Nodal-chain metals (1604.03112v2)

Abstract: The band theory of solids is arguably the most successful theory of condensed matter physics, providing the description of the electronic energy levels in a variety of materials. Electronic wavefunctions obtained from the band theory allow for a topological characterization of the system and the electronic spectrum may host robust, topologically protected fermionic quasiparticles. Many of these quasiparticles are analogs of the elementary particles of the Standard Model, but others do not have a counterpart in relativistic high-energy theories. A full list of possible quasiparticles in solids is still unknown, even in the non-interacting case. Here, we report on a new type of fermionic excitation that appears in metals. This excitation forms a nodal chain -- a chain of connected loops in momentum space -- along which conduction and valence band touch. We prove that the nodal chain is topologically distinct from any other excitation reported before. We discuss the symmetry requirements for the appearance of this novel excitation and predict that it is realized in an existing material IrF$_4$, as well as in other compounds of this material class. Using IrF$_4$ as an example, we provide a detailed discussion of the topological surface states associated with the nodal chain. Furthermore, we argue that the presence of the novel quasiparticles results in anomalous magnetotransport properties, distinct from those of the known materials.

• The paper introduces symmetry-protected nodal chains in electronic band structures, expanding the theory of topological semimetals.
• It demonstrates how non-symmorphic glide plane symmetries connect nodal lines into chains, validated by first-principles calculations on IrF₄.
• The study suggests these nodal chain metals may exhibit unusual electromagnetic responses, offering new avenues for quantum device applications.

Overview of "Nodal-chain metals"

The paper "Nodal-chain metals" introduces a novel class of fermionic excitations in metallic systems characterized by topologically protected degeneracies in their electronic band structures. This research extends the current understanding of condensed matter systems by outlining the properties and implications of nodal chain metals, a phenomenon involving interconnected loops of band touching known as nodal chains. These structures manifest in the momentum space of certain materials and represent a distinct topological state.

Nodal Chains and Their Characteristics

Nodal chains are a higher-order extension of nodal lines, where valence and conduction bands touch along loops in the Brillouin zone (BZ). Specifically, the paper reveals that these chains are formed by connecting non-symmorphic nodal lines (NSNLs) which are enforced by glide plane symmetries. Unlike previously reported nodal lines that occur due to band inversion, the nodal chains are structurally unique as they are symmetry-protected and unavoidable due to the material's space group symmetries. The research identifies specific space groups where these nodal chain configurations are inherently present whenever the electron count per unit cell meets a specific criterion (4n+2 electrons).

Material Realizations: IrF₄

The paper highlights IrF₄ as a prime candidate for demonstrating nodal chain metal properties. Iridium tetrafluoride's orthorhombic crystal structure supports two orthogonal NSNLs, satisfying the conditions necessary for a nodal chain. The first-principles calculations demonstrate that the topological properties lead to notable consequences in the electronic structure of IrF₄, including the presence of topological surface states characterized by Fermi arcs. These arcs provide evidence of the surface manifestation of the nodal chain's topology, which can be potentially verified experimentally through techniques like ARPES.

Theoretical and Practical Implications

Nodal chain metals introduce new electromagnetic response properties, considerably affecting magnetotransport phenomena. The researchers predict anomalous characteristics due to the response of these systems to magnetic fields, such as field-driven topological transitions and changes in Hall conductance, suggesting that these materials could serve as platforms for exploring novel quantum mechanical effects.

Theoretically, the paper posits that the presence of nodal chains could pave the way for understanding interactions beyond the standard model of elementary particles, given their unique topology. Furthermore, the association of NSNLs with unexpected low-energy excitations provides a new perspective on the modeling of topological states.

Speculation on Future Developments

The paper's introduction of nodal chains adds a significant chapter to the ongoing exploration of topological phases of matter. It encourages further examination into other material classes that might host similar phenomena, particularly focusing on crystal symmetries that permit such electronic degeneracies. An exploration of possible superconductivity or exotic magnetic phases could reveal applications in quantum computing or novel electronic devices. Additionally, future research could explore the interplay between electron correlations and nodal chain topology, possibly uncovering new physical states and behaviors.

In conclusion, this investigation advances both the theoretical framework and practical understanding of topological semimetals, with nodal chain metals representing a new frontier in condensed matter physics. As experimental techniques advance, the verification and exploitation of these properties may become an integral part of the development of future quantum technologies.