Rivero Jose D H, Fleming Courtney, Qi Bingkun, Feng Liang, Ge Li
College of Staten Island, CUNY, Staten Island, New York 10314, USA.
The Graduate Center, CUNY, New York, New York 10016, USA.
Phys Rev Lett. 2023 Dec 1;131(22):223801. doi: 10.1103/PhysRevLett.131.223801.
We present an approach to achieve zero modes in lattice models that do not rely on any symmetry or topology of the bulk, which are robust against disorder in the bulk of any type and strength. Such symmetry-free zero modes (SFZMs) are formed by attaching a single site or small cluster with zero mode(s) to the bulk, which serves as the "nucleus" that expands to the entire lattice. We identify the requirements on the couplings between this boundary and the bulk, which reveals that this approach is intrinsically non-Hermitian. We then provide several examples with either an arbitrary or structured bulk, forming spectrally embedded zero modes in the bulk continuum, midgap zero modes, and even restoring the "zeroness" of coupling or disorder-shifted topological corner states. Focusing on viable realizations using photonic lattices, we show that the resulting SFZM can be observed as the single lasing mode when optical gain is applied to the boundary.
我们提出了一种在晶格模型中实现零模的方法，该方法不依赖于主体的任何对称性或拓扑结构，并且对任何类型和强度的主体无序具有鲁棒性。这种无对称性零模（SFZM）是通过将具有零模的单个位点或小簇连接到主体上形成的，主体充当扩展到整个晶格的“核心”。我们确定了该边界与主体之间耦合的要求，这表明该方法本质上是非厄米的。然后，我们提供了几个具有任意或结构化主体的示例，在主体连续谱中形成光谱嵌入零模、带隙中间零模，甚至恢复耦合或无序移动拓扑角态的“零性”。聚焦于使用光子晶格的可行实现，我们表明当在边界施加光学增益时，产生的SFZM可以作为单激射模被观测到。
