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The understanding of the interlayer transport in low-dimensional conductors is a longstanding challenge. The major question is: how is it possible to have a metallic-like resistivity (?) in-between planes when the mean free path (l) deduced from ? is in order of magnitude lower than the lattice spacing. The enigma is even deeper in cases when nominally for the same compound (e.g. Bi2Sr2CaCu2O8 high Tc superconductor, abbreviated as BISCO) there are reports with d/dT >0, and also with d/dT <0. This problem has received further relevance with the advent of exfoliated 2D materials where it is necessary to first understand the bulk material before going to single layer. Furthermore, in device configuration more than one layer could be used or in their heterostructures, where the transport between the layers must be also considered.Usually, the resistivity anisotropy in low-dimensional systems is measured by the Montgomery or Van der Pauw methods, which are not advantageous for platelet-shaped crystals if the out-of-plane size (usually called c-axis) is very small. The conflicting results for ?c, very often are due to ill-defined current flow and voltage probe geometries. With the development of the Focused Ion Beam (FIB) tool this hurdle could be overcome since structures are tailored and contacted on micron sizes where the current-voltage paths are reliably defined.In this proposal we plan to challenge few major questions in a selected set of model 2D materials (transition metal dichalcogenides (TMDs), cuprates, manganites, graphite) by studying simultaneously the ab-plane (?ab) and c-axis (?c) charge transport in FIB-cut structures. We will explore the phase space of temperature, pressure and magnetic field. The questions we want address are:i)What is the limit of maximum metallic resistivity?ii)In the highly resistive metallic-like state does the magnetoresistance confirm metallicity, e.g. is the Kohler’s rule obeyed?iii)When ?c turns non-metallic due to an increased layer separation with intercalated molecules, what is the role of disorder?iv)Can one bring back d ?c /dT< 0 to a metallic regime with hydrostatic pressure?v)How do correlations (Mott, charge density wave, pseudogap…) influence the interlayer transport?vi)How do intercalated magnetic degrees of freedom (long range odered or disordered) change the inter-layer charge transport?These questions are important for a detailed understanding of 2D materials. Our preliminary data show a rich physics beyond any expectation.