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

Three-dimensional topological semimetals (TSMs) are a novel class of Dirac materials, categorized as either Dirac semimetals (DSMs) or Weyl semimetals (WSMs) depending on their time reversal and inversion symmetry. While previous research has shown reversible Dirac-to-Weyl phase transitions under low temperatures or strong magnetic fields, this study aims to achieve a permanent transition. The research focuses on understanding the manipulation of topological properties by ion implantation, a room-temperature process offering advantages in selective doping. The study investigates the effects of implanting both non-magnetic (Au) and magnetic (Mn) ions into Bi0.96Sb0.04, a known DSM, to determine if a permanent phase transition is possible and to elucidate the role of magnetic ions in the process. The importance of this work lies in its potential to provide a simple and effective method for manipulating the topological properties of materials, opening new avenues for the development of advanced electronic devices based on TSMs. The unique transport properties of TSMs, such as large magnetoresistance, chiral anomalies, and the anomalous Hall effect, stem from the relativistic fermions at the Dirac/Weyl points. DSMs, the 3D counterpart of graphene, exhibit linear energy-momentum relations in all three directions. The degeneracy of a Dirac node is protected by both time reversal and inversion symmetry. The Bi0.96Sb0.04 alloy is chosen due to its known DSM properties resulting from band overlap at the L points in the Brillouin zone, achieved at an Sb concentration of 0.04. Ion implantation is a suitable technique for this study as it allows for room-temperature doping, enabling independent investigation of doping and annealing effects, and permits selective doping of devices and structures. The study compares the magnetoresistance response of Bi0.96Sb0.04 implanted with Au and Mn ions to investigate the possibility of a permanent Dirac-to-Weyl transition.

Extensive research exists on topological semimetals (TSMs), focusing on different phases like DSMs, WSMs, nodal-line semimetals, and triple-point semimetals. Several studies have demonstrated novel transport properties in TSMs, attributed to relativistic fermions near Dirac/Weyl nodes. The 3D Dirac fermions in DSMs are analogous to 2D Dirac fermions in graphene, possessing linear energy-momentum relations in all three directions. The protection of Dirac nodes requires both time-reversal and inversion symmetry. The Bi1-xSbx system, with its rhombohedral structure, exhibits tunable electronic properties depending on Sb concentration. At x = 0.04, a DSM phase is formed due to band overlap at the L points. Prior research has explored Dirac-to-Weyl transitions, but these have been primarily reversible, induced by low temperatures or high magnetic fields. The Bi0.96Sb0.04 system has been studied using Raman spectroscopy and magnetotransport measurements, providing insights into its electronic properties. Previous work using ion implantation has demonstrated its utility in altering material properties; however, its application to inducing a permanent topological phase transition has not been extensively explored. Studies on Raman scattering in materials have shown its effectiveness in detecting inversion symmetry breaking, providing a valuable tool for identifying topological phase transitions. The chiral anomaly in Weyl fermions is usually associated with the negative longitudinal magnetoresistance (NMR), a phenomenon observed in various Weyl semimetals.

High-purity Bi0.96Sb0.04 single crystals were grown using a high-temperature furnace, followed by annealing. The crystal structure was confirmed using X-ray diffraction. Crystals were cleaved along the (001) plane and implanted with 1 MeV Au+ ions at various fluences [(0.8, 3.2, 8.0, 10.4, and 12.8) × 10¹⁶ Au cm⁻²] or with 300 keV Mn+ ions [(4.0 and 8.0) × 10¹⁶ Mn cm⁻²] at room temperature. The peak Au or Mn concentrations were calculated using the TriDyn code. Post-implantation, samples were annealed at 230 °C for 1 h under Ar flow. Raman spectroscopy, using a 532 nm excitation wavelength, characterized the optical properties. Magnetotransport measurements were performed in a cryogen-free magnet system, applying magnetic fields (B) from -9 T to +9 T parallel and perpendicular to the applied current (I), using the six-probe method. The Shubnikov-de Haas (SdH) oscillations were analyzed by Fast Fourier Transform (FFT) to determine quantum oscillation parameters. The Lifshitz-Kosevich (LK) formula was employed to fit the FFT amplitude data. The parameters obtained included Dingle temperature, quantum scattering time, carrier density, quantum mobility, cross-sectional area of Fermi pockets, cyclotron mass, Fermi velocity, Fermi wave vector, mean free path, and Fermi level. The Berry phase was also extracted from the phase shift in the Landau fan diagram. XRD analysis employed a glancing incidence technique to avoid issues arising from the difference in penetration depth of the X-rays compared to implantation depth. The temperature dependent longitudinal magnetoresistance (LMR) was studied to confirm the NMR behavior.

Raman spectroscopy revealed a significant change in the spectral features above a critical Au fluence (Φc) of 3.2 × 10¹⁶ Au cm⁻². A new Raman peak, U(Bi), emerged, and the A1g(Sb) peak, absent in the pristine sample, appeared, indicating inversion symmetry breaking. The shifts in the Raman peaks exhibited a fluence dependence. Magnetotransport measurements showed a clear negative longitudinal magnetoresistance (NMR) above Φc, while samples implanted with Mn ions showed only positive magnetoresistance, independent of the field orientation and fluence. The NMR, observed only in the B//E orientation, is a characteristic feature of Weyl semimetals and confirms the existence of a chiral anomaly in Weyl fermions. Shubnikov–de Haas (SdH) oscillations analysis using FFT revealed significant changes in the oscillation frequencies above Φc. Specifically, the secondary frequency (Fβ) increased abruptly at Φc, while the primary frequency (Fα) remained relatively unchanged. The analysis of SdH oscillations based on the LK formula showed that almost all the parameters, including the cross-sectional area of the Fermi pockets, for the β Fermi pocket exhibited abrupt changes at Φc, indicating a topological phase transition within the β Fermi pocket. The small cross-sectional area of the β Fermi pocket (~0.09 nm²) suggests linear band dispersion, typical of Weyl semimetals. The absence of similar changes in the α Fermi pocket suggests the phase transition is specific to the β pocket. The extracted Berry phase from the SdH oscillations analysis further supports the proposed topological phase transition.

The observed changes in Raman spectra, the appearance of NMR, and the modification of SdH oscillation parameters strongly suggest a permanent Dirac- to Weyl-semimetal phase transition induced by Au ion implantation. The critical fluence of 3.2 × 10¹⁶ Au cm⁻² marks the onset of this transition. The absence of a similar effect with Mn implantation points to the crucial role of nonmagnetic elements in inducing this transition, suggesting that the inversion symmetry breaking is primarily driven by the structural disorder introduced by the non-magnetic Au ions, rather than magnetic exchange interactions. The NMR confirms the presence of a chiral anomaly, a hallmark of Weyl semimetals. The analysis of the Shubnikov-de Haas oscillations provides further evidence, with the changes in the β Fermi pocket parameters supporting the transition to a WSM. These findings establish a simple and effective technique to induce a permanent phase transition in a single TSM material.

This work demonstrates the first possible permanent Dirac- to Weyl-semimetal phase transition achieved through ion implantation using nonmagnetic Au ions in a Bi0.96Sb0.04 DSM. The transition is evidenced by distinct changes in Raman spectra, the appearance of negative longitudinal magnetoresistance (NMR), and modifications in Shubnikov-de Haas oscillation parameters. The results highlight the potential of ion implantation as a tool for tailoring topological properties in materials. Future research could explore other nonmagnetic elements and their effect on the transition, investigate the role of implantation parameters, and explore the applications of this technique in creating novel devices based on Weyl semimetals.

The study focuses on a specific material (Bi0.96Sb0.04) and implantation parameters. The generalizability of the findings to other DSMs requires further investigation. The exact mechanism underlying the transition, particularly the specific role of the implanted Au atoms in breaking the inversion symmetry, warrants further detailed investigation. While the NMR is a strong indicator of a Weyl semimetal, direct observation of Weyl points and Fermi arcs through techniques such as angle-resolved photoemission spectroscopy (ARPES) would further solidify the findings.