g -factor and well-width fluctuations as a function of carrier density in the two-dimensional hole accumulation layer of transfer-doped diamond

The two-dimensional (2D) hole gas at the surface of transfer-doped diamond shows quantum-mechanical interference effects in magnetoresistance in the form of weak localization and weak antilocalization (WAL) at temperatures below about 5 K. Here we use the quenching of the WAL by an additional magnetic field applied parallel to the 2D plane to extract the magnitude of the in-plane $g$-factor of the holes and fluctuations in the well width as a function of carrier density. Carrier densities are varied between 1.71 and $4.35\ifmmode\times\else\texttimes\fi{}{10}¹³\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}2}$ by gating a Hall bar device with an ionic liquid. Over this range, calculated values of $|g|$ vary between 1.6 and 2.3 and the extracted well-width variation drops from 3 to 1.3 nm rms over the phase coherence length of 33 nm for a fixed geometrical surface roughness of about 1 nm as measured by atomic force microscopy. Possible mechanisms for the extracted variations in the presence of the ionic liquid are discussed.