Floating topological phases

While quasi-two-dimensional (layered) materials can be highly anisotropic, their asymptotic long-distance behavior generally reflects the properties of a fully three-dimensional phase of matter. However, certain topologically ordered quantum phases with an emergent (2 + 1)-dimensional gauge symmetry can be asymptotically impervious to interplane couplings. We discuss the stability of such "floating topological phases," as well as their diagnosis by means of a nonlocal order parameter. Such a phase can produce a divergent ratio rho(perpendicular to)/rho(parallel to) of the interlayer to intralayer resistivity as T -> 0, even in an insulator where both rho(perpendicular to) and rho(parallel to) individually diverge. Experimental observation of such a divergence would constitute proof of the existence of a topological (e.g., spin-liquid) phase.