Gap Control by Singular Schrödinger Operators in a Periodically Structured Metamaterial - Exner, Pavel; Khrabustovskyi, Andrii (Журнал математической физики, анализа, геометрии, 2018)
We consider a family Hεε>0 of εZⁿ-periodic Schrödinger operators with δ′-interactions supported on a lattice of closed compact surfaces; within a minimum period cell one has m ∊ N surfaces. We show that in the limit when ε→0 and the interactions strengths are appropriately scaled, Hε has at most m gaps within finite intervals, and moreover, the limiting behavior of the first m gaps can be completely controlled through a suitable choice of those surfaces and of the interactions strengths.