Scannig Tunneling Spectroscopy of a 2DES in magnetic field

Two dimensional electron systems (2DES) in magnetic field exhibit the quantum Hall effect. This effect means that the conductivity of the 2DES vanishes except at half filling. This intriguing property has been explained by the formation of drift states in each Landau level. In simple terms, these drift states are caused by electrons running in skipping orbits along equipotential lines of the 2DES. For topological reasons all these drift states except the one in the center of the Landau level form a closed path and thus the corresponding electron states are localized. The single extended state in the center is responsible for the conductivity at half filling.

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Fig.1: (a) dI / dV-curves of the 2DES taken at different magnetic fields at the same lateral position reveal the subbands (0 T) and the spin-split Landau Levels (6 T to 12 T) of the 2DES. (b) Experimentally determined Landau fan diagram; blue (red) dashed lines: spin-down LLs of the 1st (2nd) subband; arrows: spin levels of the lowest LL.

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Fig. 2: dI/dV-images (a-g) of the 2DES taken at different energies with respect to the position of the lowest spin-split Landau Level (LL) as shown in (h). The images reveal the transition from localized drift states in the insulating phases at the low and high energy tails of the LL (a,b; f,g) to branched extended drift states at the quantum critical point in the centre of the LL (c-e).


With STS we were able to image the drift spin-resolved states. Landau quantization of the adsorbate induced 2DES is shown in Fig. 1. Fig. 2 shows the corresponding LDOS, where stripe like structures running irregularly through the area are visible. The detection of drift states offers the unique possibility to study multifractal properties of a quantum critical state, which is the extended one.