Family of third-order topological insulators from Su-Schrieffer-Heeger stacking

Abstract

We construct a family of chiral symmetry-protected third-order topological insulators by stacking Su-Schrieffer-Heeger (SSH) chains and provide a unified topological characterization by a series of Bott indices. Our approach is informed by the analytical solution of corner states for the model Hamiltonians written as a summation of the extended SSH model along three orthogonal directions. By utilizing the generalized Pauli matrices, an enumeration of the constructed model Hamiltonians generates ten distinct models, including the well-studied three-dimensional Benalcazar-Bernevig-Hughes model. By performing a boundary projection analysis for the ten models, we find that certain surfaces and hinges of the systems can exhibit, respectively, nontrivial second-order and first-order topology in the phase of the third-order topological insulators. Furthermore, we analyze the phase diagram for one of the predicted models and reveal a rich set of topological phases, including the third-order topological insulators, second-order weak topological insulators, and second-order nodal semimetals.

13 pages, 6 figures

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• Boundary topological insulators and superconductors of Altland-Zirnbauer tenfold classes
• Layer-number parity induced topological phase transition
• Majorana vortex phases in time-reversal invariant higher-order topological insulators and topologically trivial insulators