Floating topological phases

TL;DR

This paper explores 'floating topological phases' in layered materials, which maintain 2+1D topological order despite interlayer couplings, and proposes their experimental detection via resistivity divergence.

Contribution

It introduces the concept of floating topological phases, analyzes their stability, and suggests a non-local order parameter for their identification.

Findings

Floating topological phases can be stable against interlayer couplings.

A divergent ratio of inter-layer to intra-layer resistivity signals topological order.

Experimental divergence of resistivity ratio indicates a topological (spin liquid) phase.

Abstract

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.