Screening and phase transitions in low-dimensional structures

We have proposed an original method of characterizing the electrostatic screening of electron gas by means of a highly sensitive capacitance bridge. Using this method, we measured, at low temperatures (1.2 K - 4 K), the dependence of the density of screening electron states in low-dimensional semiconductor structures on the magnetic field. From the shape of the curves obtained at different temperatures we have concluded that in the quantum Hall regime at certain magnetic fields the two-dimensional electron gas is transformed into one-dimensional conducting channels (so-called dragon curves). It is a topological phase transition that is similar to the transition between vortex and non-vortex flux observed in superfluid helium.

The dependence of capacitance CM of a structure with two-dimensional electron gas on magnetic induction B (blue curve). The dependence shows maxima at magnetic induction values where quantization of the so-called Hall resistance Rxy (red curve) takes place. From the height and from the structure of the maxima we can deduce the screening ability of the electron gas. This information cannot be acquired only from the measurement of the Hall resistance itself.

Reference
J. J. Mareš, A. Siddiki, D. Kindl, P. Hubík, and J. Krištofik
Electrostatic screening and experimental evidence of a topological phase transition in a bulk quantum Hall liquid
New Journal of Physics 11 (2009) 083028 (17pp).