Nodal Quasiparticles in Quantum Materials

• Nodal quasiparticles are low-energy excitations characterized by vanishing gaps at nodes determined by symmetry and topology in quantum materials.
• They manifest through distinct experimental signatures such as Fermi arcs, pseudogaps, and anomalous superfluid density in techniques like ARPES and microwave spectroscopy.
• Their unique transport properties, including anisotropic conductivity and mass renormalization, provide insights into disorder, non-Hermitian effects, and interaction-driven phenomena.

Nodal quasiparticles are low-energy excitations whose spectrum vanishes along isolated points, lines, or more elaborate manifolds in momentum space—so-called "nodes"—rather than being fully gapped. This structure underpins the unconventional thermodynamic and dynamic properties observed in a wide variety of quantum materials, including high-T_c d-wave superconductors, topological semimetals, certain magnets, and engineered quantum systems. The interplay of symmetry, topology, interactions, disorder, and non-Hermitian (NH) effects controls the stability, spectral features, and transport properties of these quasiparticles. Recent work has revealed that nodal quasiparticles encapsulate both fundamental theoretical phenomena (such as topological invariants and anomalous transport) and emergent, experimentally accessible signatures (such as Fermi arcs, pseudogaps, mass enhancements, and superdiffusive dynamics).

1. Fundamental Structure and Symmetry Protection

Nodal quasiparticles arise in systems where the gap function—whether originating from the superconducting order parameter, the band crossing in semimetals, or exchange-coupled magnets—vanishes along specific manifolds in the Brillouin zone. In d-wave superconductors, the order parameter $\Delta(\mathbf{k})$ vanishes linearly along zone diagonals, yielding isolated nodal points hosting gapless Dirac-like excitations (0810.3217). By symmetry, more elaborate nodal manifolds are possible: nodal lines, nodal rings, nodal chains, and surfaces are enforced or stabilized by group theoretical constraints. For example, in nodal chain metals, the presence of mutually orthogonal glide planes and time-reversal symmetry enforces band crossings along intersecting nodal lines, forming chain structures protected by the filling condition $\nu_\mathrm{filled} = 4n+2$ and non-symmorphic symmetry elements (Bzdušek et al., 2016). In topological semimetals, generic two-band (spin-½) Hamiltonians can support Weyl points and nodal lines dictated by the absence of inversion-time-reversal product symmetry and constrained by the representations of the magnetic point group at each $\mathbf{k}$ (Knoll et al., 2021).

Symmetry protection can extend to more exotic cases. In graphene-based nodal ring semimetals, a $\mathbb{Z}_2$ symmetry arising from spin interchange and a double-orthogonality structure in sublattice and spin spaces protects quadratic Fermi liquid-like crossings, ensuring the stability of a topological nodal ring (Hur et al., 2022). In phononic systems such as CsBe$_2$F$_5$, eight entangled bands yield coexisting spin-1 Weyl points, charge-2 Dirac points, and nodal surfaces, each protected by symmetries such as screw rotations, time reversal, and composite antiunitary operations (Kang et al., 2023).

2. Experimental Signatures and Spectroscopy

Nodal quasiparticles manifest in observable quantities due to the presence of a low-energy density of states (DOS) that scales as a power law near the Fermi level. In clean d-wave cuprate superconductors, the superfluid density $\rho_s(T) = 1/\lambda^2(T)$ follows a linear-in-temperature law driven by the nodal DOS $N(\omega) \propto |\omega|$ (0810.3217). When disorder is introduced, the residual density of states at zero energy becomes finite, resulting in a crossover to quadratic temperature dependence at low $T$ and a characteristic $T^2$ law for $\rho_s(T)$, while the broadband microwave conductivity $\sigma_1(\Omega)$ directly probes the uncondensed quasiparticle spectral weight (0810.3217).

Angle-resolved photoemission spectroscopy (ARPES), particularly in time-resolved (trARPES) and ultrafast implementations, has illuminated the dynamics of nodal versus antinodal quasiparticles. In Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$, pump-probe photoemission reveals that ungapped nodal states display transient responses at the superconducting transition ($T_c$), pairing fluctuation onset ($T_p$), and pseudogap crossover ($T^*$), with the appearance of a critical fluence marking the energy scale for Cooper pair breakup (Zhang et al., 2013). Time- and angle-resolved ARPES also enables the mapping of near-nodal gap filling under photoexcitation and direct tracking of the reformation of the pairing gap on the picosecond timescale, with fluence-dependent relaxation channels distinguishing normal and superconducting regimes (Zhang et al., 2017).

Fermi arcs—Valleys of enhanced spectral weight in momentum-space maps near the former nodal region with partial spectral suppression—have been observed in both simulation and experiment, intimately tied to phase fluctuations of the superconducting order parameter. The evolution and emergence of these features are quantitatively governed by the superconducting correlation length $\xi(T)$ and the nodal BCS coherence length $\xi_\text{BCS}(\mathbf{k})$, with the phase-fluctuation-induced scattering rate $\Gamma_\text{pf} \propto v_F/\xi$ consistently verified in unbiased quantum Monte Carlo simulations (Wang et al., 2023).

3. Transport Phenomena and Quasiparticle Dynamics

Nodal quasiparticles govern numerous transport signatures through their unique low-energy dispersion and scattering properties. In d-wave superconductors, the anisotropy of the Dirac nodes (characterized by $v_\Delta/v_F$) crucially determines the temperature dependence of the superfluid density, thermal conductivity, and $T_c$. Near quantum critical points where order parameter fluctuations couple to the nodes, renormalization-group analyses reveal that $v_\Delta/v_F$ may flow to 0, 1, or diverge, yielding distinct fixed points that manifest as suppression or enhancement of $T_c$ and $\rho_s$ (Wang, 2013). The influence of disorder is highly sensitive to type: random mass and gauge potentials are RG irrelevant, preserving the fixed points, while random chemical potential is marginal, generating instability in the nodal spectrum (Wang, 2013).

In nodal-ring semimetals, the vanishing DOS at the nodal line leads to only partially screened long-range Coulomb interactions. Renormalization group and large-$N_f$ analyses show that the screened Coulomb potential becomes an irrelevant perturbation at low energies, allowing for a well-defined quasiparticle picture with a quadratic decay rate $1/\tau \sim E_p^2$—Fermi liquid-like despite a vanishing DOS (Huh et al., 2015). Experimental consequences include anisotropic DC conductivity, nonstandard sound attenuation and velocity renormalization, and a unique $\omega(q) \sim \sqrt{q}$ phonon dispersion (Huh et al., 2015).

Mass renormalization phenomena are documented in quantum oscillation studies: in ZrSiS, the effective mass for the "dog-bone" Fermi surface pocket is strongly enhanced with field—by up to a factor of 3—suggesting the presence of substantial many-body correlation effects on Dirac loop quasiparticles (Pezzini et al., 2017). The association of mass enhancement with field and topologically protected Berry phase (π) windings provides direct insights into the interplay between electronic topology and correlations.

4. Interactions, Non-Hermitian and Quantum Chaotic Effects

Interactions among nodal quasiparticles introduce a rich set of phenomena ranging from anomalous transport to exotic spectral features. In interacting lattice models, nodal lines and Weyl points may shift, shrink, or gap out under increasing interaction strength, with their stability hinging on microscopic symmetries and the presence or absence of ferromagnetic order (Kang et al., 2019). In certain semimetal models, gap formation occurs only after the coalescence and annihilation of nodal features, with symmetry-protected Weyl points remaining robust until a Mott gap opens (Kang et al., 2019).

Non-Hermitian effects, whether induced by disorder or intrinsic lifetime broadening, fundamentally modify the nodal spectrum. In 2D Dirac superconductors, the disorder self-energy renders the Hamiltonian non-Hermitian, replacing conventional nodes with Fermi arcs bounded by exceptional points; in 3D systems, nodes expand into Fermi ribbons bounded by exceptional lines, their extent determined by the competition between disorder and supercurrent-induced tilt (Zyuzin et al., 2019). The transition between gapped and "arch-shaped" Fermi arc spectra can be tuned via the disorder strength, with the emergence of exceptional points or lines as topological boundaries of the real-part spectrum (Zyuzin et al., 2019).

More generally, the NH topology—the braiding of complex quasiparticle bands in the frequency plane—protects crossings in the real part of the quasiparticle dispersion even in the absence of explicit symmetry. This yields nodal spectral functions distinguished by robust non-reciprocal transport and dynamical features such as ballistic or unidirectional modes reminiscent of chiral edge states, realized even in 1D interacting models with sublattice-dependent interactions (Lehmann et al., 8 May 2024).

In chaotic quantum systems with nodal interactions (where the interaction term commutes with the particle number at specific $k_0$), "quasi-conserved" modes near those nodes yield long-lived quasiparticles even in a fully chaotic and otherwise thermalizing environment. The resulting superdiffusive transport is characterized by anomalous charge dynamics with diverging time-dependent diffusion constants and dispersion relations of the form $\omega(q) \sim q^z$ with $z = \mathrm{min}[(2n+d)/2n,2]$, leading to scaling exponents such as $z=3/2$ for single-node 1D systems and confirmed by tensor network simulations (Wang et al., 14 Jan 2025).

5. Topological Properties, Surface States, and Magnetotransport

Nodal quasiparticles in topologically nontrivial systems are associated with quantized invariants (Chern numbers, Berry phases) and protected surface states. In nodal chain metals, NSNLs meeting at chain nodes require non-symmorphic symmetries and, upon surface projection, manifest as drumhead and Fermi-arc surface modes (Bzdušek et al., 2016). Application of magnetic fields can induce Landau level crossings where the Berry phase changes by $\pi$, leading to quantized charge pumping and anomalous magnetotransport (Bzdušek et al., 2016).

In graphene-based nodal ring semimetals, the quadratic spectrum supports a Fermi liquid with coexisting quasiparticles and quasiholes, robust against symmetry-preserving perturbations and hosting a quantized quantum Hall effect with a unique half-integer Chern number per spin, realized experimentally as topologically protected chiral edge states (Hur et al., 2022). In CsBe$_2$F$_5$, phononic Fermi arcs link surface projections of bulk spin-1 Weyl and charge-2 Dirac points, forming double-helicoid surface sheets and connecting bulk band topology to measurable edge phenomena (Kang et al., 2023).

INS experiments on honeycomb cobaltates have demonstrated that nodal magnons and spin-orbit excitons form Dirac-like nodes with experimentally observed intensity windings around nodal points (1 ± cos(α – α₀)), directly reflecting the topologically non-trivial structure of the quasiparticle wavefunction and associated Berry phase (Elliot et al., 2020).

6. Nodal Quasiparticles in Strongly Correlated and Competing-Order Systems

Nodal quasiparticles persist across diverse correlated regimes and in the presence of competing order. In underdoped YBa$_2$Cu$_3$O$_{6+y}$, penetration depth and microwave conductivity data are consistent with pure d-wave superconductivity plus unitarity-limit strong-scattering disorder, enabling the nodal spectrum to remain robust while ruling out most gapped competing states except commensurate density waves not "nesting" the nodes (0810.3217). In contrast, in heavy-fermion CeCu$_2$Si$_2$, thermodynamic experiments reveal exponential suppression of the specific heat and a lack of the predicted Volovik signature, indicating an unexpected absence or severe deficiency of nodal quasiparticles and supporting a fully gapped, two-gap superconducting state (Kittaka et al., 2013).

In the pseudogap phase of cuprates, "fractionalized Fermi liquid" (FL*) models encode the emergence of nodal Bogoliubov quasiparticles at the onset of d-wave superconductivity, even when the underlying Fermi surface violates the Luttinger count due to fractionalization and coupling to a $\pi$-flux spin liquid. Higgs condensation restores the nodal points, leading to characteristic Dirac-like dispersions with strong velocity anisotropy, and unifies the nodal Bogoliubov spectrum in both hole- and electron-doped systems (Christos et al., 2023).

7. Outlook and Universalities

Nodal quasiparticles embody the confluence of complex topology, symmetry-enforced protection, many-body interactions, and nonequilibrium or NH effects. The universality of Fermi arc formation via phase fluctuations (Wang et al., 2023), the emergent anomalous transport in nodal-interaction chaotic systems (Wang et al., 14 Jan 2025), and the optical tuning of many-body renormalization in Dirac systems (Gatti et al., 2019) illustrate the breadth and adaptability of the nodal quasiparticle paradigm. The diverse realization of nodal structures in electronic, phononic, and magnonic systems, together with their distinctive experimental fingerprints, continues to drive advances in the understanding and manipulation of unconventional quantum matter.