SciPost Submission Page
Topological chiral modes in random scattering networks
by Pierre A. L. Delplace
|As Contributors:||Pierre Delplace|
|Submitted by:||Delplace, Pierre|
|Submitted to:||SciPost Physics|
|Subject area:||Condensed Matter Physics - Theory|
Using graph theory, we show the existence of interface chiral modes in random oriented scattering networks and discuss their topological nature. For particular regular networks (e.g. L-lattice, Kagome and triangular networks), an explicit mapping with time-periodically driven (Floquet) tight-binding models is found. In that case, the interface chiral modes are identified as the celebrated anomalous edge states of Floquet topological insulators and their existence is enforced by a symmetry imposed by the associated network.
Submission & Refereeing History
Reports on this Submission
Anonymous Report 1 on 2019-8-2 Invited Report
Clear and well-written; elucidates and generalizes anomalous Floquet topological phases in a satisfying way.
No serious weaknesses; a few small suggestions below in the Report.
In this paper, the author maps the two-dimensional anomalous Floquet Anderson insulator (and related Floquet models) onto unitary scattering networks. Using graph theory and a “phase rotation symmetry” that such graphs obey, he gives a simple picture of when an anomalous phase (having a topological edge mode despite a vanishing Chern number) occurs in these models. This perspective allows him to generalize to non-Floquet evolution and unifies independent known results on scattering networks with known results in the Floquet setting. It also allows him to determine when an edge mode will occur even in cases where there is no known bulk invariant.
This is a very nice paper, based around an insightful idea. I think it’s essentially publishable as-is, but I have a couple of minor points for the author:
1. It would be good to comment on what happens to this picture with interactions. It seems at first glance that if the interactions are local, the scattering network map would still apply. Does this imply that the author’s graph-theoretic results also hold for the interacting case? Specifically does the argument in section 5.2 go through, and if not, why?
2. On p8 the author writes, “According to the mapping established above, one can now interpret the topological transition between the Floquet anomalous and trivial regimes in discrete-time tight-binding models as a percolation transition.” The implications of this claim should be expanded. What are the universal features of the transition, if it maps onto percolation? Is this known in the literature? If not, it seems like an important result.
3. There are a few small typos scattered throughout, so the paper should be given another close proofing. For instance, the labels (a) and (b) are missing in Fig 8.
I recommend the paper for publication.