Introduction

Transition metal dichalcogenides (TMDCs) provide a prototypical quasi-two-dimensional system, possessing various electronic instabilities to periodic charge modulations1. These instabilities often induce complex charge-density-wave (CDW) phases with different commensurability conditions2,3,4,5, sometimes associated with Mott-2 or excitonic insulating6 phases. Upon chemical doping4,5,7,8, these phases are commonly driven into a superconducting phase, resulting in a characteristic dome-shaped phase diagram, reminiscent of those found in other unconventional superconductors9,10,11 (Fig. 1a). Understanding the complex interplay between charge ordering and superconducting instabilities in TMDCs is a long standing issue, which has often been hampered by presence of quenched disorders, introduced in chemical doping. Recently, utilising the weak van der Waals (vdW) coupling between layers, TMDCs were found to be thinned down to atomic length scale12, comparable with the coherence lengths of their various electronic orders. This offers another effective way to tune stability or properties of the competing phases, as demonstrated for 1T-TaS213,14,15 and NbSe216,17, in which distinct thickness dependence of the transition temperatures is observed for superconducting and CDW phases.

Fig. 1: Structure and phase diagram of IrTe2 nanoflakes.
figure 1

a Schematic phase diagrams of TMDCs as a function of control parameter p, showing commensurate (C), incommensurate charge order (IC), and superconductivity (SC). Three different types of dome-shaped superconducting phase diagram, where the dome lies at the centre of a presumed quantum critical point (top), near the C-IC transition line (middle), or well inside the parent order (bottom). b Crystal structure of IrTe2. c, d Schematic illustrations of the stripe order in IrTe2 below Ts. The Ir-Ir dimerization (red) with a modulation vector q = (\(\frac{1}{5}\),0,\(\frac{1}{5}\)) is depicted (blue shade) on the triangular Ir layer (c) and across the stacked layers (d). The crystallographic axes for the high-T (a, b, and c) and the low-T (a*, b*, and c*) structures are shown, together with the unit cell of the stripe phase (orange box). e Temperature dependence of the normalised resistivity ρ(T)/ρ(300 K) for IrTe2 crystals with thickness (d) of 21, 56, and 90 nm. For clarity, ρ(T)/ρ(300 K) curves are offset vertically. Transition temperatures Ts,up and Ts,dn are determined (arrows) in opposite temperature sweeps. f Optical microscope image of a 56-nm-thick IrTe2 crystal. g ρ(T)/ρ(3 K) curves for IrTe2 crystals with d = 12–140 nm. h Phase diagram of IrTe2 nanoflakes as a function of thickness d, obtained by transport (circle) and Raman spectroscopy (square) measurements. The transition temperatures Ts,up (red) and Ts,dn (blue) during warming and cooling are plotted with the superconducting transition temperature Tc (black), scaled by a factor of 10 for clarity. The error bars from the resistivity and Raman spectroscopy are defined by the width of the corresponding resistive transitions and the temperature step of 5 K between the measurements, respectively.

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IrTe2 is one of the TMDCs in vdW structure (Fig. 1b), showing a similar dome-shaped superconducting phase diagram18,19,20,21,22,23. IrTe2 undergoes a stripe charge ordering transition at Ts ~ 260 K, and by suppressing it with e.g. chemical doping18,19,20,21,22,23 the superconducting phase eventually appears, similar to TMDCs hosting the parent CDW orders4,5,7,8. The stripe order in IrTe2, however, is accompanied by the first-order structural transition involving in-plane Ir–Ir dimerization and interlayer Te–Te depolymerisation24,25, which forms stripe patterns with a predominant period of 5a0 (a0, the a axis lattice constant) as depicted in Fig. 1c and d19,26. No clear evidence of gap opening in the Fermi surface (FS) is observed27,28, unlike the typical CDW gap formation in TMDCs29. Instead, FS reconstruction to the so-called cross-layer two-dimensional (2D) state30,31 occurs due to suppression of the density of states (DOS) in the planes of Ir–Ir dimers running across the vdW gaps. These aspects suggest that the relationship between the stripe and superconducting orders in IrTe2 may differ significantly from those of other TMDCs, as indicated by recent discoveries on the superconductivity in quenched or thinned IrTe2 crystals32,33,34. Here using Raman spectroscopy, scanning tunnelling microscopy, and transport property measurements, we found that the parent stripe phase encompasses the whole superconducting dome in the thickness-dependent phase diagram (Fig. 1a). This unusual coexistence of the stripe and superconducting orders significantly increases the interlayer coherence length and the coupling strength of superconductivity in IrTe2 nanoflakes, revealing the collaborative role of the stripe order to the superconductivity in IrTe2.

Results

Thickness dependent phase transitions

In order to vary the thickness of IrTe2, we employed the mechanical exfoliation method of single crystals and obtained thin flakes with thickness (d) down to ~10 nm, which show a systematic thickness dependence of the in-plane resistivity ρ (Fig. 1e). For the temperature sweeps in both directions, we took a slow cooling rate of ~0.5 K/min, in order to minimise inhomogeneous domain formation of the stripe-charge-ordered and charge-disordered phases, found in rapid-cooled IrTe2 crystals32,33,35. The temperature dependent ρ(T) follows a metallic temperature dependence with abrupt changes at Ts,dn and Ts,up, due to the first-order stripe ordering transition as found in bulk crystals24,25. These resistive anomalies across the transitions, however, become much smaller in size with reducing d, and eventually disappears for d < 50 nm. This does not mean full suppression of the stripe order in thin nanoflakes, since the size of the resistive anomaly is known to be strongly suppressed by introducing strain, reducing the sample volume, and increasing the cooling rate even in bulk samples34. Rather, the stripe order is found to be stable in all the nanoflakes we studied, as discussed below (Fig. 2). At low temperatures, all the nanoflakes, except the thinnest one with d = 12 nm, exhibit a superconducting transition as found in the temperature-dependent normalised resistance ρ(T)/ρ(3 K) (Fig. 1g). The superconducting transition temperature, defined as a 50% resistive transition, is Tc = 1.43–2.64 K, somewhat lower than Tc ~ 3 K for the optimally doped bulk IrTe218,19, mostly due to the 2D nature as discussed below (Fig. 3). Unlike the stripe charge ordering transition, the superconductivity is found to be quite stable in nanoflakes. The superconducting transition temperatures and widths remain almost the same in different thermal cycling (Supplementary Fig. 7).

Fig. 2: Stripe charge ordering formation in IrTe2 nanoflakes.
figure 2

a, b Raman spectra (a) and corresponding temperature dependent Raman frequency (b) of a 65-nm-thick IrTe2 nanoflake at various temperatures during cool-down and warm-up procedures. At T < Ts, the Raman modes, Eg at 126 cm−1 and A1g at 165 cm−1, split into multiple peaks as the flake forms the stripe charge order in a. The temperature ranges for the normal (red), the stripe (blue), and intermediate coexistence (yellow) phases, are identified in b, during cooling (upper panel) and warming (lower panel). Transition temperatures Ts,dn and Ts,up are indicated by the arrows, respectively. c Spatial profile of Raman intensity map for 129 cm−1 for a 43-nm-thick IrTe2 nanoflake at T ~ 70 K. Inset: optical microscope image of the flake. d Large-scale scanning tunnelling microscopy (STM) image of a 20-nm-thick IrTe2 flake at T = 85 K (scale bar, 300 nm). The flake has only stripe-phase charge-ordered domains, illustrated by red, green, and blue lines. Black lines indicate domain boundaries between three equivalent stripe-phase charge-ordered domains. e Atomically resolved STM image of d at T = 85 K representing a uniform striped area with 5 × 1 surface reconstruction (scale bar, 2 nm). f Zoomed-in STM image of two charge-ordered phases indicated by red square in d showing that the two phases coexist at the boundary (scale bar, 20 nm). g Scanning tunnelling spectroscopy (STS) spectra at T = 85 K taken on IrTe2 nanoflakes with d = 47, 80, and 148 nm, as indicated in the plot.

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Fig. 3: Two dimensional superconductivity of IrTe2 nanoflakes.
figure 3

a, Magnetic field dependence of ρ(H) of a 56-nm-thick IrTe2 nanoflake, measured with different field orientations θ at T = 0.35 K. b, Upper critical field Bc2 as a function of field angle θ for IrTe2 nanoflakes with different thickness (d) at T = 0.35 K, together with the fit (solid line) to the 2D Tinkham model. Inset: the anisotropy factor \({{\Gamma }}={B}_{c2}^{ab}\)/\({B}_{c2}^{c}\) as a function of d, following 1/d dependence (grey line). Schematic illustration shows the field orientation θ. c, Angle dependence of Bc2(θ) of IrTe2 nanoflakes with d = 56 and 140 nm at T = 0.35 K. Good agreement with the 2D Tinkham model (red), rather than the 3D Ginzburg-Landau model (black), confirms the 2D superconductivity. d, Normalised Bc2/Bc2(0) as a function of T/Tc for IrTe2 nanoflakes with different d. All data collapse into dashed lines described by 1 − T/Tc and \({(1-T/{T}_{c})}^{1/2}\) for B∥c (open circles) and B∥ab (solid circles), respectively. e, Ginzburg-Landau coherence length ξab (square) and the effective superconducting thickness dSC (circle) as a function of d. ξab is nearly independent of d, whereas dSC grows linearly with d (dSC ~ 0.8d) and exceeds ξc of doped bulk IrTe2. f, Schematic illustration of the size effect of vdW superconductors. In normal vdW superconductors with a large anisotropy ξc ≪ ξab, 2D superconductivity appears only for a-few-layer-thick crystals. In IrTe2 with a stripe order and the resulting cross-layer quasi-2D state, the increased ξc ~ ξab induces 2D superconductivity in relatively thick nanoflakes.

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The stripe ordering transition of IrTe2 nanoflakes is characterised by Raman spectroscopy. For bulk IrTe2, two Raman active modes, Eg at 126 cm−1 and A1g at 165 cm−1, in a trigonal structure (space group \(P\bar{3}m1\)) split into multiple peaks due to the lowered symmetry and the emergence of a super unit cell for the stripe order below Ts30,36. Raman spectra taken from the 65-nm-thick nanoflake with sequential decrease and increase of temperature (Fig. 2a) reveal that both Eg and A1g Raman modes at room temperature split into multiple Raman modes at T = 70 K, well below Ts, consistent with previous studies on the bulk36. This behaviour is also shown for the flakes with different thicknesses (Supplementary Fig. 2a and Fig. 3a) and confirms formation of the stripe charge order in our IrTe2 nanoflakes.

In IrTe2 nanoflakes, however, the temperature dependence of the stripe phase evolution is distinct from the bulk case. We found that below Ts there is an intermediate temperature range (yellow range in Fig. 2b) where the high temperature Raman modes coexist with the low temperature modes, for both temperature sweeps. This contrasts to the abrupt change found in bulk IrTe2 with a negligible coexistence range36 and indicates macroscopic phase separation of the normal and stripe phases in IrTe2 nanoflakes at the intermediate temperature. We defined Ts,dn and Ts,up as the temperatures where the contribution from the normal and stripe phase disappears during the cool-down and warm-up procedures, respectively (Fig. 2b). As the flake thickness decreases, the transition temperatures monotonically decrease, which are in good agreement with those from ρ(T) (Fig. 1h). In addition, we measured the Raman spectroscopy on IrTe2 flakes, cooled down to T = 4 K, just above Tc ~ 2 K. For IrTe2 flakes with various thicknesses from 10 nm to 174 nm, which cover the whole superconducting dome in the thickness-dependent phase diagram, we observed clear splitting of Raman modes, consistent with the stripe-charge-order formation (Supplementary Fig. 3). These results clearly show that the region of the stripe phase overlaps with the entire superconducting dome in a wide range of thickness.

Coexistence of stripe order and superconductivity

This phase diagram significantly differs from the doping-dependent phase diagram of bulk IrTe218,19,20,21,22,23. In the bulk case, the stripe and superconducting phases are mutually exclusive, and the coexisting region appears in the very narrow doping range18,19,20,21,22,23. Even in this coexisting phase, two ordered phases are macroscopically separated22,23. Such a macroscopic phase separation is also suggested in the super-cooled case32,33,35. However, in IrTe2 nanoflakes, the stripe phase completely covers the whole regions of the sample, as confirmed by the spatial mapping of Raman signal, taken at ~ 70 K well below Ts (Fig. 2c). The intensity map of the 129 cm−1 Raman mode, which is the hallmark of the stripe phase, reveals a strong Raman intensity profile over the entire nanoflake as in the optical microscope image (Fig. 2c inset), while the signal from the normal phase is absent (Supplementary Fig. 2c). This indicates that the stripe phase dominantly prevails in the macroscopic length scale and serves as a normal state for the superconductivity, in contrast to the doped bulk IrTe2 case.

The dominant stripe phase formation is further confirmed by scanning tunnelling microscopy (STM) for a representative nanoflake with d = 20 nm (Fig. 2d). At room temperature, the hexagonal lattice of top-most Te atoms is clearly resolved by STM in all IrTe2 nanoflakes (Supplementary Fig. 4b). When cooled down below the stripe ordering temperature (TSTM = 85 K < Ts), the ultrathin nanoflake develops clear stripe patterns with a period of 5a0 due to the charge ordering and dimerization of Ir atoms (Fig. 2e), as observed in bulk crystals25,26. By scanning over the nanoflake with sufficient spatial resolution (Fig. 2f), we confirm that the whole surface of the flake hosts one or two predominant stripe phases among three energetically equivalent phases (Fig. 2d), and the stripe patterns are often oriented nearly parallel to the long edges of nanoflakes. In thicker nanoflakes (Supplementary Fig. 5a), stripe domain patterns became more complex, similar to bulk IrTe235. We note that even with fast cooling at ~ 1 K/sec, neither thin nor thick nanoflakes show the hexagonal phase that is often observed in either super-cooled or doped bulk IrTe222,35 and considered to be responsible for the superconductivity. Consistently, in the scanning tunnelling spectroscopy (STS) measurements on IrTe2 nanoflakes, we observe similar local DOS over the wide range of thicknesses. In STS spectra (Fig. 2g), obtained on different IrTe2 nanoflakes with 47 ≤ d ≤ 148 nm, the local spectral features are qualitatively consistent with the total DOS for the stripe phase of bulk IrTe2, as estimated using first principle calculations30. Our results from STM and Raman spectroscopy provide strong evidence that the superconductivity emerges from the preexisting stripe phase in IrTe2 nanoflakes.

2D superconductivity

Now we focus on the effect of the underlying stripe order on the superconducting properties. To address this issue, we investigated the upper critical field Bc2 of each nanoflake as a function of field orientation below Tc. Figure 3a shows the resistivity ρ(H) curves of a representative nanoflake with d = 56 nm, collected at T = 0.35 K under a magnetic field, for which the angle θ is defined with respect to the ab plane. The anisotropy of Bc2, \({{\Gamma }}={B}_{c2}^{ab}\)/\({B}_{c2}^{c} \sim 5.3\) for d = 56 nm, becomes stronger with lowering d and reaches up to Γ ~ 38 for d = 21 nm (Fig. 3b), an order of magnitude larger than Γ ~ 2 of doped bulk IrTe237. This large increase in Γ with moderate changes in Tc (Fig. 1g) and the in-plane coherence length ξab(0) (Fig. 3e) can only be explained by 2D superconductivity. In the Tinkham model of 2D superconductivity38, the angle dependent Bc2(θ) at the zero-temperature limit is described by \(| {B}_{c2}(\theta )\sin \theta /{B}_{c2}^{c}| \,+ {({B}_{c2}(\theta )\cos \theta /{B}_{c2}^{ab})}^{2}=1\), where \({B}_{c2}^{ab}= (\sqrt{12}{{{\Phi }}}_{0})\)/(2πξab(0)dSC) and \({B}_{c2}^{c}={{{\Phi }}}_{0}\)/(2πξab(0)2) (Φ0, a flux quantum). Thus by reducing the effective thickness of the superconducting layer dSC, Γ becomes large with a constant ξab(0), and a discontinuous cusp in the Bc2(θ) curve near θ = 0∘ is expected. These predictions are distinct from those of the Ginzburg-Landau model for anisotropic three-dimensional (3D) superconductors38, as described by Bc2(θ) = Bc2(0∘)/\(\sqrt{{{{\Gamma }}}^{2}{\sin }^{2}\theta +{\cos }^{2}\theta }\). All Bc2(θ) curves exhibit a clear cusp near θ = 0∘ and are successfully fitted by the 2D Tinkham model rather than the anisotropic 3D model (Fig. 3b and Supplementary Fig. 9). For d = 140 nm, the thickest sample, Bc2(θ) slightly deviates from the 2D model, but still far from 3D model (Fig. 3c). These results demonstrate that IrTe2 nanoflakes with d ≤ 140 nm clearly show the 2D superconductivity.

The temperature dependence of Bc2(T) under in-plane (B∥ab) and out-of-plane (B∥c) magnetic fields further confirms the 2D superconductivity of IrTe2 nanoflakes. For seven samples with different d’s, we determined Bc2(T) by taking 50% of the resistive transition as a function of the normalised temperature t = T/Tc (Fig. 3d and Supplementary Fig. 8). The out-of-plane \({B}_{c2}^{c}(t)\) is almost the same, following the linear dependence (Fig. 3d), as observed in the doped bulk sample37. The in-plane \({B}_{c2}^{ab}(t)\) increases strongly with lowering d, but the normalised Bc2(t)/Bc2(0) curves for all samples collapse into a single curve following the 2D Ginzburg-Landau model38, \({B}_{c2}^{ab}(t)=\frac{{{{\Phi }}}_{0}}{2\pi }\frac{\sqrt{12}}{{\xi }_{ab}{d}_{{\rm{SC}}}}{\left(1-t\right)}^{1/2}\). Using ξab(0), estimated from the observed \({B}_{c2}^{c}(0)\), we obtained dSC is ~ 80% of the measured thickness d (Fig. 3e). Considering that 2D superconductivity is induced at d ( ~ dSC) smaller than the out-of-plane coherence length ξc, i.e. d < ξc, we conclude that ξc(0) of IrTe2 nanoflakes should be larger than the maximum value of dSC ~ 100 nm, obtained in experiments (Fig. 3e), This value is significantly larger than the typical ξc(0) ~ 25 nm of doped IrTe2 bulk samples37, and comparable to the in-plane coherence length ξab(0) ~ 70 nm39 (Fig. 3e). These findings clearly indicate that the superconducting characteristics of IrTe2 nanoflakes are distinct from those of the doped IrTe2.

Characteristics of superconductivity coexisting stripe order

The drastically increased ξc(0) in IrTe2 nanoflakes is a consequence of the coexisting stripe order. In anisotropic superconductors, the interlayer coherence length ξc(0) is determined by the superconducting gap (ΔSC) and the Fermi velocity (\({v}_{{\rm{F}}}^{c}\)), i.e. \({\xi }_{c}(0)\propto {v}_{{\rm{F}}}^{c}\)/ΔSC. Assuming a similar ΔSC, ξc(0)/\({\xi }_{ab}(0)\approx {v}_{{\rm{F}}}^{c}\)/\({v}_{{\rm{F}}}^{ab}\gtrsim 1\) seems incompatible with the vdW structure of IrTe2. This however can be explained by considering the coexisting stripe order. In the stripe phase of IrTe2, Ir-Ir dimerization and Te-Te depolymerisation produce conducting planes between the dimer planes, running across the vdW gaps (Fig. 1d). This cross-layer 2D conducting state30 affects the electronic structure such that the interlayer \({v}_{{\rm{F}}}^{c}\) is even larger than the in-plane \({v}_{{\rm{F}}}^{ab}\), which greatly increases ξc(0) (Fig. 3f). Unlike the conventional vdW superconductors in which 2D superconductivity can only be induced in a-few-layer-thick crystals, IrTe2 hosts 2D superconductivity in the relatively thick crystals due to the microscopically coexisting stripe order.

The distinct superconducting nature in IrTe2 nanoflakes is also found in their superconducting gap as compared to the doped bulk. Figure 4a presents the current-voltage (IV) characteristics at different temperatures for a representative nanoflake with d = 21 nm. Near Tc ≈ TBKT, they follow Berezinskii-Kosterlitz-Thouless transition for 2D superconductivity (Fig. 4b), in which the exponent α extracted from V ∝ Iα crosses α = 3 at TBKT. Well below Tc, the self-field critical current density Jc,sf(T) can be obtained from the IV characteristics with variation of temperature, which is proportional to temperature dependent London penetration depth λ(T) for d ≪ λ40,41. From the critical current Ic(T), at which the measured voltage jumps due to the superconducting-to-normal transition, we obtained the corresponding Jc,sf(T) and λ(T) curves (Fig. 4c and Supplementary Fig. 10), which can be nicely reproduced by the fit based on BCS theory using ΔSC ≈ 0.38 meV. The superconducting gap (ΔSC), taken from IrTe2 nanoflakes with different thicknesses, varies linearly with their Tc with a superconducting gap ratio of 2ΔSC/kBTc ~ 5.3, which is much larger than the BCS value of 3.53 and 2ΔSC/kBTc ~ 3.7 of doped bulk IrTe237,42 (Fig. 4d). Thus, superconductivity in IrTe2 nanoflakes is in the strong coupling regime, whereas that of doped bulk IrTe2 is in the weak coupling regime.

Fig. 4: Strong superconducting coupling in IrTe2 nanoflakes.
figure 4

a Current-voltage (IV) characteristics at various temperatures for a representative IrTe2 nanoflake with d = 21 nm. b Temperature dependence of the normalised resistivity and the exponent α for a 21-nm-thick IrTe2 nanoflake. Exponent α is determined from the power-law behaviour V ∝ Iα in the IV curves, as expected by BKT transition. c Critical current density (blue) and the penetration depth (red) as a function of temperature for a 21-nm-thick IrTe2 nanoflake. Solid lines are the fits to the self-critical-current model described in the text. d Superconducting gap ΔSC as a function of Tc, extracted from the critical current density for IrTe2 nanoflakes with different d (red). The slope of their linear dependence, corresponding to the superconducting gap ratio, 2ΔSC/kBTc = 5.3, is much larger than the case of doped bulk IrTe2 (black) from refs. 37,42. This difference confirms the strong coupling nature of the superconductivity in IrTe2 nanoflakes.

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Discussion

Our findings unequivocally emphasise that the superconductivity in IrTe2 nanoflakes, which emerges from the preexisting stripe order, is highly distinct from that in doped bulk IrTe2. On pristine IrTe2 bulk or surface, the 5a0 stripe phase undergoes multiple transitions to other nearly-degenerate stripe phases that have different periods such as 8a0 and 6a0, and also a honeycomb phase35,43,44,45. The complex stripe ordering formation is a result of subtle balance between local interactions of Ir-Ir dimerization and Te-Te depolymerisation. These incipient instabilities and the resulting strong electron-lattice coupling of the parent 5a0 stripe phase can facilitate pairing interaction for superconductivity in a proper condition and thereby enhancing the superconducting coupling strength as observed in IrTe2 nanoflakes. This coexisting phase of stripe and superconducting orders, however, cannot be accessed by chemical doping, e.g. Pt doping at the Ir sites. A few % of doping directly perturbs Ir dimerization and melts the stripe order to a quasi-periodic hexagonal order18,22. In this case, the onset of superconductivity coincides with disorder-induced melting of the parent order23, reminiscent of other TMDCs such as Cu-doped TiSe23,4,5.

In contrast, the thickness control of IrTe2 tunes the stripe order without introducing quenched disorders. The stripe order in IrTe2 may be mildly suppressed by the thinning-induced out-of-plane elongation13,46 or the substrate-induced in-plane tensile strain as opposite to the pressure effect enhancing Ts24. Typically, the thinning-induced out-of-plane elongation of Δc/c ~ 0.1%, as found in TaS213,46 and the substrate-induced in-plane strain of Δa/a ~ 0.1–0.3% (Supplementary Note 6) are expected in the thinned IrTe2, where a and c are the in-plane and out-of-plane lattice constants, respectively. A recent study on a strained IrTe2 single crystals47 revealed that only ~ 0.1% of tensile strain induces the transition between the stripe-charge-ordered phases with different periods of 5a0 and 6a0, which significantly modifies the electronic structures. Our first principle calculations for electron-phonon coupling constant λep of the 5a0 stripe phase show that the in-plane tensile strain is more effective to drive the system to the structural instability and to enhance λep than the out-of-plane elongation, which increases Tc by a factor of ~ 3 (Supplementary Table 1). While the corresponding critical strain is much larger in calculations and also the calculated Tc remains lower than the measured Tc ~ 2 K, these observations imply that the stripe phase of IrTe2 is intrinsically in close proximity to the superconducting phase, which can be accessed by reducing thickness or by thermal quenching32,33. It has been known that, in the vicinity of full charge order melting, strong electron-phonon coupling48,49 can play an important role to promote the superconductivity, as found in the charge-ordered organic metals50,51. This appears to be consistent with the enhanced superconducting gap ratio, found in IrTe2 flakes (Fig. 4). Our results unveil the collaborating relationship, rather than the competing one, between the parent stripe and the superconducting orders in IrTe2, highlighting IrTe2 as a unique example among superconducting TMDCs. Further investigations, for examples, scanning tunnelling microscopy and spectroscopy as well as Raman spectroscopy below the Tc are highly desirable to identify the local superconducting gap structure along the charge modulation patterns and the electron-phonon coupling, which would elucidate the interplay of the stripe-charge-order and superconductivity in IrTe2.

Methods

Single crystal growth and bulk properties

IrTe2 single crystals were synthesised using the Te-flux method31. Ir and Te powders were mixed in a stoichiometric ratio Ir:Te = 1:4, heated to 1160 ∘C for 1 day as sealed in a quartz ampoule, and then cooled. The crystallinity and stoichiometry were confirmed by X-ray diffraction and energy-dispersive X-ray spectroscopy.

Exfoliation and fabrication of nanoflakes

We used mechanical exfoliation of bulk single crystals to obtain thin nanoflakes of IrTe2 on top of a Si/SiO2 substrate that had been pre-cleaned in acetone, 2-propanol, and deionised water, then treated by oxygen plasma (O2 = 10 sccm, P ~ 100 mTorr) for 5 min. All cleaving and handling were done in inert atmosphere (H2O < 0.1 ppm, O2 < 0.1 ppm) of pure Ar gas except the atomic force microscopy (AFM) measurements. In some cases, a thin h-BN crystal was subsequently transferred onto the IrTe2 nanoflake in Ar atmosphere. We found that the optical contrast, the AFM thickness, and Raman spectra were unchanged even after 1 week in ambient conditions (Supplementary Fig. 1), indicating that the nanoflakes are stable in ambient conditions. To fabricate devices for electrical measurements, we used conventional e-beam lithography to pattern electrodes on top of IrTe2 nanoflakes with metal deposition of Cr(10 nm)/Au(50 nm). The optical microscope image for the typical device is shown in Fig. 1f.

Transport property measurements

Transport measurements were performed in a cryogenic 3He refrigerator equipped with a superconducting vector magnet (9/2/2 T). Each measurement wire was filtered by a room-temperature π filter and low-temperature π and low-pass RC filters at 0.35 K to minimise the electrical noise on the sample. Electrical resistance was measured in standard four-probe configuration using DC delta mode with bias current 1 μA to 10 μA determined by the sample resistance and signal to noise ratio. Magnetic fields with desired field orientations were applied by the vector magnet at one cooling without altering sample position.

Raman spectroscopy

Raman spectra were obtained using a confocal microscopy set-up with laser beam size of ~ 1 μm and laser power of ~ 1 mW. A HeNe laser (632.8 nm) was used to excite IrTe2 flakes in an optical cryostat at normal incidence. The Raman signal was collected in the backscattering configuration and analysed using a monochromator equipped with a liquid nitrogen-cooled silicon CCD. Two linear polarizers in the parallel configuration were placed immediately after the laser and before the monochromator to define the polarization of incident and scattered light, respectively. The crystal orientation relative to the polarisation of the incident light was controlled using a half waveplate between a beam splitter and IrTe2 flakes. The sample position was precisely controlled using a piezo stage.

Scanning tunnelling microscopy and spectroscopy

For scanning tunnelling microscopy (STM) and spectroscopy (STS) measurements, IrTe2 nanoflakes were exfoliated in a glove box (H2O < 0.1 ppm, O2 < 0.1 ppm) filled with Ar gas, and transferred onto graphene, grown epitaxially on a 4H-SiC(0001) substrate. The samples were then transferred to a ultrahigh vacuum chamber (P ≤ 1 × 10−10 Torr) for STM/STS measurements without any exposure to air to ensure clean surfaces of IrTe2 nanoflakes. STM images were typically obtained using a bias voltage Vb = − 2.5 V and a tunnelling current It = 20 pA for large-scale imaging; Vb = 15 mV and It = 1 nA for charge-ordered stripe phases; Vb = 5 mV and It = 2 nA for atomically-resolved images. For STS, we used the lock-in technique with a bias modulation of 7 mVrms.

Density functional theory calculations

Density functional theory (DFT) calculations for electronic structures and the electron-phonon coupling (EPC) were performed by the Quantum Espresso package implementing the pseudo-potential band method and the density functional perturbation theory52,53. We utilised Perdew-Burke-Ernzerhof sol (PBEsol, revised PBE for solid)54 as an exchange-correlation functional and included the spin-orbit coupling (SOC). The dynamical matrices were calculated using 2 × 2 × 2 q-mesh and 16 × 10 × 4 k-mesh with 40 Ry energy cutoff. We applied the various in-plane tensile strains in the range of Δa/a ~ 2.1–3.1% and the fixed compressive strain of Δb/b ~ 0.65% to model the experimental situations (Supplementary Note 6). Atomic positions were optimised in each case.