Emergent topology in thin films of nodal line semimetals

TL;DR

This paper explores how thin films of nodal line semimetals exhibit various emergent topological phases due to finite-size effects, revealing transitions between gapless and gapped states with distinct topological invariants.

Contribution

It introduces a detailed analysis of finite-size topological phases in nodal line semimetal films, including the emergence of lower-dimensional states and the role of hybridized surface and bulk states.

Findings

Thin films can transition into lower-dimensional nodal line states or trivial phases.

Hybridization of bulk states can produce topologically nontrivial gaps.

Film thickness controls the topological invariant and phase transitions.

Abstract

We investigate finite-size topological phases in thin films of nodal line semimetals (co-dimension 2) in three dimensions. By analyzing the hybridization of drumhead surface states, we demonstrate that such systems can transition into either a lower-dimensional nodal line state (co-dimension 1) or a fully gapped trivial phase. Additionally, we explore the hybridization of bulk states along the nodal loop when the system is finite in directions parallel to the loop's plane. This generally results in a topologically nontrivial gap. In films finite along a single in-plane direction, a partial gap opens, giving rise to two-dimensional Weyl cones characterized by a one-dimensional $\mathbb{Z}$ invariant. When the system is finite along both in-plane directions, a fully gapped phase appears, distinguished by a $\mathbb{Z}$ invariant whose value increases with film thickness. We further discuss the bulk-boundary correspondence associated with these emergent topological phases.