A comprehensive ARPES study on the type-II Dirac semimetal candidate Ir_1−xPt_xTe₂ Open Access

Transition metal dichalcogenides (TMDs) have attracted much attention due to their layered two-dimensional structure with strong in-plane bonding and weak out-of-plane van der Waals interactions. The layered structure of TMDs results in interesting physical phenomena, such as charge density wave (CDW) in TaSe₂,^1–3 superconductivity in NdSe₂,^4,5 and topological Dirac/Weyl semimetal (TDS) phases in PtTe(Se)₂ and MoTe₂.^6–8 Recently, the class of TMDs with the 1T structure has been predicted to display a systematically controlled range of band structures including type-I and Lorentz-violating type-II 3D bulk Dirac states, as well as ladders of topological surface states.^7–11 The topology of these band structures is determined by the p-orbital manifold of the chalcogenide, rather than the transition metal. This observation motivates a search for superconductivity within this class that may allow tuning the band structure to achieve topological superconductivity, which has been predicted to host exotic Majorana bound states that obey non-Abelian statistics and can be exploited in topological quantum computing.¹² 

The TMD IrTe₂ is a member of this class, which also hosts superconductivity. However, it has a competing CDW ground state that reduces the 1T structure to a monoclinic structure at low temperature, which competes with superconductivity.¹³ The CDW ground state is associated with a type-II van Hove singularity (vHs) (namely, a vHs associated at momenta away from time-reversal invariant momenta) near the Fermi level (E_F) at room temperature, which drives a reconstruction of the electronic structure below the CDW phase transition.¹⁴ To fully suppress the CDW transition and stabilize the 1T structure, IrTe₂ can be doped with Pt, where a Dirac dispersion has been found near E_F without affecting the superconducting properties.^15–17 The coexistence of the topological band structure near E_F and superconductivity in Ir_1−xPt_xTe₂ suggests possible intrinsic topological superconductivity. Although the nature of the superconductivity in these TDSs and its link to a topological band structure is still unclear, they remain a promising class of materials to realize topological superconductivity. Our goal here is to characterize the 3D band structure with high resolution to identify the properties of the band structure that can induce superconductivity and look for connections between superconductivity and the topological band structure.

Here, we investigate the evolution of the 3D electronic band structures for a range of Pt doping, Ir_1−xPt_xTe₂ (x = 0.1, 0.2, 0.3, and 0.4), using ARPES. The doping levels we study are above the CDW region in the phase diagram, and the samples maintain the 1T structure at low temperature. Strong 3D α (Te p_z), β (Te p_x + p_y), and γ (Te p_z) Fermi surface (FS) sheets have been observed, where the touching point of the β and γ bands defines a type-II Dirac point, namely, one with a tilted Dirac cone in momentum space. Doping with Pt successfully tunes the Fermi level (E_F) to be at the Dirac point for x = 0.1 meV and 200 meV below E_F for x = 0.4. We also find that the β band dispersion preserves a saddle point (SP) below E_F in the superconducting samples, while it disappears in the more highly doped samples. This indicates that the superconducting samples are very close to a type-II van Hove singularity, which theoretically may lead to spin triplet pairing and suggests the possible existence of topological superconductivity in Ir_1−xPt_xTe₂.^18,19

High quality Ir_1−xPt_xTe₂ single crystals are synthesized by the flux method.¹⁶ (Sample characterization is shown in Fig. S1.) We study samples with different doping levels varying from x = 0.1 to x = 0.4. For x = 0.1, the superconducting transition temperature is ∼1.7 K, x = 0.2 (∼0.65 K), x = 0.3 (∼0.15 K), and no superconductivity is observed for x = 0.4 down to 400 mK. ARPES measurements are performed at the beamline 21-ID-1 of the National Synchrotron Light Source II (NSLS II) equipped with a Scienta DA30 electron analyzer. The photon energies used for mapping out the 3D electronic structures range from 60 eV to 120 eV, with an overall energy resolution better than 25 meV for all photon energies. The samples are cleaved in situ to achieve a fresh surface for the measurement in a vacuum chamber at a pressure below 2 × 10⁻¹¹ Torr. All measurements are performed at 11 K.

To determine the 3D electronic structure of Ir_1−xPt_xTe₂, we conduct ARPES measurements with various photon energies. This approach enables us to reconstruct the 3D electronic structures across the ΓMK plane (120 eV), AHL plane (96 eV), and TDS plane (90 eV). We describe how k_z and the work function of the spectrometer are determined in the supplementary material. Figure 1 shows the 2D Fermi surfaces (FS’s) of Ir_0.9Pt_0.1Te₂ measured at different photon energies that cover from the BZ center (ΓMK plane) to the BZ boundary (ALH plane), as illustrated in Fig. 1(a). For simplicity in terminology, we use $Γ¯$⁠, $M¯$ for the high symmetry points in other k_z planes. The 2D FS’s change dramatically for different k_z, indicating the 3D band structure nature of Ir_1−xPt_xTe₂. The strong 3D nature in such a layered 2D material originates from the strong Te–Te interaction between different layers, as reported previously in Ref. 20. There are mainly two bands α and β contributing to the FS’s, which originate from the Te p_z orbital and p_x + p_y orbital, respectively. From the layout of the FS’s in Figs. 1(c)–1(h), the α and β bands are well resolved and quite separated from each other near the BZ center [Figs. 1(f)–1(h)], then start touching each other, and finally change dramatically when approaching the BZ boundary [Figs. 1(c)–1(f)]. Near the BZ boundary when the two FS sheets are close to each other, one can also see substantial spectral weight beside the two FS’s, making the bands less well resolved than when they are near the BZ center; this is due to the strong 3D behavior of the bands and the limited k_z resolution of the measurements, as reported in other material systems.²¹ We extract the shape of the α and β FS’s from our experimental data and plot them in Figs. 1(c-ii)–1(h-ii). Our results are consistent with a previous calculation of Ir_0.85Pt_0.05Te₂.²⁰ A threefold symmetry of the band structure is clearly visible for all doping levels, especially for the k_z plane closest to the BZ boundary (see the supplementary material, Figs. S3 and S4).

To obtain a comprehensive picture of the 3D electronic structure of Ir_1−xPt_xTe₂, we plot the band dispersions for all the samples on the high symmetry planes, ΓMK and AHL (Figs. 2 and 3). As we show, these planes are important to establish the 3D character and detect changes in dispersion with doping. To better describe the threefold symmetry characteristic of the 1T space group, we use two sets of high symmetry points M₁K₁, M₂K₂ in the ΓMK plane, H₁L₁, H₂L₂ in the AHL plane, and T₁S₁, T₂S₂ in the TDS plane. The electronic structure along the ΓMK plane is presented in Fig. 2, where the measured plane in momentum space is highlighted in the 3D BZ in Fig. 2(a–i). On this high symmetry plane, α and β are well separated in momentum space. Data for x = 0.1 and x = 0.3 are presented in Fig. 2 (data of all the samples are shown in Fig. S3). The 3D volume plot in Fig. 2(a–ii) clearly shows the sharp FS and the band dispersion of the x = 0.1 sample. One can see a flower-shaped FS α and a hexagonal-shaped FS β, as indicated in Fig. 2(b). The dispersion of the α and β bands along K₂ΓK₁ for x = 0.1 and x = 0.3 is plotted in Figs. 2(c) and 2(d), respectively, showing that the two FS’s are both hole-like. Along the ΓK₂ direction, the α band crosses E_F at 0.77 Å⁻¹ for x = 0.1 and at 0.71 Å⁻¹ for x = 0.3, while the β band crosses E_F at 0.25 Å⁻¹ in x = 0.1 and at 0.24 Å⁻¹ in x = 0.3 [top inset in Figs. 2(c) and 2(d)]. The evolution of the α and β bands along the ΓK₂ direction can be seen in the momentum distribution curves (MDCs) plotted in Fig. 2(e). The MDCs at the FS along the M₂ΓM₁ direction are presented in Figs. 2(f)–2(h). The α band crosses E_F at 0.47 Å⁻¹ for x = 0.1 and 0.53 Å⁻¹ for x = 0.3, while the β band crosses E_F at 0.27 Å⁻¹ for x = 0.1 and 0.25 Å⁻¹ for x = 0.3 along the ΓM₂ direction. Comparing the spectra along both ΓK₂ and ΓM₂ directions for different x, doping does not result in a simple rigid band shift. In addition, the α and β pockets shrink upon doping up to x = 0.3 and then expand a little bit for x = 0.4. This might arise from a change in lattice parameters with doping. While Pt occupies the Ir sites, there is a change in the lattice parameter from 3.95 Å (x = 0.1) to 3.99 Å (x = 0.4), which is a ∼1% change.¹³ In addition to the electron doping effect, the bandwidth may also change and result in such a non-rigid band shift.

The band structures at the BZ boundary [AHL plane as indicated in Fig. 3(a)] of x = 0.1 and x = 0.3 samples are plotted in Fig. 3. The topology of the FS on the AHL plane is very different from the one on the ΓMK plane, indicating a strong 3D band structure. Figure 3(a–ii) shows the 3D volume plot of the band structure for x = 0.1, where the threefold symmetry is clearly visible. The outer α FS turns into a star-shape [Fig. 3(b)], while the β FS evolves into several broken pieces. The band dispersions of the α band along the H₂AH₁ direction show a sharp Fermi crossing at 0.52 Å⁻¹, while the β band bends back at around 0.37 Å⁻¹, which contributes to small hole pockets for x = 0.1 in Fig. 3(c).The β band also contributes to a saddle point along the L₂AL₁ direction, which becomes a van Hove singularity in the parent compound IrTe₂, as will be discussed later.¹⁴ For x = 0.3, the α band crosses E_F at 0.5 Å⁻¹ along the AH₂ direction in Fig. 3(d). The α band dispersion along the L₂AL₁ direction is broad close to the BZ boundary L, but we still observe a sharp crossing at ∼0.4 Å⁻¹ for x = 0.1, as plotted in Fig. 3(f). This crossing is due to the effect of the highly 3D nature of the α band close to the A point and is a consequence of strong hopping across p_z orbitals perpendicular to the TMD layers, as reported before. A weak Fermi crossing around 0.25 Å⁻¹ (named β′) in Fig. 3(d) and 0.75 Å⁻¹ (named α′) have also been resolved, which originate from the projection of the β and α bands from other k_z planes due to the limited k_z resolution. The β band bends back and sits slightly below E_F at the A point, contributing to the lower branch of the type-II Dirac crossing bands, which is discussed below. Figure 3(g) presents the band structure of x = 0.3 along the L₂AL₁ direction. The dispersions of all the samples along both directions are listed in Fig. S4, and their MDCs at E_F are presented in Figs. 3(e) and 3(h) to show the evolution of each band upon doping. The α band along AH₂ shrinks in k_∥ and the β band sinks down to E_F upon doping, which is qualitatively consistent with electron doping into the system. A tiny electron pocket γ starts to appear at x = 0.3, as shown in Figs. 3(d) and 3(g), it is non-degenerate with the β band at the A point. Since the type-II Dirac crossing along the k_z direction is defined by the degenerate point of the β and γ bands, the Dirac point will be closer to the A point than to the Γ point.

To search for the Dirac point position, we scan k_z with different photon energies and locate the Dirac point at 96 eV photon energy, which is close to the A point. The band structures in the TDS plane for x = 0.1 and x = 0.3 are plotted in Fig. 4. From the 3D volume plot in Fig. 4(a) and the FS plots in Fig. 4(b), a non-zero intensity is visible at the BZ center. In the 2D plots of the band dispersions in Figs. 4(c)–4(g), the finite density at the D point is from the lower cone in the x = 0.1 sample and the upper cone in the x = 0.3 sample, respectively. The β′ band along the T₂DT₁ direction is from the projections of the β band in other k_z planes. From the dispersions of the β and γ bands, one sees that the β band for both x = 0.1 and x = 0.3 goes up compared to their dispersions in the AHL plane, while in the x = 0.3 sample, the γ band sinks down to touch the β band at 120 meV below E_F. The evolution of the β and γ bands is consistent with type II Dirac fermion behavior. To see the Dirac dispersion more clearly, we measure the band dispersion at lower photon energy (50 eV) along the DAL plane with enhanced energy resolution. The band dispersions across the Dirac point in the TDS plane for all samples are plotted in Fig. 5, where their in-plane dispersion directions, taking into consideration the experimental geometry, are indicated with the red arrows on top of each figure. The shallow Dirac band dispersions add difficulty to the direct imaging of its dispersion along the k_z direction due to the limited k_z resolution. However, one sees that the top of the β band at the D point sinks upon Pt doping, and at the same time, the bottom of the γ band at the D point starts to appear at x = 0.2. Such evolution of β and γ bands gives a type II bulk Dirac point (BDP) around 40 meV, 120 meV, and 200 meV below the E_F for x = 0.2, 0.3, and 0.4 samples [Fig. 5(e)]. This result demonstrates that the type-II Dirac points can be successfully tuned by the Pt doping effect in IrTe₂.

The superconducting behavior of Ir_1−xPt_xTe₂ shows a dome-like feature in the superconducting phase diagram: with increased doping, the structural and CDW transitions are suppressed, giving rise to superconductivity.¹³ This phase diagram mimics those of cuprate and iron pnictide superconductors, suggesting the possibility of unconventional superconductivity in this system. This behavior is in contrast to that in a related 1T superconductor, PdTe₂, which is thought to be a conventional BCS superconductor.^22–24 Although the thermal conductivity results demonstrate a nodeless gap structure in Ir_1−xPt_xTe₂,²⁵ suggesting conventional s-wave superconductivity, the nature of the superconducting pairing symmetry in this system remains inconclusive. A second notable feature of Ir_1−xPt_xTe₂ is that the type-II Dirac points are very close to the Fermi level for the x = 0.1, 0.2 samples, suggesting that intrinsic topological superconductivity might be induced due to the finite density of states around the Dirac points.¹⁵ It has also been predicted that spin-triplet paring can happen in Ir_1−xPt_xTe₂ when the band filling is near a type-II vHs away from the time-reversal invariant momenta.^18,19 For the parent compound, IrTe₂, the CDW transition is associated with a vHs originating from the β band, schematically shown in Fig. 6(a), which reconstructs strongly below the transition temperature.¹⁴ To characterize the evolution of this type-II vHs in the doped samples using ARPES, we plot the dispersion of the β band in the HAL plane at the BZ boundary of all the samples in Fig. 6(c). A saddle point (SP) can be observed along the AL₁ direction from the 3D dispersion of the β band in Figs. 6(a) and 6(c)–6(f). The observation of a saddle point is apparent in Fig. 6(a) where the extrema of the parabolic dispersion of the β band vary from a maximum at the TP₁/TP₂ point to a minimum at the SP point, where the saddle point is located. As the sample is doped, the vHs persists and moves from around 150 meV below E_F for x = 0.1 and 200 meV below E_F for x = 0.2. For x = 0.3 and 0.4, the saddle point weakens considerably. Notably, the extremum at the TP₁/TP₂ point, where the DOS is large, touches the FS for x = 0.1, implying that the β band plays an important role in the superconductivity. However, how these states interact with the Dirac point derived from the β band and γ band is an open question needed to understand the pairing symmetry and existence of topological superconductivity.

In summary, we obtain a detailed 3D band structure of Ir_1−xPt_xTe₂ with doping levels from x = 0.1 to 0.4. With different photon energies, we are able to distinguish the band structure evolution across different k_z planes. A large outer FS sheet α, an inner FS sheet β, and tiny γ FS sheets together form the 3D band structure. The type-II Dirac point represented by the crossing of the β and γ bands along the k_z direction is clearly resolved. With Pt doping, we are able to tune the energetics of the Dirac point in Ir_1−xPt_xTe₂. One might expect similar results by alkali metal dosing, which will be an informative experiment to carry out. More intriguing is the coexistence of superconductivity and Dirac points close to the Fermi level, together with the existence of a type-II van Hove singularity for x = 0.1 and 0.2. Together, these features leave open the possibility of hosting topological superconductivity, which can be exploited to future topological computing, calling for future theory to understand the relation between the superconductivity and the topological nontrivial bands. Experimentally, our comprehensive 3D band structure study in the normal state calls for further low-temperature studies of quantum oscillations in electronic transport measurements, such as scanning tunneling spectroscopy.

See the supplementary material for details of sample characterization, k_z determination of the electronic structure, and electronic structures of all the samples along ΓMK and ZAR planes.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

This work was supported by the U.S. Department of Energy (DOE), Offices of Science, Office of Basic Energy Sciences under Award No. DE-SC0019211, the National Natural Science Foundation of China (Grant Nos. U1732273, 11904165, and 11904166). Operation of ESM beamline at the National Synchrotron Light Source was supported by the U.S. DOE User Facility Program operated for the DOE Office of Science by Brookhaven National Laboratory under Contract No. DE-AC02-98CH10886.