Non-Hermitian Two-Kink Control of Corner States in Twisted Chern Bilayers

Abstract

Corner states are bound by boundary-mass defects, but this geometric anchoring restricts their spatial and internal control. Focusing on twisted bilayers assembled from Chern insulators with opposite Chern numbers, we show that a mass-phase kink carried by a non-Hermitian interlayer mass and an independent imaginary-momentum kink separate the spectral, in-plane, and interlayer control of mass-defect corner states. The mass-phase kink creates the parent corner pole and fixes its energy and intrinsic decay, while directed interlayer tunneling encodes its layer polarization. The imaginary-momentum texture instead reshapes the closed-boundary envelope and redistributes stationary right-state weight between corners. A twisted Qi--Wu--Zhang bilayer verifies this division on arbitrary, including concave, boundaries. A $30^\circ$ twisted Haldane dodecagon realizes twelve finite-energy parent states whose in-gap spectral manifold persists while boundary patterns redistribute its normalized right-subspace weight toward six, three, two, or one target corners. The two kinks therefore cooperate or compete while keeping spectral ancestry, spatial weight, and layer character distinct, thereby establishing a unified framework for controlling mass-defect corner states across disparate boundary geometries and mass textures.