Confined Coherence in Strongly Correlated Anisotropic Metals

We present a detailed discussion of both theoretical and experimental evidence in favour of the existence of states of ``confined coherence'' in metals of sufficiently high anisotropy and with sufficiently strong correlations. The defining property of such a state is that single electron coherence is confined to lower dimensional subspaces (planes or chains) so that it is impossible to observe interference effects between histories which involve electrons moving between these subspaces. The most dramatic experimental manifestation of such a state is the coexistence of incoherent, non-metallic transport in one or two directions with coherent transport in at least one other direction. The magnitude of the Fermi surface warping due to transverse (inter-subspace) momentum plays the role of an order parameter (in a state of confined coherence, this order parameter vanishes) and the effect can occur in a pure system at zero temperature..... ..anomalous transport data in the (normal state of the) cuprate superconductors and in the low temperature, metallic state of the highly anisotropic organic conductor (TMTSF)$_2$PF$_6$ cannot be understood within a Fermi liquid framework, and, we argue, the only plausible way to understand that transport is in terms of a state of confined coherence.