‘Confined coherence’ in strongly correlated anisotropic metals

Abstract

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 (transverse to the lower dimensional subspaces) with coherent transport in at least one other direction (within the subspaces). The magnitude of the Fermi surface warping due to transverse (intersubspace) 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. Our theoretical approach is to treat an anisotropic two (2D)- or three (3D)-dimensional electronic system as a collection of one (1D)- or two-dimensional electron liquids coupled by weak interliquid single-particle hopping. We find that a necessary condition for the destruction of coherent interliquid transport is that the intraliquid state be a non-Fermi liquid. We present a very detailed discussion of coupled 1D Luttinger liquids and the reasons for believing in the existence of a phase of confined coherence in that model. This provides a paradigm for incoherent transport between weakly coupled 2D non-Fermi liquids, the case relevant to the experiments of which we are aware. Specifically, 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)₂PF₆ 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.