOLUME 58, NUMBER 7
PRB 58 0163-1829/98/587/40287/$15.00 4028 © 1998 The American Physical Society