Engineering Ideal 2D Type-II Nodal Line Semimetals via Stacking and Intercalation of van der Waals Layers

TL;DR

The paper tackles the challenge of engineering robust 2D type-II nodal-line semimetals by proposing a bottom-up approach that combines van der Waals bilayer stacking with atomic intercalation to independently control interlayer coupling and the Fermi level. A minimal two-orbital tight-binding model is developed to capture the interlayer hopping physics, showing that type-II NLs arise from a delicate balance of intra- and interlayer interactions and can undergo Lifshitz transitions as parameters vary. Using hexagonal nitrides, the authors identify fluorine-intercalated bilayer AlN (F@BL-AlN) and GaN (F@BL-GaN) as ideal platforms where a symmetry-protected NL can be pinned at $E_F$, with first-principles results in excellent agreement with a TB model. The intercalation not only tunes the interlayer coupling but also induces charge transfer that aligns the nodal energy with $E_F$, giving a high DOS at the nodal energy and driving magnetic instabilities into ferromagnetic or antiferromagnetic topological semimetals under strain or fields. Overall, the work provides clear design principles and a practical path toward experimentally realizable, tunable 2D type-II NLSMs in van der Waals materials, with rich interplay between topology, electronic correlations, and magnetism.

Abstract

Two-dimensional type-II topological semimetals (TSMs), characterized by strongly tilted Dirac cones, have attracted intense interest for their unconventional electronic properties and exotic transport behaviors. However, rational design remains challenging due to the sensitivity of band tilting to lattice geometry, atomic coordination, and symmetry constraints. Here, we present a bottom-up approach to engineer ideal type-II nodal line semimetals (NLSMs) in van der Waals bilayers via atomic intercalation. Using monolayer $h$-AlN as a prototype, we show that fluorine-intercalated bilayer AlN (F@BL-AlN) hosts a symmetry-protected type-II nodal loop precisely at the Fermi level, enabled by preserved mirror symmetry ($\mathcal{M}_z$) and tailored interlayer hybridization. First-principles calculations reveal that fluorine not only tunes interlayer coupling but also aligns the Fermi energy with the nodal line, stabilizing the type-II NLSM phase. The system exhibits tunable electronic properties under external electric and strain fields and features a van Hove singularity that induces spontaneous ferromagnetism, realizing a ferromagnetic topological semimetal state. This work provides a versatile platform for designing type-II NLSMs and offers practical guidance for their experimental realization.

Figures (4)

• Figure 1: (a) Schematic illustration of the bilayer square-lattice model with intralayer hopping $t$ and interlayer hoppings $t_{1}$ and $t_{2}$. (b) Phase diagram of the minimal tight-binding model in the $(t_{1}/t, t_{2}/t)$ parameter space, showing three distinct NL phases. (c) Representative 3D band dispersions corresponding to the three NL types along the path $l_{1}$ indicated in (b). (d) Schematic illustration of the three-step bottom-up strategy for designing ideal 2D type-II NLSMs using van der Waals bilayer stacking and ionic intercalation.
• Figure 2: (a,c) Top and side views of the crystal structures of monolayer (ML) and AA-stacked bilayer (BL) $h$-BN, respectively. (b,d) Electronic band structures and projected density of states (PDOS) of ML and BL $h$-BN, respectively, with with the wave-function distributions for the $\alpha$ and $\beta$ bands around the K point shown alongside.
• Figure 3: (a) Top and side views of the atomic structure of fluorine-intercalated bilayer AlN (F@BL-AlN). (b) Electronic band structure and PDOS of F@BL-AlN. (c) Comparison between the TB and DFT band structures near the Fermi level. (d) Real-space distributions of the $\alpha$ and $\beta$ states at the K point. (e) Top and side views of the 3D band dispersion around the nodal line. (f) Differential charge density of F@BL-AlN, where yellow (blue) regions indicate charge accumulation (depletion).
• Figure 4: (a) Electronic band structures of F@BL-AlN under biaxial strains. (b) Evolution of the NL structure with applied strain. (c) Evolution of the local band gaps ($\Delta_1$, $\Delta_2$) and electric polarization ($P_e$) under increasing vertical electric field, $\mathcal{E}_z$. (d) Band structures of F@AlN with $\mathcal{E}_z$=0.25 eV/Å. (e) Total energy of F@BL-AlN under FM and AFM configurations as a function of applied strain, with the nonmagnetic state taken as the zero-energy reference. (f) Spin-polarized band structure of BL-F@AlN in the FM configuration. (g) Spin-polarized band structure of BL-F@AlN in AFM.