Porous-B${}_{18}$: An Ideal Topological Semimetal with Symmetry-Enforced Orthogonal Nodal-Line and Nodal-Surface States

Abstract

Topological semimetals (TSMs) featuring symmetry-protected band degeneracies have attracted considerable attention due to their exotic quantum properties and potential applications. While nodal line (NL) and nodal surface (NS) semimetals have been extensively studied, the realization of a material where both NL and NS coexist and are intertwined, particularly with an ideal electronic band structure, remains a significant challenge. Here, we predict via first-principles calculations and symmetry analysis a metastable boron allotrope, Porous-B${}_{18}$ (space group $P{6}_3/m$, No.~176), as a pristine TSM hosting a NS and two straight NLs near the Fermi level. The structure, a honeycomb-like porous 3D framework, exhibits excellent dynamical, thermal (stable up to 1000~K), and mechanical stability. Its electronic band structure is remarkably clean: only the highest valence band (HVB) and the lowest conduction band (LCB) cross linearly within a large energy window of 1.84~eV, free from trivial-band interference. The nodal surface lies on the $k_z=\pm \pi$ planes, protected by combined time-reversal symmetry ($T$) and twofold screw-rotational symmetry ($S_{2z}$), yielding a full-plane Kramers-like degeneracy. The two nodal lines along $K$--$H$ and $K^{\prime }$--$H^{\prime }$ are protected by inversion and time-reversal symmetries, carry a quantized Berry phase of $\pm \pi$, and connect orthogonally to the nodal surface, forming an intertwined nodal network. Drumhead surface states on the $(1\bar{1}0)$ surface further confirm the nontrivial topology. Porous-B${}_{18}$ thus provides an ideal platform for investigating the interplay between nodal-line and nodal-surface fermions and exploring novel quantum transport phenomena.

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