Existence of a low-gap damping-free window at the smallest type-II tilts

Determine whether a low-gap damping-free collective-mode window opens at the smallest type-II tilt parameters in the tilted nodal-line semimetal, below the approximately \(\eta_z\gtrsim1.2\) threshold identified in the reported numerical scan.

Background

For type-II tilt, ηz>1\eta_z>1, the intraband particle–hole continuum develops a low-frequency gap between its lower and upper kinematic edges. The numerical analysis identifies a candidate acoustic-like branch lying below both the intraband and interband continua for ηz≳1.2\eta_z\gtrsim1.2, producing a low-gap damping-free window within the stated hard-cutoff regularization.

At ηz=1.1\eta_z=1.1, the candidate acoustic branch is not resolved on the numerical momentum grid, so the existence of such a window at the smallest type-II tilts remains unresolved. Establishing the answer would require more reliable mode tracking and likely systematic tests of momentum resolution and regularization dependence.

References

At $\eta_z=1.1$ the acoustic branch is not resolved in the present $q$ grid (the loss spectrum is dominated by the inter-band damped optical branch at all $q$), so whether a window opens at the smallest type-II tilts remains an open question; no known nodal-line compound is established to reach type-II tilts, so the low-gap window is currently a theory-side prediction with the tilt to be surveyed compound-by-compound from first principles.

— Tilt-controlled Drude anisotropy in nodal-line semimetals: logarithmic enhancement, interband correction, gauge consistency, and the Landau-damping window  (2609.26639 - Li et al., 22 Sep 2026) in Section 5.1, “Landau damping and the self-consistent plasmon window”; Section 7, “Limitations and open questions”