Tunable three-way topological energy-splitter

Mehul P Makwana,Gregory Chaplain

doi:10.1038/s41598-019-55485-0

Abstract

Strategically combining four structured domains creates the first ever three-way topological energy-splitter; remarkably, this is only possible using a square, or rectangular, lattice, and not the graphene-like structures more commonly used in valleytronics. To achieve this effect, the two mirror symmetries, present within all fully-symmetric square structures, are broken; this leads to two nondistinct interfaces upon which valley-Hall states reside. These interfaces are related to each other via the time-reversal operator and it is this subtlety that allows us to ignite the third outgoing lead. The geometrical construction of our structured medium allows for the three-way splitter to be adiabatically converted into a wave steerer around sharp bends. Due to the tunability of the energies directionality by geometry, our results have far-reaching implications for applications such as beam-splitters, switches and filters across wave physics.

Highlights

Combining four structured domains creates the first ever three-way topological energysplitter; remarkably, this is only possible using a square, or rectangular, lattice, and not the graphenelike structures more commonly used in valleytronics
We examine a square cellular structure containing only a single mirror symmetry in Sec. 3; we demonstrate how this restricts a medium, comprised of these cells, to solely yield straight valley-Hall guides i.e. the energy cannot be navigated around a bend
We demonstrate how the additional reflectional symmetry enables mode coupling from the pre-bend to post-bend zero-line modes (ZLMs) thereby allowing for energy navigation around a corner

Summary

Introduction

Combining four structured domains creates the first ever three-way topological energysplitter; remarkably, this is only possible using a square, or rectangular, lattice, and not the graphenelike structures more commonly used in valleytronics To achieve this effect, the two mirror symmetries, present within all fully-symmetric square structures, are broken; this leads to two nondistinct interfaces upon which valley-Hall states reside. The transmission along the outgoing leads would be heavily contingent upon the location of the mode within the topologically nontrivial band-gap; an alternative method whereby the energy is partitioned away from a well-defined nodal point as opposed to a nodal region is highly desirable This is only possible using a square or rectangular lattice; the three-way energy splitting is dependent upon the equivalence of the interfaces (modulo time-reversal symmetry) that is only achievable using the four-fold symmetric cellular structure.

Methods

Results

Conclusion