# Tunable three-way valley Hall energy-splitter: venturing beyond graphene-like structures

## TL;DR

This paper introduces the first three-way topological energy-splitter using a square lattice, breaking mirror symmetries to enable valley-Hall states and tunable energy directionality for advanced wave control applications.

## Contribution

It demonstrates a novel three-way energy-splitter based on square lattices that breaks mirror symmetries, enabling new topological wave manipulation beyond graphene-like structures.

## Key findings

- First three-way topological energy-splitter created using square lattice.
- The splitter's energy directionality can be tuned by geometry.
- The structure allows adiabatic conversion into a wave steerer.

## 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.