Transport study of Berry's phase, the resistivity rule, and quantum Hall effect in graphite

Transport measurements indicate strong oscillations in the Hall-,$R_{xy}$, and the diagonal-, $R_{xx}$, resistances and exhibit Hall plateaus at the lowest temperatures, in three-dimensional Highly Oriented Pyrolytic Graphite (HOPG). At the same time, a comparative Shubnikov-de Haas-oscillations-based Berry’s phase analysis indicates that graphite is unlike the GaAs/AlGaAs 2D electron system, the 3D n-GaAs epilayer, semiconducting $H{g}_{0.8}C{d}_{0.2}Te$, and some other systems. Finally, we observe the transport data to follow $B\times d{R}_{xy}\mathrm{/}dB\approx -\mathrm{\Delta }{R}_{xx}$. This feature is consistent with the observed relative phases of the oscillatory $R_{xx}$ and $R_{xy}$.