Introduction

Studies on topological semimetals (TSMs), highly attractive as a novel class of topological matter, are at the frontiers of materials science and technology, with many theoretical and experimental breakthroughs being made on several TSM phases, such as Dirac semimetals (DSMs), Weyl semimetals (WSMs), nodal-line semimetals, and triple-point semimetals1,2. A broad range of novel transport properties, such as extremely large magnetoresistances, chiral anomalies, and the intrinsic anomalous Hall effect, have been experimentally demonstrated and attributed to relativistic fermions that represent low-energy excitations around the Dirac/Weyl nodal points or nodal line. DSM fermions are the three-dimensional (3D) counterpart of the two-dimensional (2D) Dirac fermions in graphene3. Unlike the Dirac cone in graphene, the dispersion surfaces in DSMs have linear energy-momentum relations along all three directions4,5. A crystal needs both time reversal symmetry and inversion symmetry to protect the degeneracy of a Dirac node from splitting into two Weyl nodes6,7. At the critical point during the transition from a topological insulator to a normal insulator, the conduction and valence band contact points are 3D Dirac or Weyl points, depending on whether inversion symmetry exists or not, respectively. Berry curvature, a quantity that can be used to characterize the topological entanglement between the conduction and valence bands, becomes singular at Weyl points that act as monopoles in momentum space with a fixed chirality8,9,10.

The crystal structure of pure Bi, pure Sb, and their crystalline alloys (Bi1−xSbx) that can be formed over a wide range of x is rhombohedral, and all have R\(\overline 3\)m symmetry with two atoms in each unit cell11. In Bi, pockets of electrons are located at the L points of the Brillouin zone (BZ), while those of holes are located at the T points. The valence band (VB) and conduction band (CB) at L originate from antisymmetric (La) and symmetric (Ls) p-type orbitals, respectively12. In Sb, pockets of electrons are also located at the L points of the BZ, while those of holes are located at the H points. The substitution of Sb atoms for Bi atoms in the Bi lattice has a significant effect on the band structure of Bi, including the overlap between the L and T bands, the magnitude of the direct band gap Eg, and the maximum energy of the H bands. For Sb concentrations (x) between 0 ≤ x < 0.04, the overlap and band gap decrease. At x = 0.04, the CB and VB edges exchange their symmetries at the L points, thereby closing the L-point energy gap between La and Ls, resulting in the formation of a DSM13,14.

For materials research, ion implantation offers two main advantages: (1) it is a room temperature (RT) process, enabling do** and annealing processes to be studied independently; and (2) it enables selective do** of devices and structures with different species. Here, we compare the magnetoresistance (MR) response of Bi0.96Sb0.04 DSMs ion-implanted with Au and Mn ions and demonstrate a possible permanent Dirac- to Weyl-semimetal phase transition in samples implanted with Au. No such behavior is observed in samples implanted with Mn, suggesting that only nonmagnetic elements are effective for the transition.

Materials and methods

Bi0.96Sb0.04 bulk single crystals with 99.99% purity were grown in a high-temperature furnace using a method previously reported12. Stoichiometric mixtures of high-purity Bi and Sb elements were sealed in a vacuum quartz tube to avoid oxidation. The mixtures were heated to 650 °C and cooled to 270 °C over a period of five days. Then, they were annealed for seven days at 270 °C. X-ray diffraction measurements demonstrated that the samples were single phase and had a rhombohedral crystal structure. Bi0.96Sb0.04 crystals cleaved along the (001) plane from the bulk crystals were implanted with 1 MeV Au+ ions to nominal fluences of (0.8, 3.2, 8.0, 10.4, and 12.8) × 1016 Au cm−2 or with 300 keV Mn+ ions to nominal fluences of (4.0 and 8.0) × 1016 Mn cm−2 at RT. The peak Au or Mn concentrations for these implantations were calculated from dynamic range simulations using the TriDyn code15 to be in the range of 1.7–5.6 at% (0.48–1.6 × 1021 Au cm−3) or 5.8–10.3 at% (1.6–2.9 × 1021 Mn cm−3), respectively. The implanted crystals were subsequently annealed at 230 °C for 1 h in a furnace under Ar flow to remove the implantation-induced damage.

Raman spectroscopy was used to characterize the optical properties of the Bi0.96Sb0.04 crystals cleaved along the (001) plane from the bulk crystals in a confocal microscope system (HEDA, NOST) with an excitation wavelength of 532 nm at RT. The laser was coupled to a ×100 objective lens (numerical aperture = 0.90) and focused to a submicrometer spot on the sample surface. The Raman signal collected with the same objective was dispersed through a monochromator with a diffraction grating of 2400 grooves/mm and detected by a charge-coupled device (Andor Technology). The Raman spectra were measured from the shiny silver-colored surface of the crystals for various ϕG in the frequency range from 50 to 180 cm−1. The penetration depth of the X-rays is much deeper than the implantation depth, so a technique of glancing incidence was employed for the XRD analysis. Magnetotransport experiments were carried out on the Bi0.96Sb0.04 crystals in a cryogen-free magnet system under B ranging from −9 T to +9 T along the directions parallel and perpendicular (B // trigonal axis for transverse MR (TMR) and B // binary axis for longitudinal MR (LMR), respectively) to the applied current I (// binary axis) using the six-probe method. Homogenous contact configurations were employed to suppress the current jetting effect of the MR, as described in our previous report16. All electrical contacts were prepared at RT with silver paste. The TMR and Hall resistance were simultaneously measured when B was perpendicular to I. The electrical resistivity of the crystals under no B field was also measured as a function of temperature from 1.7 to 300 K.

Results and discussion

Bi0.96Sb0.04 crystals cleaved along the (001) plane from bulk crystals with 99.99% purity were implanted with 1 MeV Au+ ions to nominal fluences (ϕG) of (0.8, 3.2, 8.0, 10.4, and 12.8) × 1016 Au cm−2 at RT. The Au range distributions were calculated using the TriDyn code15, which includes sputtering effects. This showed that the peak Au concentration saturated at ~5.6 at% for ion fluences above ~6 × 1016 Au cm−2. (Supplementary Fig. S1). X-ray diffraction analysis of the implanted crystals was performed for various ϕG in the angular range of 2θmin = 20° and 2θmax = 80° (Supplementary Fig. S2). All the samples exhibited sharp (00l) reflections that were well indexed along the c-axis, indicating a single-crystalline, c-axis-oriented rhombohedral structure of the space group R\(\overline 3\)m11,12,13. An additional peak appeared at 2θ ≈ 49.5° along with the characteristic peaks of the (00l) plane for all the samples and was identified as the (202) peak, originating from the misaligned plane of Bi0.96Sb0.0417. The XRD patterns did not show any particular dependence on ϕG, even though a technique of glancing incidence was employed considering that the penetration depth of the X-rays was much deeper than the implanted layer. This is possible because the XRD patterns do not reflect the (111) plane (L point of the BZ) directly related to the inversion symmetry of Bi0.96Sb0.04 DSMs12,18.

Figure 1a shows the ϕG-dependent Raman spectrum of Bi0.96Sb0.04. At ϕG = 0 (without implantation), two peaks are clearly observed at 72.3 and 97.5 cm−1, referred to as Eg(Bi) and A1g(Bi), respectively, while one other peak is weakly visible at 119 cm−1, referred to as Eg(Sb)17,19,20. It is well known that the Bi1−xSbx system commonly exhibits four major Raman peaks, two of which are observed at ~72–75 and ~97–100 cm−1 and correspond to the Bi–Bi vibrations of the Eg(Bi) and A1g(Bi) modes, respectively, typical of single crystals with rhombohedral R\(\overline 3\)m symmetry17,21, and the other two peaks are observed at ~118–120 and ~138–141 cm−1 and correspond to the Sb–Sb vibrations of the Eg(Sb) and A1g(Sb) modes17,19,20. The A1g mode is singly degenerate, while the Eg mode is doubly degenerate. In our Bi0.96Sb0.04 system, the A1g(Sb) mode is absent before implantation, possibly due to local deviation from the stoichiometric condition, as the A1g(Sb) mode is very sensitive to the atomic compositions of the crystal19,20.

Fig. 1: Effect of implantation on Raman spectra.
figure 1

a Raman spectra of Bi0.96Sb0.04 for various implant fluences. The Eg(Bi)/A1g(Bi) and Eg(Sb)/A1g(Sb) peaks indicate Bi–Bi and Sb-Sb vibration modes, respectively, and the A1g modes are singly degenerate, while the Eg modes are doubly degenerate. The additional U(Bi) peak is an unknown new mode, different from the Eg and A1g modes expected from group theory for the rhombohedral structure. b Shifts of the Raman peaks as functions of implant fluence.

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Figure 1a also shows little change from the three Raman peaks of the pristine (unimplanted) Bi0.96Sb0.04 crystal for implant fluences up to ϕG = 0.8 × 1016 Au cm−2, but a drastic change is observed for fluences above ϕG = 3.2 × 1016 Au cm−2. In particular, a new peak appears at 85.7 cm−1 between the Eg(Bi) and A1g(Bi) modes, named U(Bi). It is not clear whether the U(Bi) mode is split from the Eg(Bi) mode or the A1g(Bi) mode. Moreover, the A1g(Sb) peak, absent in the pristine Bi0.96Sb0.04 crystal, appears at 149.7 cm−1, which is a higher wavenumber than that conventionally reported (~138–141 cm−1), indicating that the A1g(Sb) peak is blueshifted by implantation to ϕG = 3.2 × 1016 Au cm−2. The overall shape of the Raman spectrum for ϕG = 3.2 × 1016 Au cm−2 is almost unchanged as the fluence is increased to 12.8 × 1016 Au cm−2 except for a gradual increase in the peak wavenumber. Some of the Raman spectra were resolved into the Eg(Bi), A1g(Bi), and U(Bi) bands to find their peak positions more accurately based on the fitting program (Supplementary Fig. S3). Figure 1b summarizes the shifts of the Raman modes as functions of ϕG. As ϕG increases from 0 to 12.8 × 1016 Au cm−2, the four Eg(Bi), U(Bi), A1g(Bi), and A1g(Sb) modes tend to be gradually blueshifted.

All the Raman peaks of MoTe2 are known to stem from two kinds of vibrations: (1) those along the zigzag Mo atomic chain (z-modes) and (2) those in the mirror plane (m-modes) perpendicular to the zigzag chain22. Some Raman inactive modes in the centrosymmetric monoclinic phase appear in the cooling-driven transition to the orthorhombic phase22,23, resulting from inversion-symmetry breaking, which is evidence for the formation of a type II WSM. On the other hand, the appearance of a Raman doublet at a higher composition of W in monoclinic Mo1−xWxTe2 alloys was attributed to the breakdown of inversion symmetry, which originates from the random substitution of Mo atoms with W atoms24. These results suggest that whether inversion symmetry in a crystalline structure is broken can be determined by analyzing the Raman scattering behaviors.

Very recently, inversion symmetry breaking was also demonstrated by first-principle calculations and Raman scattering of the CdTiO3 ilmenite phase belonging to the rhombohedral R\(\overline 3\)m group21. Additional Raman peaks, different from the Eg and Ag modes expected from group theory for the ilmenite rhombohedral structure, appeared in both low-temperature and high-pressure spectra, with the Raman wavenumbers being blueshifted at higher pressures. These results were very similar to the ϕG-dependent Raman behavior observed here for the Bi0.96Sb0.04 crystal and were successfully accounted for by assuming the local loss of inversion symmetry operation, which reduces the overall space group from R\(\overline 3\) to R3. Such arguments can be extended to the Bi0.96Sb0.04 crystal with the same rhombohedral R\(\overline 3\) symmetry, suggesting that inversion symmetry breaking in the crystal occurred for implant fluences ϕG ≥ 3.2 × 1016 Au.cm−2, resulting in the transition of the DSM Bi0.96Sb0.04 to a Weyl semimetal.

MR measurements under parallel (B // E) (i.e., B parallel to the binary axis for LMR and perpendicular (B ⊥ E) (i.e., B parallel to the trigonal axis for TMR) orientations in TSMs always show different behavior, as orbital quantum interference effects are sensitive to the field orientation25,26,27. Parallel (B // E) measurements for the present samples are shown in Fig. 2a, with perpendicular (B ⊥ E) measurements included in Supplementary Fig. S4a. It has also been observed that the LMR in some TSMs shows a sharp increase as the B field is initially increased from zero, before decreasing at intermediate fields and then further increasing at higher fields. This phenomenon is referred to as negative LMR (NMR)27,28,29,30. Significantly, NMR is only observed in the B // E orientation and not in the B ⊥ E orientation30,31, consistent with current observations (Supplementary Fig. S4b). Figure 2b shows the T-dependent LMR of the Bi0.96Sb0.04 crystal at ϕG = 3.2 × 1016 Au cm−2, measured from −9 to +9 T. The amplitude of the NMR is observed at T = 1.7 K and increases with increasing T up to 100 K, but above 100 K, it decreases. Similar temperature-dependent behavior has been reported in WSMs by several groups. In Cd3As2 nanowires28, the NMR increased as T increased from 1.5 to 60 K but decreased as it increased further from 80 to 300 K. The NMR found in Cd3As2 nanoplates32 and NbP31 increased monotonically with increasing temperature up to 150 and 300 K, respectively. In contrast, the NMR in TaAs decreased monotonically with increasing T27,29.

Fig. 2: Longitudinal magnetoresistance.
figure 2

a Schematics for the crystalline structure of Bi0.96Sb0.04 and the longitudinal orientation of B parallel to I (// binary axis). b Temperature-dependent LMR at a fluence of 3.2 × 1016 Au cm−2. NMR is observed at T = 1.7 K and increases with increasing T up to 100 K, but above 100 K, it decreases. c LMR at 1.7 K for various implant fluences. Positive LMR is observed in the crystal without ion implantation, but NMR behavior becomes apparent for samples implanted to a fluence of ϕG = 3.2 × 1016 Au cm−2 and reaches a maximum for a fluence of ϕG = 8.0 × 1016 Au cm−2 before decreasing as the fluence is increased further to 12.8 × 1016 Au cm−2.

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Figure 2c shows the variation in the LMR at 1.7 K for various implant fluences. Positive LMR is observed in the crystal with no ion implantation, but NMR behavior becomes apparent for samples implanted to a fluence of ϕG = 3.2 × 1016 Au cm−2 and reaches a maximum for a fluence of ϕG = 8.0 × 1016 Au cm−2 before decreasing as the fluence is increased further to 12.8 × 1016 Au cm−2. In contrast, only positive MR is observed from Mn-implanted Bi0.96Sb0.04 crystals, irrespective of the relative orientation of the B and E fields and ϕG (Supplementary Fig. S5). Implantation with Mn ions is expected to break both time reversal and inversion symmetries because Mn is a magnetic element, implying that no phase transition from DSM to WSM occurred and that the crystal was potentially changed into a trivial metallic state by Mn implantation. If no magnetic exchange interaction exists, conventional metals should exhibit positive MR33,34, and the appearance of a negative MR in normal metals is limited to special cases35,36. An important aspect of NMR is that it confirms the existence of a chiral anomaly in Weyl fermions, as shown in Cd3As228,32, Bi0.97Sb0.0337, TaAs27,29, ZrTe538, Na3BiS8) nearly the same as those estimated by direct fitting (Supplementary Fig. S7b).

WSMs possess nontrivial topological surface states that form unique Fermi arcs1,2,46 and unusual Fermi surfaces consisting of unclosed curves that start and end at Weyl points split from a Dirac point. This explains why AF should increase in the Dirac- to Weyl-semimetal phase transition at ϕG ≥ 3.2 × 1016 Au cm−2, as shown for the β Fermi pocket in Fig. 3d. In contrast, no meaningful variation in AF is visible for the α Fermi pocket, indicating that the phase transition occurs only in the β Fermi pocket. The AF of the β Fermi pocket (∼0.09 nm−2 in Fig. 3d) is extremely small, indicating linear band dispersion, as previously reported47,48. Combining this fact with the inversion symmetry breaking further explains why Bi0.96Sb0.04 implanted to ϕG ≥ 3.2 × 1016 Au cm−2 should show NMR. It is well known that a π ϕB is expected for DSMs such as the pristine Bi0.96Sb0.04 crystal because their electronic band is topologically nontrivial8,9,40,43. As shown in Fig. 3h, the ϕ values for the α and β Fermi pockets show somewhat different dependences on ϕG compared to the other parameters of the quantum oscillations, as shown above. They show gradually decreasing behavior with increasing fluence from 0 to 12.8 × 1016 Au cm−2, with the decreasing rate being much smaller for the α pocket. The ϕ values for the β Fermi pocket are within ±∼0.2. This near-zero ϕ, with zero being the widely accepted value for 3D DSMs/WSMs8,49,50, possibly indicates a nontrivial π ϕB. An increase or decrease in the other parameters for the β Fermi pocket at ϕG ≥ 3.2 × 1016 Au cm−2 can be understood by simple physical considerations and the following related equations40,41,42,43: \(F = (\hbar /2\pi e)A_F\), \(T_D = \hbar /2\pi k_B\tau _Q\), \(k_F = \sqrt {2eF/\hbar }\), \(E_F = (\hbar k_F)^2/m^ \ast\), \(l_Q = v_F \cdot \tau _Q\), \(v_F = \hbar k_F/m^ \ast\), and \(\mu _Q = e\tau _Q/m^ \ast\). These results suggest that the α Fermi pocket remains a Dirac semimetal phase even after implantation.

Figure 4a shows the ϕG-dependent resistivity as a function of T under no B field. All the samples show an increase in resistivity with temperature, irrespective of ϕG, typical of TSMs. Figure 4b–d shows ϕG-dependent resistivity, carrier density, and mobility for the Fβ and Fα Fermi pockets obtained by Hall-effect measurements. Abrupt changes at ϕG = 3.2 × 1016 Au cm−2, as shown in the ϕG-dependent behaviors of the Raman scattering and quantum oscillations, were not observed in the Hall mobility or carrier density, but both show ϕG-dependent behavior for both Fermi pockets, consistent with what is expected from the fundamental characteristics of materials with larger impurity concentrations.

Fig. 4: Electrical and Hall-effect properties.
figure 4

a Electrical resistivities as functions of temperature under no B field for various implant fluences. b Hall resistivities as functions of B for various implant fluences. c Hall carrier densities and d mobilities as functions of implant fluence for the α and β Fermi pockets.

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Conclusion

Here, we demonstrated a possible permanent Dirac- to Weyl-semimetal phase transition in a single DSM resulting from inversion-symmetry breaking induced by implantation with nonmagnetic Au ions. This phenomenon is evidenced by Raman analysis and the quantum-oscillation parameters extracted from the LMR, which show abrupt changes at the critical fluence, and the negative LMR, indicating the existence of a chiral anomaly in Weyl fermions. The approach of implantation using nonmagnetic elements for phase transitions may be a suitable method for simple modifications of TSMs in the vertical direction as well as in the lateral direction and useful for diverse science studies and device applications.