Experimental evidence for edge-like states in three-dimensional electron systems

Abstract

The local density of states ͑DOS͒ of n-InAs͑110͒ is measured in the extreme quantum limit by lowtemperature scanning tunneling microscopy. Based on the general trends published previously ͓Phys. Rev. Lett. 86, 1582 ͑2001͔͒ we analyze the data in more detail. First the influence of the tip induced quantum dot is studied. It turns out that the observed serpentine structures are not correlated with the properties of the quantum dot, which lead us to the conclusion that they are caused by the three-dimensional ͑3D͒ DOS of the semiconductor. The serpentine structures move with increasing energy similar to equipotential lines of a twodimensional potential landscape. With increasing magnetic field additional serpentines appear until a complete network penetrates the visible area. Moreover, an uncorrugated DOS coexists with the serpentine structures up to the highest magnetic field of 6 T. The results lead us to the conclusion that an increasing part of the DOS is localized in the direction parallel to the magnetic field, effectively acting as a two-dimensional DOS and thus exhibiting edgelike states. This implies that the steplike feature of the Hall resistance in the extreme quantum limit is a precursor of a quantized Hall step.

Scanning Tunneling Spectroscopy

“…Probably, a partial localization of the electrons parallel to the magnetic field arises in the extreme quantum limit prior to magnetic freeze out. This could lead to local 2D properties of the electrons [37]. Thus, electrons running along equipotential lines of the disorder also exist in 3D at sufficiently strong magnetic fields.…”