Visualizing the multifractal wavefunctions of a disordered two-dimensional electron gas*

The wavefunctions of a disordered two-dimensional (2D) electron gas near the quantum-critical Anderson transition are predicted to exhibit multifractal scaling in their real space amplitude. We experimentally investigate the appearance of these characteristics in the spatially resolved local density of states (LDOS) of the 2D mixed surface alloy BixPb(1−x)/Ag(111), combining scanning tunneling microscopy (STM) with spin- and angle-resolved inverse-photoemission experiments [1]. Our detailed knowledge of the mixed surface alloy’s electronic band and lattice structure enables us to construct a realistic Anderson tight binding model and to directly compare the calculated LDOS characteristics with those from STM measurements. The analyses of these 2D LDOS maps reveal their log-normal distributions and multifractal scaling characteristics of the underlying wavefunctions with a finite anomalous scaling exponent. Finally, our experimental results confirm predictions of an exact scaling symmetry for Anderson quantum phase transitions in the Wigner-Dyson classes.
[1] B. Jäck et al., https://arxiv.org/abs/2010.07554 (2020).