[Paper Review] Symmetry-Guaranteed and Accidental Nodal-Line Semimetals in FCC Lattice

Takuto Kawakami, Xiao Hu|arXiv (Cornell University)|Nov 22, 2016

Photonic Crystals and Applications3 citations

TL;DR

This paper demonstrates that face-centered-cubic (fcc) lattices of dielectric spheres can host symmetry-guaranteed and accidental nodal lines (NLs) in momentum space, leading to topologically protected drumhead-shaped surface states that significantly slow down light. The emergence of these NLs explains previously observed photonic pseudogaps and offers a pathway to experimentally confirm a novel topological photonic state.

ABSTRACT

Light cone with the speed of light independent of its wavelength in vacuum has been known for long time. In the present work, we unveil that in a face-centered-cubic (fcc) lattice of dielectric spheres novel light cones can be created over closed loops in momentum space, dubbed as nodal lines (NL), and that as a consequence of the nontrivial topology of NL interface states with a drumhead-shaped band structure appear where light can be slowed down significantly. We discuss that photonic pseudogaps found in previous experimental and theoretical studies for fcc photonic crystals are consistent with the present finding of NL. This offers a unique chance to confirm the existence of NL as a novel topological state.

Motivation & Objective

• To identify and classify nodal lines in face-centered-cubic (fcc) photonic lattices based on symmetry and topology.
• To explain the origin of photonic pseudogaps observed in prior experimental and theoretical studies in terms of nodal line formation.
• To establish a connection between topological nodal lines and the emergence of drumhead-shaped surface states in photonic systems.
• To provide a theoretical framework that enables experimental verification of nodal line semimetals in photonic crystals.

Proposed method

• Analyzing the band structure of an fcc lattice of dielectric spheres using first-principles photonic band theory.
• Identifying nodal lines as closed loops in momentum space where photonic bands degenerate due to symmetry protection and accidental crossings.
• Employing topological invariants and symmetry analysis to distinguish between symmetry-guaranteed and accidental nodal lines.
• Mapping the surface states using surface mode calculations, revealing drumhead-shaped dispersion features.
• Relating the observed nodal line topology to the presence of photonic pseudogaps in previous studies.
• Validating the theoretical predictions through consistency checks with existing experimental and theoretical data on fcc photonic crystals.

Experimental results

Research questions

• RQ1 What types of nodal lines—symmetry-guaranteed or accidental—can emerge in an fcc photonic lattice?
• RQ2 How do nodal lines in fcc lattices give rise to topologically protected surface states with drumhead-like dispersion?
• RQ3 Why do photonic pseudogaps observed in fcc photonic crystals correlate with the presence of nodal lines?
• RQ4 Can the existence of nodal lines in fcc lattices be experimentally confirmed through their unique photonic response?
• RQ5 What is the role of topology in shaping the light-confining and slow-light properties of these photonic systems?

Key findings

• Nodal lines in fcc lattices of dielectric spheres form closed loops in momentum space, resulting in topologically protected drumhead-shaped surface states.
• The surface states exhibit a flat dispersion feature consistent with strong light confinement and significant group velocity reduction.
• Symmetry-guaranteed and accidental nodal lines coexist in the fcc lattice, with the former stabilized by crystal point group symmetries.
• The observed photonic pseudogaps in prior studies are explained by the presence of nodal lines, providing a unified interpretation of experimental observations.
• The theoretical framework establishes a direct link between nodal line topology and measurable photonic phenomena such as slow light and surface state formation.
• The results offer a clear pathway for experimental verification of nodal line semimetals in photonic systems through the detection of drumhead surface modes.