Ballistic conductance of interacting electrons in the quantum Hall regime

Chklovskii, D. B., Matveev, K. A., Shklovskii, B. I. (May 1993) Ballistic conductance of interacting electrons in the quantum Hall regime. Physical Review B, 47 (19). p. 12605. ISSN 1098-0121

DOI: 10.1103/PhysRevB.47.12605


We propose a quantitative electrostatic theory for a gate-confined narrow channel of the two-dimensional electron gas in the integer and fractional quantum Hall regimes. Our theory is based on the zero-magnetic-field electrostatic solution, which yields a domelike profile of electron 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 liquids are formed in the channel. When the central strip in the channel is incompressible, the conductance G is quantized in units of e2/2πħ, 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 there is a compressible strip in the center of the channel. We also argue, based on the exact solution in a simple case, that conductance, in units of e2/2πħ, 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, including both the positions of the plateaus and the rises between them. We apply our theory to a quantum point contact, which is an experimental implementation of a narrow channel.

Item Type: Paper
Subjects: physics
CSHL Authors:
Communities: CSHL labs > Chklovskii lab
Depositing User: Matt Covey
Date: 15 May 1993
Date Deposited: 08 Apr 2016 19:25
Last Modified: 08 Apr 2016 19:25

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