On the Geometry of Nanowires and the Role of Torsion

Research output: Contribution to journalJournal article – Annual report year: 2018Researchpeer-review

DOI

View graph of relations

A detailed analysis of the Schrödinger equation in curved coordinates, exact to all orders in the cross sectional dimension is presented, and we discuss the implications of the frame rotation for energies of both open and closed structures. For a circular cross-section, the energy spectrum is independent of the frame orientation for an open structure. For a closed curve, the energies depend on the holonomy angle of a minimal rotating frame (MR) which is equal to the area enclosed by the tangent image on the unit sphere. In the case of a curve with a well-defined torsion at all points this is up to a multiple of 2π equal to the total torsion, a result first found in 1992 by Takagi and Tanzawa. In both cases we find that the effect on the eigenstates is a phase shift. We validate our findings by accurate numerical solution of both the exact 3D equations and the approximate 1D equations for a helix structure and find that the error is proportional to the square of the diameter of the cross section. We discuss Dirichlet versus Neumann boundary conditions and show that care has to be taken in the latter case.
Original languageEnglish
Article number1800357
JournalPHYSICA STATUS SOLIDI (RRL) - RAPID RESEARCH LETTERS
Number of pages11
ISSN1862-6254
DOIs
Publication statusPublished - 2018
CitationsWeb of Science® Times Cited: No match on DOI

    Research areas

  • Acoustics, Frame orientation, Quantum mechanics, Torsion

ID: 156599997