Switching of topological phase transition from semiconductor to ideal Weyl states in Cu$_2$SnSe$_3$ family of materials

The exploration of topological phase transition (TPT) mechanisms constitutes a central theme in quantum materials research. Conventionally, transitions between Weyl semimetals (WSMs) and other topological states rely on the breaking of time-reversal symmetry (TRS) or precise manipulation of lattice symmetry, thus constraints the available control strategies and restrict the scope of viable material systems. In this work, we propose a novel mechanism for TPT that operates without TRS breaking or lattice symmetry modification: a class of semiconductors can be directly transformed into an ideal WSM via bandgap closure. This transition is driven by chemical doping, which simultaneously modulates the band gap and enhances spin-orbit coupling (SOC), leading to band inversion between the valence and conduction bands and thereby triggering the TPT. Using first-principles calculations, we demonstrate the feasibility of this mechanism in the Cu$_2$SnSe$_3$ family of materials, where two pairs of Weyl points emerge with energies extremely close to the Fermi level. The bulk Fermi surface becomes nearly point-like, while the surface Fermi surface consists exclusively of Fermi arcs. This symmetry-independent mechanism bypasses the constraints of conventional symmetry-based engineering, and also offers an ideal platform for probing the anomalous transport properties of WSMs.

💡 Research Summary

The paper introduces a symmetry‑independent route to convert a conventional semiconductor directly into an ideal Weyl semimetal (WSM) without breaking time‑reversal symmetry (TRS) or altering the crystal lattice. The authors focus on the Cu₂SnSe₃ family of compounds, which crystallize in a non‑centrosymmetric Cc (No. 9) structure resembling enargite. Using density‑functional theory (DFT) with the Perdew‑Burke‑Ernzerhof (PBE) functional, both plane‑wave (VASP) and full‑potential linearized augmented‑plane‑wave (WIEN2k) methods are employed to obtain accurate bulk band structures. Spin‑orbit coupling (SOC) is systematically switched on and off to assess its impact on the electronic gaps.

A systematic survey of nine members (Cu₂SiS₃, Cu₂SiSe₃, Cu₂SiTe₃, Cu₂GeS₃, Cu₂GeSe₃, Cu₂GeTe₃, Cu₂SnS₃, Cu₂SnSe₃, Cu₂SnTe₃) reveals a clear trend: as the anion changes from S → Se → Te and the group‑IV element progresses from Si → Ge → Sn, the lattice expands, the Cu–X bond lengths increase, and the intrinsic SOC strength of the X‑p orbitals grows (≈0.1 eV for S, ≈0.22 eV for Se, ≈0.55 eV for Te). Consequently, the indirect band gaps shrink dramatically. For the Si‑based and Ge‑S compounds the gaps remain finite (0.02–0.36 eV) even with SOC, and they are topologically trivial (Z₂ = 0). In contrast, Cu₂GeSe₃, Cu₂SnS₃, and Cu₂SnSe₃ lose their global gap once SOC is included; the valence and conduction bands cross linearly near the Γ point, signaling a band inversion that creates Weyl nodes.

To confirm the Weyl nature, the authors construct maximally‑localized Wannier functions for Cu 3d and X p orbitals, generate a tight‑binding Hamiltonian, and analyze it with WannierTools. Four Weyl points are located in Cu₂SnSe₃ at (±0.043, ±0.074, ∓0.01) Å⁻¹, each carrying a chirality of +1 or –1, as evidenced by the Berry curvature distribution (two sources and two sinks in the kₓ‑kᵧ plane). The energy of these nodes lies within a few meV of the Fermi level, producing an almost point‑like bulk Fermi surface. No other bulk pockets intersect the Fermi energy, making Cu₂SnSe₃ an “ideal” WSM. Cu₂GeSe₃ hosts the same four Weyl points but also exhibits additional electron and hole pockets at the Brillouin‑zone corners, slightly compromising its ideality.

Surface calculations on the (001) Se‑terminated slab reveal the hallmark of a Weyl semimetal: bulk‑derived point‑like features at the zone center and two well‑defined Fermi arcs that connect Weyl nodes of opposite chirality. For Cu₂SnSe₃ the arcs are clean and isolated, whereas Cu₂GeSe₃ shows extra surface projections of bulk pockets. Surface‑state dispersions along three high‑symmetry cuts further illustrate the coexistence of bulk gaps (away from Weyl points) and topological surface states crossing those gaps, confirming the bulk‑boundary correspondence.

The key insight is that chemical substitution simultaneously tunes the lattice constant (affecting band dispersion) and the SOC strength of the p‑orbitals, driving a semiconductor‑to‑Weyl transition without any external field or symmetry breaking. This “doping‑induced band‑gap closure” mechanism bypasses the conventional reliance on magnetic order, strain, or pressure, expanding the pool of candidate materials to include abundant, non‑magnetic semiconductors compatible with existing fabrication technologies.

In summary, the work demonstrates a practical, symmetry‑agnostic pathway to engineer ideal Weyl semimetals from conventional semiconductors, provides a comprehensive first‑principles validation for the Cu₂SnSe₃ family, and opens new avenues for exploring chiral anomaly‑driven transport, topological optics, and spintronic applications in readily synthesizable materials.