Tunable topological phases in quantum kirigamis

Advances in engineering mesoscopic quantum devices have led to new material platforms where electronic transport can be achieved on foldable structures. In this respect, we study quantum phases and their transitions on a kirigami structure---a Japanese craft form---where its individual building blocks are topologically nontrivial. In particular, we find that by mechanically deforming the kirigami structure one can engineer topological phase transitions in the system. Using a multipronged approach, we show that the physics of the system can be captured within a transfer matrix formalism, akin to Chalker-Coddington networks, where the junctions describe scattering between effective non-Hermitian one-dimensional edge channels. We further show that the nature of the kirigami structure can affect the critical folding angles where the topological phase transitions occur. Our study shows the rich interplay between topological quantum phenomena and structural configuration of an underlying kirigami network reflecting its potential as an intriguing platform.