ABSTRACT Strain is ubiquitous in solid-state materials, but despite its fundamental importance and technological relevance, leveraging externally applied strain to gain control over material

properties is still in its infancy. In particular, strain control over the diverse phase transitions and topological states in two-dimensional transition metal dichalcogenides remains an

open challenge. Here, we exploit uniaxial strain to stabilize the long-debated structural ground state of the 2D topological semimetal IrTe2, which is hidden in unstrained samples. Combined

angle-resolved photoemission spectroscopy and scanning tunneling microscopy data reveal the strain-stabilized phase has a 6 × 1 periodicity and undergoes a Lifshitz transition, granting

results highlight the potential to exploit strain-engineered properties in layered materials, particularly in the context of tuning inter-layer behavior. SIMILAR CONTENT BEING VIEWED BY

OTHERS DEVIATORIC STRESS-INDUCED METALLIZATION, LAYER RECONSTRUCTION AND COLLAPSE OF VAN DER WAALS BONDED ZIRCONIUM DISULFIDE Article Open access 22 June 2024 EVIDENCE OF STRIPED ELECTRONIC

PHASES IN A STRUCTURALLY MODULATED SUPERLATTICE Article 03 July 2024 TWO-DIMENSIONAL FERROELASTICITY IN VAN DER WAALS _Β’_-IN2SE3 Article Open access 16 June 2021 INTRODUCTION Using external

stimuli to manipulate the diverse phenomena observed in quantum materials may allow for tunable control over technologically relevant material properties. Within this context uniaxial

strain has recently emerged as a powerful approach to influence the properties of solids1,2,3,4,5,6 and offers a path to tailor both physical properties and device functionalities,

particularly in the 2D transition metal dichalcogides (TMDs)7,8,9,10. While efforts to control phase transition behavior with strain have focused predominantly on oxide materials, there also

exist many opportunities within the 2D semimetals, which routinely host multiple nearly degenerate structural, electronic, and topological phases11, thereby making them sensitive to

external perturbation. In this regard, the family of layered tellurides are particularly promising12, a prime example of which is 1_T_-IrTe2. This high-atomic number material is predicted as

a type-II bulk-Dirac semimetal with a Dirac point slightly above the Fermi level13 and presents first-order bulk phase transitions to a 5 × 1 × 5 structure at 280 K, and to an 8 × 1 × 8

structure at 180 K14,15. At the surface a complex staircase of nearly degenerate low-temperature phases with periodicity 3_n_ + 2 (i.e., 8 × 1, 11 × 1, 17 × 1…) coexist over scales of a few

tens of nanometers15,16. All of the broken-symmetry phases display characteristic quasi-1D modulations typically identified as Ir dimers15,17, although the changes to the in-plane bonding

suggest a multicenter bond as a more complete description18 (for brevity we will continue to use “dimers” throughout the text). The proposed ground state, a 6 × 1 phase15,19,20,21, is

typically observed only within nanoscale regions, making it all but inaccessible to most techniques. As a result, the electronic structure of the ground state, as well as any influence of

the phase transitions on the bulk-Dirac states, remains unclear, hindering efforts to elucidate the transition mechanism or exploit the topological properties. A number of phases can also be

produced via doping: superconductivity is induced by partial substitution of Ir with Pt22 or Pd23, or by temperature quenching24, while partial substitution of Te with Se induces charge

order19,20,25, further emphasizing the metastable nature of the material. The range of competing phases observed in IrTe2 strongly implies that its macroscopic behavior may be tunable via

strain, allowing individual phases to be selectively stabilized without the need for external doping. In this work, by applying a modest uniaxial tensile strain (ε ~ 0.1%) to IrTe2 single

crystals, we demonstrate the selective stabilization of a single structural phase transition with domain sizes four orders of magnitude larger than in unstrained samples. Complementary real

and momentum space probes reveal this as a 6 × 1 charge ordered phase, a configuration that maximizes both the formation of Ir dimers and of Ir to Te charge transfer. We show that strain

initiates this charge transfer already at room temperature, thereby removing the near degeneracy of the 3_n_ + 2 ladder of phases and favoring the 6 × 1 phase at low temperatures. This

energetic bias allows unprecedented spectroscopic access to the ground state of IrTe2, including the previously unobserved bulk-Dirac-like states, which undergo a Lifshitz transition due to

the charge transfer. Concurrently, charge transfer results in a significant weakening of the majority of interlayer Te bonds in the unit cell, resulting in a tenfold reduction of interlayer

hopping in the relevant states, and leaving the bulk-Dirac states as the dominant interlayer transport channel. These results demonstrate the power of strain to influence phase transitions,

bonding and topology in the layered tellurides, and more broadly in the 2D semimetals. RESULTS AND DISCUSSION STRAIN-STABILIZED ELECTRONIC STRUCTURE Figure 1a shows the hexagonal crystal

structure, typical of the layered TMDs, in the high-temperature 1 × 1 phase of 1_T_-IrTe2. In comparison, all low-temperature phases in IrTe2, including the 6 × 1 (Fig. 1b), are

characterized by the formation of Ir dimers stabilized by electronic energy gain18,19. The density of these dimers increases in each of the successive charge ordered phases, reaching a

maximum in the 6 × 1 phase19,26, which is generally considered as the ground state of the system. The band dispersion along the high-symmetry _LAL_ direction of the bulk Brillouin zone (Fig.

 1c), as obtained by angle-resolved photoemission spectroscopy (ARPES), is displayed in Fig. 1e for the high-temperature phase in an unstrained sample. The corresponding Fermi surface (Fig. 

1h) shows three-fold rotational symmetry consistent with the literature26,27,28,29. Upon cooling the unstrained sample (Fig. 1f), subtle changes occur due to the phase transitions. The

overall form of the electronic structure in the low-temperature phase strongly resembles that at high temperatures, but with broadened bands and a reduction of spectral weight. The lack of

clear features results from the presence of multiple domains and phases (see Fig. 2). While the disappearance of the three-fold symmetry in the Fermi surface (Fig. 1i) implies a dominant

domain orientation within the probed region (50 μm), the absence of a single-phase domain hinders analysis of the resulting electronic structure. In dramatic contrast, the strained sample

(Fig. 1g) displays a rich spectrum of remarkably sharp bands over a wide energy range, implying a uniform signal over the probed region originating from a single phase. Strain was applied

along the _a_-axis of the high-temperature phase using the home-built device pictured in Fig. 1d (see Methods). Of particular interest are sharp surface states and an apparent bulk-like

hyperbolic dispersion close to _E_F (red arrows, Fig. 1g), discussed in more detail below, which are undiscernible in unstrained samples. The Fermi surface (Fig. 1j), reveals a clear

directionality, breaking the rotational symmetry of the high-temperature phase and resulting in a mirror-plane along the _k_x = 0 line. Cuts along the _k_y direction (Supplementary Fig. S2)

showing repeated surface and bulk states reveal this phase has a 6 × 1 in-plane periodicity, which is difficult to discern in Fig. 1j due to the small size of the repeated features and the

variation of spectral weight. REAL-SPACE STRUCTURE AND MAPPING OF THE STRAINED PHASE The 6 × 1 periodicity of the strain-induced state is confirmed in Fig. 2, which demonstrates the effect

of strain on the real-space surface structure as revealed by low-temperature scanning tunneling microscopy (STM) measurements. Unstrained samples display a mixture of differently oriented

domains (Fig. 2a), which form due to the three-fold degeneracy of the high-temperature phase. Within these rotational domains, there exist multiple phases with different 3_n_ + 2

periodicities (Fig. 2d). Again, in contrast, strained samples reveal a clear unidirectional domain (Fig. 2b), with a single 6 × 1 periodicity (Fig. 2f). The line cut in Fig. 2g shows that

two nonidentical groups of three atoms comprise the 6 × 1 periodicity in agreement with previous work15,20. Although the individual STM images are limited in size, the same 6 × 1

phase—always with the same orientation—is found in multiple images across the sample surface over hundreds of microns: more than half of the sample area (Supplementary Fig. S3). This

macroscopic domain size is also seen in low energy electron diffraction (LEED), which averages over a region of similar dimensions (Fig. 2c and e). In the strained case, we indeed record a

single domain orientation with 6 × 1 periodicity, contrasting the clear three-fold directionality of the unstrained sample. Further corroboration is obtained from micro-ARPES mapping (Fig. 

2h), obtained by integrating the intensity of the sharp surface states characteristic of the 6 × 1 phase (Supplementary Fig. S4) across the sample surface. This reveals that the 6 × 1 phase

is found over a continuous region of dimensions ~0.5 × 0.4 mm2. CHARGE TRANSFER AND IMPACT ON INTERLAYER BONDING As is typical of phase transitions in the metal-chalcogenides30 evidence of

charge transfer is observed during the formation of the 6 × 1 phase. Due to the presence of polymeric bonds, the structure of IrTe2 lies between that of pure 2D and 3D materials12. This

results in an Ir3+ configuration and hence a partial charge of Te1.5- on average in the high-temperature phase. In the low-temperature phase, a charge _δ_ is transferred, which produces

modified Ir3+_δ_+ and Te1.5−_δ_/2− species19,26. The electronic energy gain from Ir-dimer formation17 competes with the lattice deformation energy31, making a complete dimerization of the

surface energetically unstable19. As a result, both Ir3+ and Ir3+_δ_+ charge species are present in the low-temperature phase. This can be readily observed in X-ray photoemission

spectroscopy (XPS) where the two distinct peaks appear in the Ir 4 _f_ spectra26,28 as shown in Fig. 3b. We note that the higher binding energy of the second peak implies reduced screening

of the core potential, consistent with a reduced electronic density on the Ir atom (Ir3+_δ_+). Further evidence for a charge transfer is discussed below (Fig. 4). The ratio of the peak areas

tracks the relative dimer density and indicates a mixture of phases in unstrained samples26,29. In contrast, for strained samples an increase of the Ir3+_δ_+ peak produces a ratio that

accords perfectly with the expectation for a single 6 × 1 phase (0.67). Crucially, XPS measurements in the high-temperature phase (Fig. 3a) reveal that a small population of the Ir3+_δ_+

species is already evident above the transition temperature in strained samples, which is absent for unstrained samples. This implies strain actually induces a charge transfer from Ir to Te,

and that this is central to understanding the phase stabilization. The analysis of the peak ratio in the high-temperature phase gives only 0.14, well below the ratio of 0.4 obtained in the

5 × 1 phase, which has the lowest dimer density of the ordered phases. An open question is whether the appearance of the second charge peak in the high-temperature phase implies the

existence of dimers above the phase transition temperature, and indeed whether an ordered phase can be induced at room temperature by increasing the strain level. We note, however, that

dimer formation depends on the competition between electronic and lattice energy, and it is therefore possible in the strained system that a charge transfer is induced without dimer

formation. Finally, we remark that no evidence for a continuous phase transition is observed in temperature dependent ARPES at this strain level (Supplementary Fig. S5). In order to gain

more insight into this redistribution of charge in the strain-stabilized phase, in Fig. 3c, d we compare the calculated charge distributions in the 1 × 1 and 6 × 1 phases, respectively.

Particularly notable is that there is a clear increase of charge density in the interlayer Te–Te region as a result of the phase transition, as charge is moved away from the Ir3+ sites and

onto the Te atoms. This implies the strain-induced charge transfer that produces the Ir3+_δ_+ signal in the high-temperature phase also redistributes charge into the interlayer region. The

impact of this charge transfer on the out-of-plane Te–Te bonds25,32 is significant (the effect on the in-plane bonds has been addressed previously18). A particularity of the tellurides in

comparison to other TMDs is the presence of 3D polymeric bonding structures12, in place of the usual van der Waals gap. IrTe2 indeed contains a network of weak interlayer covalent bonds in

the high-temperature phase32. In Fig. 4a we present a calculation in the 6 × 1 phase highlighting the different interlayer bond lengths and their strengths relative to the high-temperature

phase. Bond strengths are obtained using the integrated crystal orbital Hamiltonian potential (COHP) method33. We find four inequivalent interlayer Te–Te bonds in the 6 × 1 phase, compared

with only one type in the high-temperature phase (see Supplementary Table S1). A number of bond strengths are changed in the 6 × 1 phase, in-line with a multicenter bond description18. In

particular, three out of the four interlayer bonds are observed to weaken significantly across the phase transition, represented in blue in the figure (see also Supplementary Table S1). The

reason for this is that the charge transferred from Ir3+ populates antibonding Te–Te states in the interlayer region, thereby reducing the overall bond strength. The resulting interlayer

bond weakening has been termed “depolymerization”12,25,26, although quantities relevant for bonding such as the out-of-plane bond strengths and hopping have not previously been addressed in

detail for the low-temperature phase. We provide a direct experimental quantification of the effect that the bond weakening has on the electronic structure and electronic hopping in the

out-of-plane direction. We do so by comparing the out-of-plane (_k_z) dispersion (Fig. 4b) in the high-temperature and 6 × 1 phases, and reemphasize that it is only via the strain

stabilization that we are able to access the electronic structure of the pure 6 × 1 phase. Between the low- and high-temperature phases, the majority of states maintain their small

out-of-plane dispersion. However, a sizeable change in the warping of the Fermi contour is observed for bulk states on either side of the Brillouin zone boundary, highlighted by the blue

lines in the two panels of Fig. 4b. In general, such warped Fermi surface contours are characteristic of a strong anisotropy in the electronic hopping parameters and are routinely observed

in low-dimensional materials. A small warping corresponds to a low coupling between chains (1D) or planes (2D) along the relevant real-space direction34,35. In the case of the present

out-of-plane dispersion, the narrowing of the warping in the _k_z direction corresponds to a reduction of the interlayer hopping in the low-temperature phase. In contrast, significant

dispersion is observed for these same states in the (_k_x, _k_y) plane, highlighting the quasi-2D behavior of IrTe2 in the 6 × 1 phase. By applying a tight-binding model34 (see Methods) we

find the interlayer hopping parameter to reduce by a factor of ten to only _t_c = −0.014 eV in the low-temperature phase (in comparison, the in-plane _t_a = −0.53 eV). This prominent

reduction of interlayer coupling in the 6 × 1 phase therefore strongly enhances the 2D nature of the system. The observed layer decoupling further supports recent calculations that show

monolayer IrTe2 has an increased tendency towards the 6 × 1 phase18 suggesting that the dimerized phases could potentially be stabilized at much higher temperatures by reducing the sample

thickness to the monolayer limit. These observations strongly implicate the interlayer bond weakening in the mechanism of the strain-stabilized phase transition25,26,32. By inducing charge

transfer, and hence interlayer bond weakening already in the high-temperature phase, strain reduces the amount of electronic energy that can be gained through dimerization of the Ir3+_δ_+

ions. This therefore destabilizes the nearly degenerate low-temperature phases, and pushes the system to favor the formation of the phase with the highest dimer density and hence highest

possible gain in electronic energy i.e., the 6 × 1 phase. In this way, the less stable 3_n_ + 2 phases are removed from the low-temperature phase diagram. The effect of strain is thus

twofold: first, by defining a preferential direction, it breaks the degeneracy of the three-fold dimer orientation;36 second, it biases the energetic landscape of the system in favor of the

6 × 1 phase. Although the effects of strain are subtle in the high-temperature phase, as expected for the perturbative strain level applied, they pave the way for the stabilized phase

transition, with dramatic results at low temperatures. We note that similar bonding behavior is realized in a number of di- and tri-telluride materials spanning the 2D and 3D regimes12,

suggesting strain or electrical gating as powerful methods to control structural behavior and dimensionality in this class of materials. TOPOLOGICAL LIFSHITZ TRANSITION In contrast to the

discussion above, a state dispersing in _k_z appears around _k_x = 0 in the low-temperature phase (red arrow, Fig. 4b). Due to its strong out-of-plane dispersion (Supplementary Fig. S6),

this state is only observed close to _k_z = 5 Å−1, i.e., the bulk A-point. This feature corresponds to the triangular block of states observed in Fig. 1g, and shown again at different _k_y

positions in Fig. 4d. The strong _k_z dependence and “filled-in” nature of these states resulting from the projection of the bulk manifold reveals them as bulk states. Of note is that these

bulk states have the cone-like hyperbolic dispersion of massless Dirac fermions (Supplementary Fig. S7), which occur ubiquitously in the group-10 TMDs and are predicted in IrTe213. However,

the location of the type-II Dirac point at room temperature is above _E_F, hence inaccessible to ARPES, while at low temperature the mixture of phases typically hides their true nature. The

observed shift of the Dirac point to 350 meV below _E_F in the 6 × 1 phase occurs as the Dirac states are derived from the out-of-plane Te _5p__z_ orbitals and hence are strongly doped by

the charge transfer into Te states as described above. As we have shown, it is only possible to access these states spectroscopically in strained samples. By moving the Dirac point and the

electron-like portion of the Dirac cone into the occupied states, strain produces a Lifshitz transition similar to the temperature-driven transitions observed in WTe237 and ZrTe538. Such a

dramatic change in Fermi surface topology is likely to have a significant impact on the transport properties in this material. In particular, the topological nature of the states involved in

the transition may explain the observed large, nonsaturating magnetoresistance39 similar to the behavior in other layered di-tellurides40,41,42. The strain-stabilized order may even enhance

such effects, paving the way to tunable magneto-resistive behavior. Given the out-of-plane character of the _5p__z_ orbitals involved in the Dirac states, it is plausible that particularly

large changes in interlayer transport may be observed, and investigations of the resistivity anisotropy using e.g., focused ion beam methods43 are highly desirable in this regard. The

potentially topological nature of this out-of-plane transport makes IrTe2 layers especially interesting for tuning interlayer behavior in heterostructure architectures44,45. While a detailed

discussion of the topological properties is beyond the scope of the current article, we nonetheless highlight a surprising observation regarding these Dirac-like states: the dispersion is

not compatible with a single Dirac cone. This can be seen, for example, from the cut at _k_y = −0.05 Å−1 in Fig. 4d, which reveals two partially overlapping cone-like dispersions. Indeed,

the in-plane dispersion of these Dirac states (Fig. 4c) reveals rich structures related to these bulk states, comprising the central hyperbola around _k_y = 0 Å−1, which has a bow tie-like

Fermi contour, and additional hyperbolic cones centered at around _k_y = ±0.15 Å−1 (see also Supplementary Fig. S7), which form asymmetric arcs. The spacing of this latter behavior is

compatible with the periodicity imposed by the 6 × 1 phase, but their unusual distributions and the origin of the additional central bow tie structure remain unclear. Further detailed

investigations including theoretical work will be required to clarify the nature of these states. CONCLUSION In summary, we have selectively stabilized the 6 × 1 charge ordered ground state

of the layered topological semimetal IrTe2 by employing uniaxial strain. The induced macroscopic domain sizes allow detailed insights into the electronic structure at the surface in both

real and momentum space. Charge transfer in the strain-stabilized phase strongly reduces the out-of-plane Te bond strengths, electronically decoupling the layers and resulting in a Lifshitz

transition, granting access to a previously inaccessible bulk-Dirac dispersion that acts as the main interlayer hopping channel. Complementary measurements of the transport properties of the

6 × 1 phase, as well as of monolayer IrTe2, are therefore highly desirable. We note that in contrast to the tensile strain utilized here, uniaxial compression may stabilize superconducting

behavior22,23,24 which, concomitant with the topological states, opens the possibility of strain-tunable topological superconductivity in IrTe2. METHODS SAMPLE GROWTH AND CHARACTERIZATION

Single crystals of IrTe2 were grown using the self-flux method32,46. Samples were characterized by magnetic susceptibility and resistivity measurements29, confirming the bulk phase

transition temperatures of _T_c1 = 278 K and _T_c2 = 180 K in unstrained samples. Samples to be prepared for straining were chosen to have large flat areas with minimal cracks or flakes at

the surface as viewed under an optical microscope, in order to allow for more homogeneous strain application. Bulk samples were initially cleaved with a scalpel to remove thicker layers, and

then mounted onto the unstrained device and further thinned by Scotch tape cleaving. STRAIN DEVICE AND CHARACTERIZATION The strain device, shown in Fig. 1d, is a home-built design

consisting of three parts: a molybdenum (Mo) base plate, a copper beryllium (CuBe) bridge, and a rounded aluminum (Al) block, which is placed under the bridge. The maximum height of the Al

block is machined to be slightly larger than the distance from the underside of the top of the CuBe-bridge to the surface of the base plate. Thus, when the pieces are screwed together, the

CuBe-bridge if forced to bend by the Al block. Samples were oriented with Laue diffraction such that the bending axis was perpendicular to one of the three-fold symmetric directions in the

high-temperature phase i.e., along the _a_-axis of the high-temperature phase (or equivalently, the _b_-axis). This is along the in-plane bond direction of half of the Ir–Ir dimers in the 6 

× 1 unit cell. The sample was mounted on the CuBe-bridge of the strain device using a two-part epoxy (EPO-TEK E4110), which was cured and allowed to cool before strain was applied. Strain

was applied manually by tightening the screws on the underside of the device, which connect the Mo base plate with the Cu-bridge. To ensure maximally directed strain, the screws were

tightened in pairs. All four screws were tightened loosely, following which the two screws on one side of the bridge were fully tightened. The remaining two screws were then gradually

tightened in an alternating fashion, in order to allow as even an application of strain across the device as possible. The strain magnitude was calibrated using commercial strain gauges

(Omega Engineering) with nominal resistance 350 Ω and gauge factor, _k_ = 2.2. The gauge was attached to an unstrained device of the design described above using the same epoxy as for the

samples, and was then connected to a home-built balanced Wheatstone bridge circuit in a “quarter bridge” configuration. Together with a second (passive) gauge, this constituted one arm of

the bridge. The second arm consisted of two 390 Ω resistors, and a variable resistor (10 Ω) was used to balance the circuit. A source voltage of _V_s = 5 V was applied. Once balanced, the

gauge was strained using the device and the output voltage was recorded with a Keithley digital multimeter. The typical output voltage induced by strain (_V_o = 4 mV) was well above the

noise level (50 μV). The voltage output was converted to a strain value via:47 $$\varepsilon = \frac{4}{k}\frac{{V_o}}{{V_s}}$$ where ε, the total strain, is the sum of bending (tensile)

strain and perpendicular (compressive) strain. In such a strain geometry, the perpendicular strain is considerably smaller than the bending strain4, hence “strain” in the main text refers to

the tensile bending strain. To separate further these components requires additional gauges to be placed on the underside of the device, which is impractical given the geometry and small

size. From the above relation, we obtained the strain characteristics of the device. A maximum strain of up to 0.2% was initially recorded during tightening due to plastic deformation of the

CuBe-bridge. This relaxed to around 0.1% once all screws were tight, which is therefore the maximum strain that could be applied to the sample using this particular device and Al block

combination. PHOTOEMISSION SPECTROSCOPY ARPES and XPS measurements were carried out at the I05 beamline48 of Diamond light source, UK, with additional data obtained at the PEARL beamline49

of the Swiss light source. Samples were cleaved in 10−9 mbar vacuum with Scotch tape at room temperature and then cooled using a liquid He flow cryostat at a rate of 5 K min−1. Measurements

were carried out in a base pressure of 10−11 mbar. The beam polarization used was linear horizontal (_p_-pol) and the beam size was 50 × 50 μm2. A photon energy range of 20–100 eV was used

for ARPES measurements, while XPS was carried out at 130 eV and 200 eV. Out-of-plane _k_z mapping was obtained by sweeping the incident photon energy through 40 eV < _hν_ < 100 eV. The

_k_z values were obtained using an inner potential of 12 eV. Spectra were acquired using a Scienta-Omicron R4000 photoelectron analyzer. Micro-ARPES mapping was carried out at the

University of Fribourg. UV photons were generated using a commercial optical setup (Harmonix, APE GmbH) generating tunable output in the range 5.7–6.3 eV in nonlinear crystals. Harmonic

generation was driven by the output of a tunable OPO pumped by a 532 nm Paladin laser (Coherent, inc.) at 80 MHz. The sample surface was scanned by the encoded motion of a 6-axis cryogenic

manipulator (SPECS GmbH). Spectra were acquired using a Scienta-Omicron DA30 analyzer. SCANNING TUNNELING MICROSCOPY STM measurements were performed at the University of Fribourg on a

commercial low-temperature STM (Scienta-Omicron) at 4.5 K in fixed current mode and with the bias voltage applied to the sample. Samples were cleaved in vacuum at 10−8 mbar pressure and

measurements carried out in 10−11 mbar. Strain measurements utilized the same strain device design as for the ARPES measurements. DENSITY FUNCTIONAL THEORY The DFT calculations were

performed using the projector augmented wave method50,51 and the Perdew-Burke-Ernzerhof (PBE)52 exchange-correlation functional within the VASP53,54,55,56 code. The kinetic energy cutoff was

set to 400 eV and a 5 × 15 × 4 k-point grid was used for Brillouin zone sampling. The starting structure for performing the structural relaxation in the 6 × 1 phase was the experimentally

determined 6 × 1 structure19 observed in IrTe2-xSex (space group C2/c, no. 15). The structure was relaxed until the forces were less than 1 meV/Å. The COHP33 analysis was performed using the

LOBSTER code57,58,59. Spin-orbit coupling was neglected in the calculations as the unit cell volumes with and without spin-orbit interaction (SOI) differ by only 0.8%. Similarly,

differences in Ir–Ir distances are, at most, 1.2%. The density plots in Figs. 3 and 4 were generated with VESTA60. TIGHT-BINDING MODEL We describe the _k_z dispersion using the tight-binding

model: $$E_{\boldsymbol{k}} = - 2t_a\cos \left( {k_xa} \right) - 2t_c\cos \left( {k_zc} \right) - \mu$$ where _t_a and _t_c are the energies associated with in-plane hopping along the

Ir-dimer chain direction and out-of-plane hopping, respectively; _a_ = 3.93 Å and _c_ = 5.39 Å are the lattice parameters along the corresponding directions; and _μ_ is the chemical

potential. Following a previously described procedure34 we use the band energy minima at _k__x_ = 0 (_E_Γ = −1.5 eV), the Fermi wave vector at _k__z_ = 0, equivalent to _k_Γ = 4.5 Å−1

(_k_F,Γ = 0.63), and the Fermi surface warping extracted from Fig. 3b to determine the relations between the parameters and extract the hopping energies for the high-temperature and

low-temperature phases. With μ = −0.45 − 2_t_c and _t_a = −0.53 eV, the extracted out-of-plane hopping value is _t_c = −0.156 eV in the unstrained high-temperature phase, and _t_a = −0.014 

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ACKNOWLEDGEMENTS This project was supported through the Swiss National Science Foundation (SNSF), Grant No. P00P2_170597. We gratefully acknowledge beam time from Diamond light source

(proposal SI24880, beamline I05) and the Swiss light source (proposal 20170698, PEARL beamline). We thank P. Aebi for access to the photoemission and STM setups at the University of Fribourg

and for helpful discussions during development of the strain device. Fruitful discussions with F. Baumberger during the initial phase of the project are warmly acknowledged. We acknowledge

J. Chang for access to the Laue diffractometer at the University of Zurich, and J. Choi for technical support. We thank R. Ernstorfer for taking time to provide critical feedback on the

manuscript. A.P. acknowledges the Osk. Huttunen Foundation for financial support, and the CSC–IT Center for Science, Finland, for computational resources. The work at the University of

Zurich was supported by the Swiss National Science Foundation under Grant No. PZ00P2_174015. Skillful technical support was provided by O. Raetzo, B. Hediger, and F. Bourqui. AUTHOR

INFORMATION AUTHORS AND AFFILIATIONS * Department of Physics and Fribourg Center for Nanomaterials, University of Fribourg, CH-1700, Fribourg, Switzerland Christopher W. Nicholson, Maxime

Rumo, Aki Pulkkinen, Geoffroy Kremer, Björn Salzmann, Marie-Laure Mottas, Baptiste Hildebrand, Thomas Jaouen & Claude Monney * School of Engineering Science, LUT University, FI-53850,

Lappeenranta, Finland Aki Pulkkinen * Univ Rennes, CNRS, IPR (Institut de Physique de Rennes)—UMR 6251, F-35000, Rennes, France Thomas Jaouen * Diamond Light Source, Harwell Campus, OX11

0DE, Didcot, UK Timur K. Kim, Saumya Mukherjee & Cephise Cacho * Department of Chemistry, University of Zurich, CH-8057, Zurich, Switzerland KeYuan Ma & Fabian O. von Rohr *

Paul-Scherrer-Institute, CH-5232, Villigen PSI, Switzerland Matthias Muntwiler Authors * Christopher W. Nicholson View author publications You can also search for this author inPubMed Google

Scholar * Maxime Rumo View author publications You can also search for this author inPubMed Google Scholar * Aki Pulkkinen View author publications You can also search for this author

inPubMed Google Scholar * Geoffroy Kremer View author publications You can also search for this author inPubMed Google Scholar * Björn Salzmann View author publications You can also search

for this author inPubMed Google Scholar * Marie-Laure Mottas View author publications You can also search for this author inPubMed Google Scholar * Baptiste Hildebrand View author

publications You can also search for this author inPubMed Google Scholar * Thomas Jaouen View author publications You can also search for this author inPubMed Google Scholar * Timur K. Kim

View author publications You can also search for this author inPubMed Google Scholar * Saumya Mukherjee View author publications You can also search for this author inPubMed Google Scholar *

KeYuan Ma View author publications You can also search for this author inPubMed Google Scholar * Matthias Muntwiler View author publications You can also search for this author inPubMed 

Google Scholar * Fabian O. von Rohr View author publications You can also search for this author inPubMed Google Scholar * Cephise Cacho View author publications You can also search for this

author inPubMed Google Scholar * Claude Monney View author publications You can also search for this author inPubMed Google Scholar CONTRIBUTIONS ARPES and XPS measurements at Diamond light

source were carried out by C.W.N., M.R., G.K., T.K., S.M., C.C., and C.M. Laser ARPES measurements at the University of Fribourg were performed by C.W.N., M.R., T.J., and C.M. STM

measurements were performed by B.S., M.-L.M., and B.H. M.M. provided support for XPS and ARPES measurements performed at the PEARL beamline that were carried out by C.W.N., M.R., G.K., and

C.M. during the initial phase of the project. ARPES data were analyzed by C.W.N. and XPS data by M.R. Samples were grown and characterized by K.M. and F.O.vR. Charge density and bond

strength DFT calculations were performed by A.P. The project was initiated and managed by C.W.N. and C.M. The manuscript was written by C.W.N. and C.M. with input and suggestions from all

authors. CORRESPONDING AUTHORS Correspondence to Christopher W. Nicholson or Claude Monney. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing interests. ADDITIONAL

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transition in the 2D topological semimetal IrTe2. _Commun Mater_ 2, 25 (2021). https://doi.org/10.1038/s43246-021-00130-5 Download citation * Received: 29 September 2020 * Accepted: 05

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