Topological semimetal with coexisting nodal points and nodal lines (2501.13636v1)

Abstract: Featuring exotic quantum transport and surface states, topological semimetals can be classified into nodal-point, nodal-line, and nodal-surface semimetals according to the degeneracy and dimensionality of their nodes. The coexistence of diverse categories of topological semimetals is of particular interest as it enables the concurrent utilization of their respective beneficial features. However, topological semimetals that possess both nodal points and nodal lines are rarely reported. Here, we propose a scheme to construct this unprecedented topological semimetal, which particularly exhibits second-order hinge Fermi arcs connecting projected nodal lines. Then, by applying periodic driving on the system, we find a hybrid-order topological semimetal with nodal points and rich nodal-lines structures and its conversion into the first-order topological semimetal, which are absent in the static system. Our results enrich the family of topological semimetals, thereby establishing a foundation for further exploration into the potential applications of these materials.

• The paper introduces a novel lattice framework that simultaneously realizes nodal points and nodal lines in a single semimetal system.
• It employs a PT-broken perturbation under open boundary conditions to reveal drumhead surface states associated with nodal lines.
• Floquet engineering is used to dynamically control the state, paving the way for multifunctional quantum device applications.

Topological Semimetals with Coexisting Nodal Points and Nodal Lines

In this paper, the authors introduce a novel framework for constructing a topological semimetal that supports both nodal points and nodal lines—a unique configuration in the paper of quantum materials. Traditional classifications of topological semimetals include nodal-point (Dirac and Weyl) semimetals, nodal-line semimetals, and nodal-surface semimetals, each distinguished by the dimensionality and degeneracy of nodes within the momentum space. The coexistence of these distinct topological features offers a promising avenue for applications that could exploit multiple exotic properties simultaneously.

The authors propose a three-dimensional (3D) lattice system in which spinless fermions exhibit coexisting nodal structures. Their approach employs a $\mathcal{PT}$-broken perturbation to transition a second-order Dirac semimetal into the target configuration. The system is primarily characterized under open boundary conditions, revealing that nodal lines emerge alongside nodal points, which are preserved from the initial high-symmetry conditions. Nodal lines here are correlated with drumhead surface states, enhancing the system's application range by enabling multifunctional device design.

Key to this configuration is the technique of Floquet engineering, which extends the structure of the semimetal beyond static capabilities. The authors employ periodic driving—a method proven effective in generating novel topological states—as either a coherent control of symmetry or a facilitator of long-range hopping effects. By dynamically modulating parameters, they convert the hybrid-order topological semimetal into both a more comprehensive hybrid-order semimetal (exhibiting enhanced and rich nodal features) and a purely first-order topological semimetal. This scalability underscores the utility of Floquet systems for dynamic state manipulation.

The implications of this work are multifaceted. Theoretically, it enriches our understanding of topological phases, enabling a simultaneous manifestation of multiple node types and their associated surface states. Practically, it sets the groundwork for experimental realizations in several physical platforms, such as photonic systems, ultra-cold atoms, and superconducting qubits, and represents a step towards devising quantum devices with integrated functionalities. Looking forward, it is anticipated that the development of such hybrid-order and multi-nodal semimetals would ignite further research into uncovering novel quantum effects and applications in condensed matter physics and materials science.