  The breakdown of scale invariance in turbulent flows, known as multifractal
scaling, is considered a cornerstone of turbulence. In solar wind turbulence, a
monofractal behavior can be observed at electron scales, in contrast to larger
scales where multifractality always prevails. Why scale invariance appears at
electron scales is a challenging theoretical puzzle with important implications
for understanding solar wind heating and acceleration. We investigate this
long-standing problem using direct numerical simulations (DNS) of
three-dimensional electron reduced magnetohydrodynamics (ERMHD). Both weak and
strong kinetic Alfv\'en waves (KAW) turbulence regimes are studied in the
balanced case. After recovering the expected theoretical predictions for the
magnetic spectra, a higher-order multiscale statistical analysis is performed.
This study reveals a striking difference between the two regimes, with the
emergence of monofractality only in weak turbulence, whereas strong turbulence
is multifractal. This result, combined with recent studies, shows the relevance
of collisionless weak KAW turbulence to describe the solar wind at electron
scales.
