Torsional strain engineering of nanotubes with flat bands

In recent years, dispersionless electronic states (or flat bands) in various 2D nanomaterials and layered structures have been intensely investigated due to their connections with strong electronic correlation and exotic phases of matter. In this work, we employ symmetry adapted first principles calculations and tight-binding models to explore the possibility of realizing and modulating flat bands in quasi-one-dimensional materials. Specifically, two prototypical nanotube systems, based on Kagome lattices of carbon and phosphorus-carbon are explored. Both these materials systems host flat bands with quadratic band crossing (QBC) and their electronic structures can be classified based on the type of singularities in the Bloch wavefunctions. We observe that the phosphorus-carbon nanotubes may have singular or non-singular QBC, based on chirality, whereas the carbon tubes are exclusively associated with singular QBC. We show that such differences can be brought out by subjecting these materials to torsional strains, with different classes of electronic phase transitions being affected in these materials, as a result to such deformations.