A Non-topological Extension of Bending-immune Valley Topological Edge States

TL;DR

This paper reveals that the robustness of valley edge states in photonic crystals is due to modal characteristics rather than topological properties, challenging the traditional understanding of their topological origin.

Contribution

It introduces the concept of non-topological valley edge states, showing their transport robustness is independent of valley topology and related to localized momentum hotspots.

Findings

Edge state robustness persists even when P-symmetry is restored.

Modal character with momentum hotspots is key to transport robustness.

Bending immunity achieved in various edge modes without topological protection.

Abstract

Breaking parity (P) symmetry in C$_6$ symmetric crystals is a common routine to implement a valley-topological phase. At an interface between two crystals of opposite valley phases, the so-called valley topological edge states emerge, and they have been proven useful for wave transport with robustness against 120$^\circ$ bending and a certain level of disorder. However, whether these attractive transport features are bound with the valley topology or due to topological-irrelevant mechanisms remains unclear. In this letter, we discuss this question by examining transport properties of photonic edge states with varied degrees of the P-breaking that tune the valley topology, and reveal that the edge states preserve their transport robustness insensitive to the topology even when the P-symmetry is recovered. Instead, a unique modal character of the edge states -- with localized momentum hotspots around high-symmetric $K$ ($K'$) points -- is recognized to play the key role, which only concerns the existence of the valleys in the bulk band structures, and has no special requirement on the topology. The "non-topological" notion of valley edge states is introduced to conceptualize this modal character, leading to a coherent understanding of bending immunity in a range of edge modes implemented in C$_3$ symmetric crystals -- such as valley topological edge states, topological edge states of 2D Zak phase, topological-trivial edge states and so on, and to new designs in general rhombic lattices -- with exemplified bending angle as large as 150$^\circ$.