Second order topology in a band engineered Chern insulator.

Haldane model is a celebrated tight binding toy model of a Chern insulator in a 2D honeycomb lattice that exhibits quantized Hall conductance in the absence of an external magnetic field. In our work, we deform the bands of the Haldane model smoothly by varying one of its three nearest neighbour hopping amplitudes ([Formula: see text]), while keeping the other two (t) fixed. This breaks the [Formula: see text] symmetry of the Hamiltonian, while the [Formula: see text] symmetry is preserved.

Higher order topology in a Creutz ladder.

A Creutz ladder, is a quasi one dimensional system hosting robust topological phases with localized edge modes protected by different symmetries such as inversion, chiral and particle-hole symmetries. Non-trivial topology is observed in a large region of the parameter space defined by the horizontal, diagonal and vertical hopping amplitudes and a transverse magnetic flux that threads through the ladder. In this work, we investigate higher order topology in a two dimensional extrapolated version of the Creutz ladder.