The incidence of topology on the band structure and physical properties of layered compounds has been extensively studied in semimetals. How those evolve in presence of electronic correlations has been less investigated so far. In the sodium cobaltates NaxCoO2 considered here, unexpected magnetic properties associated with correlations on the Co sites have been disclosed about 15 years ago. The distinct Na orders of the stable phases of these cobaltates have been shown to induce specific Co charge disproportionation with large size unit cells in the CoO2 planes, linked with the diverse magnetic behaviors. This provides an original playground in the studies of interplays between topology and correlations in these layered materials. We present here transport measurements on a series of single crystals and demonstrate that we do synthetize pure phases with quite reproducible transport properties. We show that above room T those display a similar behavior whatever the Na content. On the contrary we provide evidence for a great diversity in Hall effect low temperature dependences which underlines the specificities of the Fermi Surface reconstructions induced by the Na order. We study in some detail the difference between two metallic phases, one (x = 0.77) antiferromagnetic below TN = 22 K and the second (x = 2/3) paramagnetic down to T = 0. Both show a sign change in the Hall effect with decreasing T. We demonstrate that this can be attributed to quite distinct physical effects. For the x = 0.77 phase the negative Hall effect occurs in similar conditions to the anomalous Hall effect found in various magnetic metals. In the x = 2/3 phase have to be assigned to specificities of its Fermi surface. In both cases the anomalies detected in the Hall effect are certainly associated with the topology of their Co electronic bands.
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