Energy Band Engineering of Periodic Scatterers by Quasi-1D Confinement

TL;DR

This paper presents a method to tune energy band structures in a chain of periodic scatterers by applying a cylindrical confinement potential, enabling continuous band gap control without altering the lattice potential.

Contribution

It introduces a novel approach to modify energy bands through quasi-one-dimensional confinement, considering full three-dimensional scattering states instead of zero-range models.

Findings

Confinement can close band gaps at various points in momentum space.

Energy bands are tunable via external confinement without changing lattice potential.

Dimensionality reduction affects bound and scattering states, altering band structure.

Abstract

A mechanism to modify the energy band structure is proposed by considering a chain of periodic scatterers forming a linear lattice around which an external cylindrical trapping potential is applied along the chain axis. When this trapping (confining) potential is tight enough, it may modify the bound and scattering states of the lattice potential, whose three-dimensional nature around each scattering center is fully taken into account and not resorting to zero-range pseudo-potentials. Since these states contribute to the formation of the energy bands, such bands could thereby be continuously tuned by manipulating the confinement without the need to change the lattice potential. In particular, such dimensionality reduction by quantum confinement can close band gaps either at the center or at the edge of the momentum k-space.