Tunable corner-like modes in generalized quadrupole topological insulator

Higher-order topological insulators harbor unique corner modes that hold immense potential for applications in information storage. However, the practical manipulation of these states has been constrained by the fixed positions and energies of conventional corner modes. In this work, we present a theoretical framework for generating topologically protected corner-like modes in higher-order topological insulators, exhibiting unprecedented tunability in their positions. These corner-like modes are characterized by a quantized generalized quadrupole moment, indicative of the presence of fractional charges. Moreover, we demonstrate the remarkable ability to modulate the energy of these topological corner modes. Our findings pave the way for the controlled manipulation of corner modes in higher-order topological insulators, opening up new avenues for their applications in advanced information technologies.