A new class of higher-order topological insulators that localize energy at arbitrary multiple sites

Abstract

$\mathbb{Z}$-classified topological phases lead to larger-than-unity topological states. However, these multiple topological states are only localized at the corners in nonlocal systems. Here, first, we rigorously prove that the multiple topological states of nonlocal Su-Schrieffer-Heeger (SSH) chains can be inherited and realized by local aperiodic chains with only the nearest couplings. Then, we report a new class of higher-order topological insulators constructed with the local aperiodic chains, which can have any integer number of 0D topological states localized at arbitrary positions in the whole domain of the insulators, including within the bulk. The 0D topological states are protected by the local topological marker in each direction, instead of the bulk multipole chiral numbers in the existing work. Our work provides multiple combinations of localized corner-bulk topological states, which enables programmable lasers and sasers by selecting the excitation sites without altering the structure, and thus opens a new avenue to signal enhancement for computing and sensing.

References in corpus (9)

• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Novel Topological Phase with Zero Berry Curvature
• Topological acoustics
• Low-threshold topological nanolasers based on second-order corner state
• Experimentally Detecting Quantized Zak Phases without Chiral Symmetry in Photonic Lattices
• Observation of degenerate zero-energy topological states at disclinations in an acoustic lattice
• Non-Hermitian engineering of single mode two dimensional laser arrays
• Realization of a Z classified chiral-symmetric higher-order topological insulator in a coupling-inversion acoustic crystal
• Smart patterning for topological pumping of elastic surface waves