LOW DIMENSIONAL SYSTEMS
The effect of a nonmonotonic potential profile on edge magnetic states
E. B. Gorokhov, D. A. Romanov, S. A. Studenikin, and V. A. Tkachenko
Institute of Semiconductor Physics, Russian Academy of Sciences (Siberian Department), 630090 Novosibirsk,
Russia
O. A. Tkachenko
Novosibirsk State University, 630090 Novosibirsk, Russia
Submitted May 5, 1997; accepted for publication May 20, 1997
Fiz. Tekh. Poluprovodn. 32, 1083–1088 September 1998
The dispersion law for electrons moving along a specularly reflecting boundary of a two-
dimensional electron gas in the presence of a near-boundary potential well and a weak magnetic
field is investigated theoretically. Numerical simulation is used to identify a number of
features of the density of edge magnetic states that can be observed by magnetotransport and
magnetooptics investigations. Ways to fabricate structures for studying these states are
discussed. It is demonstrated that perfect-crystal interterrace boundaries can be created for a two-
dimensional electron gas by introducing oblique slip planes into the heterostructure.
© 1998 American Institute of Physics. S1063-78269801509-9
I. INTRODUCTION
Edge magnetic states EMS have recently been success-
fully used in recent times to explain various experiments on
quasi- two-dimensional 2D electron gases in strong mag-
netic fields, in particular the integer-valued quantum Hall
effect and Shubnikov-de Haas oscillations in semiconductor
heterostructures.
1
In fact, EMS are the only current carrying
states in the quantum-Hall-effect regime; therefore, they are
responsible for all the phenomena of electron transport in
quantizing magnetic fields.
During the earlier stages of investigating EMS, the edge
of the region where an electron gas exists was treated simply
as a geometrical boundary. This was followed by inclusion
of the smooth electrostatic barrier of the depletion layer, and
features of electronic screening in the quantum-Hall-effect
regime were discussed extensively in Refs. 2, 3, and 4. Until,
there have been no further discussions of more complex na-
tures or shapes of the potential near the boundary. This is not
surprising, since at low temperatures and strong magnetic
fields the current-carrying quasi-1D quasiparticles are
pressed tightly against the boundary and can avoid scattering
by fluctuation-induced obstacles in the potential around
them. In the one-electron picture, regardless of the behavior
of the potential near the boundary, the current in the final
analysis is determined by the number of Landau levels below
the Fermi level far from the boundary, where the potential
and electron gas are assumed to be uniform, the simplest
regime from a theoretical point of view.
The situation changes radically in weaker magnetic
fields, where scattering can no longer be ignored. In this case
we can find the current along the boundary by solving the
kinetic Boltzmann equation, in which we should use the dis-
persion relation for carriers in edge magnetic states. This
dispersion relation, in turn, is determined by solving the
Schro
¨
dinger equation with a specific profile for the near-
boundary potential. The roadmap to solving this problem
taking into account collisions and the combined action of
magnetic, electric, and high-frequency fields on an electron
as applied to EMS has not yet been fully identified. How-
ever, a number of useful conclusions from the point of view
of experiment can be derived directly from analyzing the
form of the dispersion relation, as we will show below by
numerically simulating the edge current states.
Here a relevant analogy with magnetic surface levels for
three-dimensional crystals is worth mentioning. Magnetic
surface levels, which were first observed as peculiar reso-
nance peaks in the rf impedance of metals at very weak
magnetic fields,
5
were later identified from their contribu-
tions to a number of static effects in semiconductors.
6,7
As
was shown, these latter effects can significantly affect the
character of the surface potential.
8
Edge magnetic states in a
two-dimensional electron gas have considerable advantages
compared to the three-dimensional case with regard to fur-
ther investigations and possible applications of these phe-
nomena.
Contemporary methods for growing GaAs/AlGaAs
structures make it possible to obtain mean-free pathS for an
electron in the 2D gas greater than 10 m. Methods available
today for lithography allow us to create various shapes of the
potential wells on scales smaller than the mean-free path of
an electron. For example, by using a system of gate elec-
trodes we can vary the depth and width of the potential well
for a 2D electron gas in the lateral direction. This creates
unique possibilities for controlling the dispersion relation of
edge magnetic states by using a nonmonotonic profile for the
edge potential. In other words, it is possible to ‘‘prepare’’
SEMICONDUCTORS VOLUME 32, NUMBER 9 SEPTEMBER 1998
970 1063-7826/98/32(9)/5/$15.00 © 1998 American Institute of Physics