Either in bulk form, or when exfoliated into atomically thin crystals, layered transition metal dichalcogenides are continuously leading to the discovery of new phenomena. The latest example is provided by 1T-WTe$_2$, a semimetal recently found to exhibit the largest known magnetoresistance in bulk crystals, and predicted to become a two-dimensional topological insulator in strained monolayers. Here, we show that reducing the thickness through facile exfoliation provides an effective experimental knob to tune the electronic properties of WTe$_2$, which allows us to identify the microscopic mechanisms responsible for the observed classical and quantum magnetotransport down to the ultimate atomic scale. We find that the longitudinal resistance and the very unconventional B-dependence of the Hall resistance are reproduced quantitatively in terms of a classical two-band model for crystals as thin as six monolayers, and that for thinner crystals a crossover to an insulating, Anderson-localized state occurs. Besides establishing the origin of the very large magnetoresistance of bulk WTe$_2$, our results represent the first, complete validation of the classical theory for two-band electron-hole transport, and indicate that atomically thin WTe$_2$ layers remain gapless semimetals, from which we conclude that searching for a topological insulating state by straining monolayers is a challenging, but feasible experiment.
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