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Viscous fingering and a shape of an electronic droplet in the Quantum Hall regime

Oded Agam·Eldad Bettelheim·P. Wiegmann·A. Zabrodin
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Abstract

We show that the semiclassical dynamics of an electronic droplet confined in the plane in a quantizing inhomogeneous magnetic field in the regime when the electrostatic interaction is negligible is similar to viscous (Saffman-Taylor) fingering on the interface between two fluids with different viscosities confined in a Hele-Shaw cell. Both phenomena are described by the same equations with scales differing by a factor of up to $10^{-9}$. We also report the quasiclassical wave function of the droplet in an inhomogeneous magnetic field.

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Oded Agam, Eldad Bettelheim, P. Wiegmann, A. Zabrodin. 2002-02-14. Viscous fingering and a shape of an electronic droplet in the Quantum Hall regime. https://doi.org/10.1103/physrevlett.88.236801

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