Topological nodal line semimetals

Abstract

We review the recent, mainly theoretical, progress in the study of topological nodal line semimetals in three dimensions. In these semimetals, the conduction and the valence bands cross each other along a one-dimensional curve in the three-dimensional Brillouin zone, and any perturbation that preserves a certain symmetry group (generated by either spatial symmetries or time-reversal symmetry) cannot remove this crossing line and open a full direct gap between the two bands. The nodal line(s) is hence topologically protected by the symmetry group, and can be associated with a topological invariant. In this Review, (i) we enumerate the symmetry groups that may protect a topological nodal line; (ii) we write down the explicit form of the topological invariant for each of these symmetry groups in terms of the wave functions on the Fermi surface, establishing a topological classification; (iii) for certain classes, we review the proposals for the realization of these semimetals in real materials and (iv) we discuss different scenarios that when the protecting symmetry is broken, how a topological nodal line semimetal becomes Weyl semimetals, Dirac semimetals and other topological phases and (v) we discuss the possible physical effects accessible to experimental probes in these materials.

arXiv commentA 10-page review article; comments and suggestions are highly appreciated

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• Quantum critical phenomena of the excitonic insulating transition in two dimensions
• Characterizing Floquet topological phases by quench dynamics: A multiple-subsystem approach
• Collective excitations and screening in two-dimensional tilted nodal-line semimetals
• Fragile topology in nodal-line semimetal superconductors
• Magnetothermopower of nodal line semimetals
• Electronic Structure of Kramers Nodal-Line Semimetal YAuGe and Anomalous Hall Effect Induced by Magnetic Rare-Earth Substitution
• Topological semimetal with coexisting nodal points and nodal lines
• Disorder induced dynamical interband response in Dirac nodal line semimetals
• Fate of superconductivity in disordered Dirac and semi-Dirac semimetals
• Nonlinear Optical Spectroscopy of Nodal-Line Semimetals
• Two-dimensional Dirac semimetals with tunable edge states
• Movable but unavoidable nodal lines through high-symmetry points in two-dimensional materials
• Unremovable linked nodal structures protected by crystalline symmetries in stacked bilayer graphene with Kekulé texture
• Unconventional Topological Insulators from Extended Topological Band Degeneracies
• Electronic properties of graphyne-$N$ monolayer and its multilayer: even-odd effect and topological nodal line semimetalic phases
• Nodal lines and boundary modes in topological Dirac semimetals with magnetism
• Existence of nodal-arc and its evolution into Weyl-nodes in the presence of spin-orbit coupling in TaAs & TaP
• Theoretical analysis of anisotropic upper critical field of superconductivity in nodal-line semimetals
• Nodal-line semimetals and their variance
• Time dependent electric transport in nodal-loop semimetals
• Topological $d$-wave Superconductivity and Nodal Line-Arc Intersections in Weyl Semimetals
• Quantum Oscillation and Landau-Zener transition in Untilted Nodal line semimetals under a time-periodic magnetic field
• Collective plasmonic modes in the chiral multifold fermionic material CoSi
• Tunable superluminal and subluminal reflected group delay in an air-Weyl semimetal film-Weyl semimetal substrate layered system
• Realization of Hopf-link structure in phonon spectra: Symmetry guidance and High-throughput investigation
• Subtle Structural Anomaly under Compression in Line-Nodal CaSb${}_2$
• Dirac Dispersions and Fermi Surface Nesting in LaCuSb${}_2$
• Tailoring higher-order van Hove singularities in non-Hermitian interface systems via Floquet engineering
• Fermi Level Fluctuations, Reduced Effective Masses and Zeeman Effect during Quantum Oscillations in Nodal Line Semimetals
• Quantum Hall effect and optical magneto-conductivity of two-dimensional topological nodal-line semimetals
• Surface magnon spectra of nodal loop semimetals
• Chiral symmetry and magnetism in a 3D Kagome lattice: RPt${}_2$B (R = La and Nd) prototype crystals
• Cartesian Nodal Lines and Magnetic Kramers Weyl Nodes in Spin-Split Antiferromagnets
• More on Topological Hydrodynamic Modes
• CeAu${}_2$Bi: a new nonsymmorphic antiferromagnetic compound
• Global phase diagram of Coulomb-interacting anisotropic Weyl semimetals with disorder
• Flat Topological Nodal Lines in Heavy-Fermion Compound CeCoGe${}_3$
• Fermi surface and Berry phase analysis for Dirac nodal line semimetals: cautionary tale to SrGa${}_2$ and BaGa${}_2$
• Essentially degenerate hidden nodal lines in two-dimensional magnetic layer groups
• Emergence of Nodal-Knot Transitions by Disorder
• Weak ${\mathbb{Z}}_2$ Supertopology
• Diffusive density response of electrons in anisotropic multiband systems
• Semiclassical perspective on Landau levels and Hall conductivity in an anisotropic Cubic Dirac Semi-Metal and the peculiar case of star-shaped classical orbits
• Biot-Savart law in quantum matter
• Magnetic susceptibility of crystals with crossing of their band-contact lines
• Energy relaxation dynamics in a nodal-line semimetal
• Topological materials with extensive flat-band surface states
• Unveiling Novel Resonant Interband Contribution to Polarizability in three-dimensional systems
• Transport through Nodal Surface Semimetal-Superconductor junction in absence/presence of light irradiation
• Accelerated Discovery of Topological Conductors for Nanoscale Interconnects
• Research on topological materials using ultrafast spectroscopy