There is now compelling evidence that the normal state of superconducting overdoped cuprates is a strange metal comprising two distinct charge sectors, one governed by coherent quasiparticle excitations, the other seemingly incoherent and characterized by non-quasiparticle (Planckian) dissipation. The zero-temperature superfluid density n_s(0)ns(0) of overdoped cuprates exhibits an anomalous depletion with increased hole doping pp, falling to zero at the edge of the superconducting dome. Over the same doping range, the effective zero-temperature Hall number n_{\rm H}(0) transitions from pp to 1 + pp. By taking into account the presence of these two charge sectors, we demonstrate that in the overdoped cuprates Tl_22Ba_22CuO_{6+\delta}6+δ and La_{2-x}2−xSr_xxCuO_44, the growth in n_s(0)ns(0) as pp is decreased from the overdoped side may be compensated by the loss of carriers in the coherent sector. Such a correspondence is contrary to expectations from conventional BCS theory and implies that superconductivity in overdoped cuprates emerges uniquely from the sector that exhibits incoherent transport in the normal state.

Strange metals exhibit a variety of anomalous magnetotransport properties, the most striking of which is a resistivity that increases linearly with magnetic field B over a broad temperature and field range. The ubiquity of this behavior across a spectrum of correlated metals -both singleand multi-band, with either dominant spin and/or charge fluctuations, of varying levels of disorder or inhomogeneity and in proximity to a quantum critical point or phase -obligates the search for a fundamental underlying principle that is independent of the specifics of any material. Strongly anisotropic (momentum-dependent) scattering can generate B-linear magnetoresistance but only at intermediate field strengths. At high enough fields, the magnetoresistance must eventually saturate. Here, we consider the ultimate limit of such anisotropy, a region or regions on the Fermi surface that impede all orbital (cyclotron) motion through them, but whose imposition can be modelled nonetheless through a modified Boltzmann theoretical treatment. Application of the proposed theorem suggests that the realization of quadratic-to-linear magnetoresistance requires the presence of a bounded sector on the Fermi surface possibly separating two distinct types of carriers. While this bounded sector may have different origins or manifestations, we expect its existence to account for the anomalous magnetotransport found in a wide range of correlated materials.

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