Possible permanent Dirac- to Weyl-semimetal phase transition by ion implantation

Topological semimetals (TSMs) comprise Dirac semimetals (DSMs), Weyl semimetals (WSMs), nodal-line semimetals, and triple-point semimetals, and host relativistic fermions that give rise to large magnetoresistance, chiral anomaly, and anomalous Hall effects. In DSMs, linear energy-momentum dispersion exists in all three directions. The degeneracy of a Dirac node is protected only when both time-reversal and inversion symmetries are present; breaking either splits a Dirac node into a pair of Weyl nodes with opposite chirality. The Bi–Sb alloy system (Bi1−xSbx) has a rhombohedral R3m structure. In Bi0.96Sb0.04, the conduction and valence band edges at the L point exchange symmetry at x = 0.04, closing the L-point gap and producing a DSM. Prior Dirac-to-Weyl transitions reported under low temperature or strong magnetic field have been reversible. This work aims to demonstrate, for the first time, a possible permanent DSM-to-WSM phase transition in a single material (Bi0.96Sb0.04) by ion implantation, leveraging the advantages of implantation (room-temperature processing and species selectivity), and to elucidate the role of nonmagnetic (Au) versus magnetic (Mn) ion implantation on symmetry breaking and transport signatures.

The paper situates the study within extensive work on TSMs showing exotic transport due to relativistic fermions near Dirac/Weyl nodes. It reviews the symmetry requirements distinguishing DSMs from WSMs and notes that at the topological to trivial insulator critical point, the band-contact points are Dirac or Weyl depending on inversion symmetry. For Bi–Sb alloys, prior band-structure studies established that at x ≈ 0.04 the L-point gap closes, forming a DSM. Previous reports of Dirac-to-Weyl transitions induced by low temperature or strong magnetic fields were reversible. Raman studies in related systems (e.g., MoTe2 undergoing structural transitions and Mo1−xWxTe2 with random substitution) have demonstrated inversion-symmetry breaking via the emergence or splitting of Raman modes. First-principles and Raman work on rhombohedral CdTiO3 (R3m) similarly associated additional, blueshifting Raman peaks with local loss of inversion symmetry (R3 → R3). These precedents motivate using Raman plus magnetotransport to diagnose inversion-symmetry breaking and Weyl physics in implanted Bi0.96Sb0.04.

Bi0.96Sb0.04 bulk single crystals (99.99% purity) were grown by sealing stoichiometric Bi and Sb in evacuated quartz, heating to 650 °C, slowly cooling to 270 °C over five days, and annealing at 270 °C for seven days. XRD verified single-phase rhombohedral R3m structure. Crystals cleaved along (001) were implanted at room temperature with either 1 MeV Au+ ions to nominal fluences Φ = (0.8, 3.2, 8.0, 10.4, 12.8) × 10^16 Au cm^−2 or 300 keV Mn+ ions to Φ = (4.0, 8.0) × 10^16 Mn cm^−2. TriDyn dynamic simulations (including sputtering) estimated peak concentrations: Au 1.7–5.6 at% (0.48–1.6 × 10^21 cm^−3) and Mn 5.8–10.3 at% (1.6–2.9 × 10^21 cm^−3); for Au, peak concentration saturated near 5.6 at% for Φ ≳ 6 × 10^16 cm^−2. Implanted samples were annealed at 230 °C for 1 h under Ar to reduce damage. Raman spectroscopy (confocal, 532 nm excitation, ×100 objective NA 0.90, grating 2400 gr/mm, CCD detection) was performed at room temperature on the shiny (001) surface over 50–180 cm^−1. XRD used glancing incidence due to X-ray penetration exceeding implantation depth; scans covered 2θ from 20° to 80°. Magnetotransport used a cryogen-free magnet with B from −9 T to +9 T. Six-probe geometry with homogeneous contacts (silver paste at RT) minimized current jetting. Current I was along the binary axis. Longitudinal MR (LMR) measured B ∥ I (B ∥ binary axis), transverse MR (TMR) and Hall were measured for B ⟂ I (B ∥ trigonal axis). Zero-field resistivity was measured from 1.7 K to 300 K. Shubnikov–de Haas (SdH) oscillations were extracted from MR after background subtraction; FFT and Lifshitz–Kosevich analysis yielded quantum parameters (e.g., frequencies Fα, Fβ; A_F, m, v_F, k_F, n_3D, τ_q, μ, T_D, l_0, E_F) and Berry phase Φ_B from Landau fan analysis.

• XRD: All samples showed sharp (001) reflections consistent with single-crystalline rhombohedral R3m structure; an additional misaligned (202) peak at 2θ ≈ 49.5° appeared for all samples. No clear Φ dependence in XRD, consistent with limited sensitivity to the (111) plane (relevant to inversion symmetry) and shallow implanted layer relative to X-ray penetration.
• Raman spectroscopy (Bi0.96Sb0.04, (001) surface): In the pristine sample (Φ = 0), observed Bi–Bi modes E2g(Bi) ≈ 72.3 cm^−1 and A1g(Bi) ≈ 97.5 cm^−1, with a weak E2g(Sb) ≈ 119 cm^−1; A1g(Sb) was absent. For Φ up to 0.8 × 10^16 Au cm^−2, spectra changed little. For Φ ≥ 3.2 × 10^16 Au cm^−2, a new peak U(Bi) appeared at 85.7 cm^−1 between E2g(Bi) and A1g(Bi), and the A1g(Sb) mode emerged at 149.7 cm^−1 (notably blueshifted versus typical ~138–141 cm^−1). With increasing Φ to 12.8 × 10^16 Au cm^−2, E2g(Bi), U(Bi), A1g(Bi), and A1g(Sb) gradually blueshifted; overall spectral shape remained similar beyond the threshold.
• Longitudinal MR (B ∥ E): In the unimplanted crystal, LMR was positive. For Φ = 3.2 × 10^16 Au cm^−2, negative LMR (NMR) emerged at 1.7 K, grew with temperature up to ~100 K, then decreased at higher T. At 1.7 K, the magnitude of NMR increased with Φ, peaking at Φ = 8.0 × 10^16 Au cm^−2 and decreasing at Φ = 12.8 × 10^16 Au cm^−2. NMR was absent for B ⟂ E (TMR). Mn-implanted samples (Φ = 4.0 and 8.0 × 10^16 Mn cm^−2) exhibited only positive MR for all orientations.
• SdH oscillations: FFT of LMR oscillations revealed two frequencies (Fα, Fβ). Fα showed negligible variation with Φ, whereas Fβ increased abruptly at Φ = 3.2 × 10^16 Au cm^−2. LK analysis showed that for the β Fermi pocket, multiple quantum parameters (e.g., A_F, m, v_F, etc.) changed abruptly at Φ = 3.2 × 10^16 Au cm^−2 and then varied weakly for higher Φ, mirroring Raman and LMR thresholds. The β-pocket cross-sectional area Aβ was ~0.09 nm^2, indicative of linear dispersion. Berry phase analysis supported nontrivial topology (details referenced to figures/supplement).
• Threshold behavior and saturation: Multiple independent observables (Raman modes, NMR onset and magnitude, Fβ and β-pocket quantum parameters) exhibited an abrupt change at a common critical fluence Φ_c ≈ 3.2 × 10^16 Au cm^−2, with modest evolution beyond, consistent with TriDyn-predicted saturation of peak Au concentration (~5.6 at% for Φ ≳ 6 × 10^16 cm^−2).
• Interpretation: The emergence of new/blueshifted Raman modes and their Φ dependence indicate inversion-symmetry breaking. The appearance of orientation-selective NMR (B ∥ E only) implies a chiral anomaly associated with Weyl fermions. Together with quantum-oscillation changes (especially in the β pocket), the data support a possible permanent DSM→WSM transition induced by nonmagnetic Au implantation, whereas magnetic Mn implantation does not produce such behavior (likely breaking both time-reversal and inversion symmetry and yielding trivial metallic transport).

The study set out to test whether ion implantation can permanently drive a DSM-to-WSM transition in a single material by breaking inversion symmetry. In Bi0.96Sb0.04, Au implantation produces a critical-fluence response across multiple probes: Raman spectra develop an additional U(Bi) mode and a strongly blueshifted A1g(Sb) mode at Φ ≥ 3.2 × 10^16 cm^−2, consistent with local inversion-symmetry breaking, analogous to behavior reported in MoTe2, Mo1−xWxTe2, and rhombohedral CdTiO3. Magnetotransport corroborates this: negative longitudinal MR appears only for B ∥ E and shows the expected temperature and orientation dependence for a chiral anomaly in Weyl fermions, while transverse MR remains positive, and Mn-implanted samples show only positive MR. Quantum oscillation analysis reveals an abrupt increase of the β-pocket frequency and cross-sectional area at the same Φ_c, while the α pocket remains largely unchanged, suggesting that Weyl-node formation and Fermi surface reconfiguration occur in specific pockets. The small Aβ (~0.09 nm^2) and linear dispersion are consistent with DSM/WSM electronic structure, and the observed increases beyond Φ_c align with expectations for Weyl-node splitting from a Dirac point. The convergence of Raman, LMR, and SdH thresholds, along with Au-concentration saturation, supports a nonmagnetic-implantation-driven, likely permanent inversion-symmetry breaking that transforms Bi0.96Sb0.04 from a DSM to a WSM, in contrast to previously reported reversible transitions under low T or high B. The absence of NMR and special Raman features in Mn-implanted samples underscores the role of nonmagnetic perturbations in selectively breaking inversion (without time-reversal) to realize Weyl physics.

This work demonstrates a possible permanent Dirac-to-Weyl semimetal phase transition in Bi0.96Sb0.04 driven by ion implantation with a nonmagnetic species (Au). A common critical fluence Φ_c ≈ 3.2 × 10^16 Au cm^−2 marks abrupt changes in Raman modes (appearance of U(Bi), blueshifted A1g(Sb)), the emergence and growth of negative longitudinal MR (chiral-anomaly signature), and quantum-oscillation parameters (notably Fβ and Aβ). These results indicate inversion-symmetry breaking and Weyl-node formation in the Au-implanted layer, persisting after annealing, i.e., consistent with a permanent modification. In contrast, Mn implantation yields only positive MR and no Raman signatures of inversion-symmetry breaking, suggesting no DSM→WSM transition. The findings introduce ion implantation with nonmagnetic elements as a simple route to engineer Weyl phases within a single material. Potential future work includes direct spectroscopic verification of Weyl nodes and Fermi arcs (e.g., ARPES), depth-resolved structural probes sensitive to inversion symmetry in the implanted layer, systematic studies across different nonmagnetic implant species, energies, and fluence profiles, and device-level demonstrations exploiting the engineered chiral anomaly.

• Structural confirmation of inversion-symmetry breaking is indirect: conventional XRD showed no Φ dependence and is insensitive to the relevant (111) plane and shallow implanted layer; direct symmetry-sensitive structural probes were not reported.
• Direct observation of Weyl nodes or Fermi arcs (e.g., by ARPES) was not presented; Weyl character is inferred from Raman, MR orientation dependence, and SdH analysis.
• Reported Mn-implantation effects are interpreted as yielding trivial metallic behavior, but detailed magnetic/structural characterization of Mn-induced phases is not provided.
• The implanted layer is near-surface and thin compared with bulk probe depths; depth inhomogeneity may complicate quantitative interpretation of bulk-averaged measurements.