We investigate finite-size topological phases in thin films of nodal line semimetals (codimension 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 (codimension 1) or a fully gapped trivial phase. Additionally, we explore the hybridization of bulk states along the nodal loop due to quantum confinement when the system is finite in directions parallel to the loops plane. This generally results in a topologically nontrivial gap. In films that are 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 the thickness of the sample. We further discuss the bulk-boundary correspondence associated with these emergent topological phases.

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• Surface states
• Symmetry protected topological states
• Topological phases of matter
• 3-dimensional systems
• Nodal-line semimetals
• Band structure methods
• Tight-binding model