Topological laser with higher-order corner states in the 2-dimensional Su-Schrieffer-Heeger model

Abstract

A nonlinear non-Hermitian topological laser system based on the higher-order corner states of the 2-dimensional (2D) Su-Schrieffer-Heeger (SSH) model is investigated. The topological property of this nonlinear non-Hermitian system described by the quench dynamics is in accordance with that of a normal 2D SSH model. In the topological phase, all sites belonging to the topological corner states begin to emit stable laser light when a pulse is given to any one site of the lattice, while no laser light is emitted when the lattice is in the trivial phase. Furthermore, the next-nearest-neighbor (NNN) couplings are introduced into the strong-coupling unit cells of the 2D SSH model, which open a band gap in the continuous band structure. In the topological phase, similar to the case of 2D SSH model without NNN couplings, the corner sites can emit stable laser light due to the robustness of the higher-order corner states when the NNN couplings are regarded as the perturbation. However, amplitude of the stimulated site does not decay to zero in the trivial phase, because the existence of the NNN couplings in the strong-coupling unit cells make the lattice like one in the tetramer limit, and a weaker laser light is emitted by each corner.

Emerging Topological Multiferroics from the 2D Rice-Mele Model

“…The topologically protected corner states [54][55][56][57] that we reported are spin-polarized. This is a distinctive feature of the multiferroic nature of the system we propose.…”

Disorder‐Enhanced Corner State and Topological Corner State Transfer in a 2D Rice–Mele Lattice

“…[25][26][27][28][29][30][31][32][33][34][35] These high order topological state can also be used to implement the topological quantum state transfer, e.g., the corner state transfer in superconducting circuits [36] and photonic lattice. [37,38] The 2D Su-Schrieffer-Heeger (SSH) lattice, [31,[39][40][41][42][43][44] as one of the simplest 2D lattices, exhibits the localized corner states around corner sites under the limit of the weak intracell coupling. Note that, these topologically trivial corner states in 2D SSH lattice cannot be protected by the quantized bulk quadrupole moment, which naturally cannot be immune to the disorders.…”

Topological laser on square lattice with gain–loss-induced higher-order corner modes

“…As an extension of traditional topological edge states, higherorder topological systems have lower-dimensional edge states. For example, the 2D breathing kagome lattice has zeroenergy states localized at three corners, [42][43][44][45] and the 2D extended Su-Schrieffer-Heeger (SSH) model has 0D corner states, [46][47][48][49][50] which are called second-order topological insulators and beyond the traditional bulk-edge correspondence.…”

“…Moreover, we also show the evolution of a topological laser system in the time domain, stimulating the cavity at any location, after a sufficiently long time, showing stable laser emission in the corner cavity. In fact, topological laser based on the second-order corner state has been studied in 2D SSH model, [49,50] in which the eigenvalues of corner states are mixed with these of many bulk states. The corner states are difficult to be distinguished unless more complex coupling is introduced.…”