Db. Chklovskii et al., BALLISTIC CONDUCTANCE OF INTERACTING ELECTRONS IN THE QUANTUM HALL REGIME, Physical review. B, Condensed matter, 47(19), 1993, pp. 12605-12617
We propose a quantitative electrostatic theory for a gate-confined nar
row channel of the two-dimensional electron gas in the integer and fra
ctional quantum Hall regimes. Our theory is based on the zero-magnetic
-field electrostatic solution, which yields a domelike profile of elec
tron density. This solution is valid when the width of the channel is
larger than the Bohr radius in the semiconductor. In a strong magnetic
field H, alternating strips of compressible and incompressible liquid
s are formed in the channel. When the central strip in the channel is
incompressible, the conductance G is quantized in units of e2/2pihBAR,
i.e., there are plateaus in G as a function of the magnetic field H.
However, we have found that in a much wider range of magnetic fields t
here is a compressible strip in the center of the channel. We also arg
ue, based on the exact solution in a simple case, that conductance, in
units of e2/2pihBAR, of a short and ''clean'' channel is given by the
filling factor in the center of the channel, allowing us to calculate
conductance as a function of magnetic field and gate voltage, includi
ng both the positions of the plateaus and the rises between them. We a
pply our theory to a quantum point contact, which is an experimental i
mplementation of a narrow channel.