On Exponentially Localized Wannier Functions in Non-Periodic Insulators

Loading...
Thumbnail Image

Date

2021

Journal Title

Journal ISSN

Volume Title

Repository Usage Stats

86
views
321
downloads

Abstract

Exponentially localized Wannier functions (ELWFs) are an orthogonal basis for the low energy states of a material consisting of functions which decay exponentially quickly in space. When a material is insulating and periodic, conditions which guarantee the existence of ELWFs in dimensions one, two, and three are well-known and methods for constructing ELWFs numerically are well-developed. In this dissertation, we consider the case where the material is insulating but not necessarily periodic and develop an algorithm for calculating ELWFs.

In Chapter 3, we propose an optimization-free algorithm for constructing Wannier functions in both periodic and non-periodic insulating systems. In this chapter, we rigorously prove that under the assumption of ``uniform spectral gaps'', a technical assumption we introduce, that our algorithm constructs ELWFs.

While the uniform spectral gaps assumption is not always met in practice, in Chapter 4, we prove that for a wide class of systems (both periodic and non-periodic) it is always possible to modify our algorithm so that the uniform spectral gaps assumption holds. As a consequence of this result, we conclude that for both periodic and non-periodic systems our algorithm can construct ELWFs whenever they exist.

The results in this dissertation open the door for extending the theory of topological insulators, a recently discovered class of materials, to fully non-periodic systems.

Department

Description

Provenance

Citation

Citation

Stubbs, Kevin (2021). On Exponentially Localized Wannier Functions in Non-Periodic Insulators. Dissertation, Duke University. Retrieved from https://hdl.handle.net/10161/22997.

Collections


Dukes student scholarship is made available to the public using a Creative Commons Attribution / Non-commercial / No derivative (CC-BY-NC-ND) license.