Fig. 4: KPFM measurements of incompressible strips.

a Schematic of bulk closed cyclotron orbits with cyclotron energy \({\hbar \omega }_{C}\) and edge quantum Hall states leading to compressible and incompressible strips at the device edge boundary. b, c Schematic of the bending of the Landau levels in a confining potential boundary (b) in a noninteraction picture and (c) in an interacting picture leading to a “wedding cake-like” series of plateaus in Landau levels near the boundary edge. A compressible strip is formed when a Landau level is at the Fermi level, separated by incompressible strips (red dashed lines) during Landau level transitions. d Kelvin probe map at \(B=5\,\text{T}\) of the chemical potential as a function of Y-position across the quantum Hall boundary (indicated in the black circle in Fig. 2a) and local-gate potential. In the local-gate area, Landau levels from \(N=-2\) [LL(−2)] to \(N=+1\) [LL(+1)] are seen in the different colored plateaus. AFM settings: 2 nm oscillation amplitude, \(\triangle f=-2\,{\rm{Hz}}\), and 20 mV sample bias modulation at 1.4 Hz. e Incompressible strips in the chemical potential are observed in the lines traces at \({\rm{G}}1=-0.9\,\text{V}\,\left({\rm{red}}\right)\,\text{and}\,{\rm{G}}1=-0.6\,\text{V}\,({\rm{blue}})\) (white horizontal lines in (d)) corresponding to filling factors \(\nu =-6,-2,\) and \(-1\). The transitions separate plateaus between Landau levels, LL(−2) to LL(−1), and LL(−1) to LL(0), confirming the “wedding cake-like” structure predicted in ref. ⁴⁶ .