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Topological chiral modes in random scattering networks
by Pierre A. L. Delplace
- Published as SciPost Phys. 8, 081 (2020)
|As Contributors:||Pierre Delplace|
|Submitted by:||Delplace, Pierre|
|Submitted to:||SciPost Physics|
|Subject area:||Condensed Matter Physics - Theory|
Using elementary 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. This work thus generalizes these anomalous chiral states beyond Floquet systems, to a class of discrete-time dynamical systems where a periodic driving in time is not required.
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Published as SciPost Phys. 8, 081 (2020)
Author comments upon resubmission
I am glad that the two referees recommend this manuscript for publication. In this resubmitted version, I made a few slight improvements to clarify or stress some important points in the abstract and the conclusion, following the feedback I got from the referees, and also corrected missprints and typos. The two referees also both had questions about possible extensions of this work when including interactions. These fair but general questions go much beyond the scope of this work, and no modification of the manuscript has been made in that direction.
List of changes
. A sentence has been added to the abstract to stress the generalization of anomalous edge states beyond Floquet systems.
. After equation (1), \hbar has been put correctly at the denominator in the expression of theta.
. The expressions of the Floquet operator (6) and (8) and (9) have been corrected so that they correspond to the figure 1. This does not alterate any result, simply reflects a convention of the basis vectors of the lattice.
. Labels (a) and (b) have been added to figure 8.
. A piece of anwer has been given to one of the possible directions in the conclusion (the one concerning the higher values of the winding number).
. A sentence has been added in the conclusion that stresses the difference between edge states of a Chern phase and that of the anomalmous one.
. A more complete calculation has been provided in the derivation of the phase rotation symmetry operators in appendix A.