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 non-local order parameter. Such a phase can produce a divergent ratio $\rho_{\perp}/\rho_{\parallel}$ of the inter-layer to intra-layer resistivity as $T\to 0$, even in an insulator where both $\rho_{\perp}$ and $\rho_\parallel$ individually diverge. Experimental observation of such a divergence would constitute proof of the existence of a topological (e.g. spin liquid) phase.