Consistent description of mesoscopic transport: Case study of current-dependent magnetoconductance in single GaN:Ge nanowires

The so called phase-coherence length ${l}_{\ensuremath{\varphi}}$ and its relation to the geometrical dimensions of a sample determine the electronic transport regime. Different approaches are established for extracting ${l}_{\ensuremath{\varphi}}$ from magnetotransport data of mesoscopic systems and need to be cross-checked by using experimental data on the same model system in order to ensure an overall consistent theoretical description. Suitable model systems for testing this consistency are single GaN:Ge nanowires. Their magnetoconductance at low temperatures exhibits universal conductance fluctuations as well as weak localization effects. We find that the values of ${l}_{\ensuremath{\varphi}}$ obtained from the established analysis of the magnitude of the conductance fluctuations rms($\mathrm{\ensuremath{\Delta}}G$) decrease with increasing measurement current, whereas the corresponding values of ${l}_{\ensuremath{\varphi}}$ determined by the analyses of the correlation field ${B}_{\text{C}}$ and the weak localization effect yield the same value for ${l}_{\ensuremath{\varphi}}$ independent of the measurement current used. We apply and modify the existing theoretical framework for bias-dependent differential conductance fluctuations, in order to explain the decrease of the conductance fluctuations rms($\mathrm{\ensuremath{\Delta}}G$) with increasing current density in our dc measurements. This leads to the same values of ${l}_{\ensuremath{\varphi}}$ independent of the analysis approach applied to the same set of data.