Scanning tunneling spectroscopic features of partially filled Landau levels under different tip conditions

Under strong magnetic fields, 2D electron gases form flat Landau levels (LL) that are highly degenerate. Such degeneracy can be lifted by electron-electron interaction and the presence of impurities which creates localized states that leads to quantization of Hall conductance. Here we perform density tuned scanning tunneling spectroscopy study of LL in graphene using tips that have different tip-sample workfunction mismatch. When the mismatch is near zero, spectral measurements reveal sashes cutting through the partially filled LL. These features, called Haldane sashes, reported in pulse tunneling experiment in GaAs, separate states with different isospins and are a result of Haldane pseudo-potential between the incoming electrons and existing electrons in LL. When the spectroscopy is taken with positive (negative) workfunction mismatch, the sashes are replaced by uptick (downtick) features emanating from integer gaps. We further study the origin of tick features by bringing the tip closer to a charged defect and observing the energy evolution of such features as the tip-induced potential interacting with the impurity potential. Similar features also manifest around fractional gaps, the origin of which require further investigation and may reveal information on the anyon.