G-factor and well width variations for the two-dimensional hole gas in surface conducting diamond

Hydrogen-terminated diamond possesses a quasi two-dimensional, sub-surface hole accumulation layer with a strong and tunable spin-orbit coupling due to surface transfer doping. We report a magnetoresistance study of the phase coherent backscattering (weak localization and antilocalization) at low temperatures. The response to an external magnetic field is highly anisotropic, confirming the 2D nature of the carriers despite the short mean free path. By simultaneously applying perpendicular and parallel magnetic fields, we are able to probe the Zeeman interaction and microroughness of the quantum well at the diamond surface. From a quantitative analysis of magnetoresistance curves at 2.5 K, we derive a hole g-factor of $2.6±0.1$ and rms fluctuations in the width of the hole quantum well of about 3 nm over the phase coherence length of 33 nm. Well width fluctuations are ascribed to surface roughness and to lateral fluctuations in carrier density, which self-consistently determines the width of the confining potential.