Higher-order topological Anderson insulator on the Sierpiński lattice

Abstract

Disorder effects on topological materials in integer dimensions have been extensively explored in recent years. However, its influence on topological systems in fractional dimensions remains unclear. Here, we investigate the disorder effects on a fractal system constructed on the Sierpiński lattice in fractional dimensions. The system supports the second-order topological insulator phase characterized by a quantized quadrupole moment and the normal insulator phase. We find that the second-order topological insulator phase on the Sierpiński lattice is robust against weak disorder but suppressed by strong disorder. Most interestingly, we find that disorder can transform a normal insulator phase to a second-order topological insulator phase with an emergent quantized quadrupole moment. Finally, the disorder-induced phase is further confirmed by calculating the energy spectrum and the corresponding probability distributions.

Higher-order topological phases in crystalline and non-crystalline systems: a review

“…Recently, it has been demonstrated that fractal lattices can also harbor HOTPs [213,224,[240][241][242][243][244]. In [240], the authors study a Hamiltonian in equation ( 127) on a square Sierpiński carpet fractal with T 0 = (m 0 + 2t 2 )σ 0 τ 3 and 2.…”

“…Apart from amorphous systems without any spatial symmetry, the HOTPs with in-gap corner modes have been found to exist in other non-crystalline systems such as quasicrystalline [228][229][230][231][232][233][234][235][236][237], hyperbolic [238,239], and fractal lattices [213,224,[240][241][242][243][244]. Since quasicrystalline and hyperbolic lattices can possess rotational symmetries that do not exist in regular crystals, they can harbor topological phases without crystalline counterparts.…”

RKKY interaction in helical higher-order topological insulators

“…The higher-order topological insulators (HOTIs) describe topological materials of d-dimensional insulated bulk and (d − n)-dimensional gapless boundary states. [1,2] There are zero-dimensional gapless corner states in two-dimensional (2D) second-order topological insulators [3][4][5][6] and threedimensional (3D) third-order topological insulators, [7,8] and one-dimensional (1D) gapless hinge states in 3D secondorder topological insulators. [9][10][11] HOTIs can be understood as a special kind of topological crystalline insulators (TCIs).…”