Charge-Stripe Order and Superconductivity in Ir1−xPtxTe2

A combined resistivity and hard x-ray diffraction study of superconductivity and charge ordering in Ir Ir1−xPtxTe2, as a function of Pt substitution and externally applied hydrostatic pressure, is presented. Experiments are focused on samples near the critical composition x c ~ 0.045 where competition and switching between charge order and superconductivity is established. We show that charge order as a function of pressure in Ir0.95Pt0.05Te2 is preempted — and hence triggered — by a structural transition. Charge ordering appears uniaxially along the short crystallographic (1, 0, 1) domain axis with a (1/5, 0, 1/5) modulation. Based on these results we draw a charge-order phase diagram and discuss the relation between stripe ordering and superconductivity.

Transition-metal dichalcogenides have long been the centre of considerable attention because of their complex quasi two-dimensional electronic properties. Semiconductor physics 1 , superconductivity [2][3][4] and spontaneous breaking of lattice symmetry, driven by charge-density waves (CDW) [5][6][7] , are commonly reported. Often, the ground state properties of these materials can be controlled by external non-thermal parameters such as chemical substitution 8 , magnetic field 9,10 or hydrostatic pressure 11 . The prototypical 1T-TaS 2 compound can, for example, be tuned from a CDW state to superconductivity by application of hydrostatic pressure 11 . Recently, a connection between charge density wave order in 1T-TaS 2 and orbital textures has been demonstrated 12 . A parallel effort has been to study dichalcogenide systems in which spin-orbit coupling is considerable. To this end, IrTe 2 has attracted interest because spin-orbit coupling on the Ir site is known to be large 13,14 . The IrTe 2 system displays high-temperature charge ordering, and superconductivity can be induced by Pt or Pd substitution that in turn quenches the charge order [15][16][17] . Several studies concluded in favour of a conventional s-wave pairing symmetry 18,19 . It remains however to be understood how charge order, lattice symmetry and superconductivity interfere.
In the parent compound IrTe 2 , charge order coincides with a lowering of the crystal structure symmetry (from hexagonal P m 3 1 to monoclinic C2/m) 15 . This effect is most likely not accidental and hence IrTe 2 falls into the category of materials such as La 2−x Ba x CuO 4 20 , Ca 2 RuO 4 21,22 , and URu 2 Si 2 23 where structural and electronic transitions appear simultaneously. For such systems, it is important to address the question whether the transition is lattice or electron driven. Resolving this issue, is often crucial to understand the electronic instability. The fact that superconductivity emerges when charge order is quenched by chemical pressure tuning, is probably also not coincidental. It may indicate that quantum criticality enters as a supporting ingredient to the formation of superconductivity. The interplay between charge ordering and superconductivity is therefore an interesting topic to explore. Charge ordering of the parent compound has been studied in great detail, and it has been shown how different modulation vectors emerge as a function of temperature. Upon cooling the system first develops a (1/5, 0, 1/5) modulation (T < 280 K) that switches to (1/8, 0, 1/8) at lower temperatures [24][25][26] , (T < 200 K). There exist, however, no x-ray diffraction studies of the charge order in Ir 1−x Pt x Te 2 near the critical composition (x c ~ 0.045) for superconductivity. Here we present a combined resistivity and x-ray diffraction study of Ir 1−x Pt x Te 2 as a function of chemical substitution and hydrostatic pressure near the critical composition x c . Just below this critical composition, we find a temperature independent charge ordering modulation vector (1/5, 0, 1/5). This signifies a difference from the parent compound where the ground state charge modulation is (1/8, 0, 1/8) 25,26 . Our pressure experiments were carried out just above x c (namely at x = 0.05) in a compound with a superconducting ground state and no evidence of charge order at, and around, ambient conditions 1-400 bar. With increasing pressure, we find a lowering of lattice symmetry above p c1 ~ 11.5 kbar. This breaking of the hexagonal lattice symmetry appears without any trace of charge ordering that emerges only for pressures above p c2 ~ 16 kbar. From this observation we conclude that charge ordering is lattice -rather than electronically -driven. Combining our results with those previously obtained in IrTe 2 , we propose a charge order phase diagram as a function of Pt substitution and hydrostatic pressure. In terms of structure, we demonstrate that charge ordering is appearing unidirectionally along the short lattice parameter axis. Finally, we discuss the interplay between charge ordering and superconductivity. The temperature versus Pt substitution phase diagram 15 suggests that these two phases are competing. Based on our resistivity data, we argue that superconductivity may survive into the uniaxial charge ordering phase however the transition gradually broadens to a point where zero resistance is not observed. We discuss possible explanations of this effect in terms of (1) chemical and electronic inhomogeneity, (2) granular superconductivity and (3) a threeto two-dimensional electronic transition.

Results
Cooling and warming resistivity curves are plotted in Fig. 1, for different compositions of Ir 1−x Pt x Te 2 as indicated. Similar curves are shown for Ir 0.95 Pt 0.05 Te 2 for different levels of hydrostatic pressures as indicated. The hysteresis loops indicate a first order transition that certainly is related to the lowering of crystal lattice symmetry and/or the emergence of charge order. From the resistivity curves, alone, it is however not possible to determine whether the transition is electronic or lattice driven. To illustrate this point, we show in Fig. 1(c) resistivity curves of the stoichiometric compounds IrTe 2 , CuIr 2 Te 4 and PtTe 2 . Among these materials, charge ordering has only been observed in IrTe 2 . The hysteretic resistive behaviour of CuIr 2 Te 4 is therefore not caused by charge ordering, but rather by a structural transition. In Fig. 1(d) and (e) the superconducting transition of Ir 1−x Pt x Te 2 is displayed and To gain further insight into the relation between the lattice and charge order, we carried out an x-ray diffraction study. In Fig. 2(a), we show the fundamental lattice Bragg peak τ = (1, 0, 1) measured at low temperature on Ir 0.95 Pt 0.05 Te 2 at different pressures as indicated. At low pressure (p = 400 bar) a single sharp Bragg peak is observed. Above a critical pressure p c1 , this peak develops a shoulder that upon further increased pressure evolves into a separate Bragg peak. When heating above 200 K, this Bragg peak splitting disappears. Altogether, this evidences a low-temperature pressure-induced lowering of the lattice symmetry.
With this knowledge, we studied the charge order in the pressure-induced twinned phase of Ir 0.95 Pt 0.05 Te 2 . The crystal was carefully aligned on the τ = (3, 0, 3) Bragg peak using the larger lattice constant. At the highest applied pressure .  p 17 7 kbar, a q co = (±1/5, 0, ±1/5) charge modulation is observed with respect to the Bragg peak with the shorter lattice parameter [see Fig. 2(c)]. The charge ordering reflection displays, just as the resistivity curves, hysteretic behaviour as a function of temperature [inset of Fig. 2(e)]. Finally, we show in Fig. 2(e) how upon cooling the charge order reflection and the short-axis Bragg peak τ = (4, 0, 4) have identical temperature dependence. This demonstrates an intimate relation between the crystal lattice symmetry breaking and charge ordering.

Discussion/Interpretation
Lattice vs electronic mechanism. We start by discussing the nature of the charge ordering transition. The pressure-induced Bragg peak splitting [ Fig. 2(a)] is most naturally explained in terms of domain formation caused by a lowering of the crystal lattice symmetry. In essence, our experiment suggests that the lattice parameters along the (1, 0, 1) and (0, 1, 1) directions become inequivalent under application of pressure. The system thus develops three domains with a short lattice parameter along the → a , → b or → − → a b axes, see Fig. 3(a). All three types of domain are observed when scanning along the (1, 0, 1) direction in the pressure-induced twinned phase and hence two Bragg peaks are found -shown in Fig. 2(a). This twinning effect clearly appears before charge ordering, suggesting that the latter is lattice driven. Given that we observe the same (1/5, 0, 1/5) modulation as in IrTe 2 (high-temperature), it is not inconceivable that the same conclusion applies to the parent compound. Combining our results with previous studies of IrTe 2 , we propose in Fig. 4(a) a schematic pressure, Pt substitution and temperature phase diagram including the charge ordering and the structural hexagonal to monoclinic transition.
Charge order structure. The surface and bulk charge ordering structure of IrTe 2 has been studied by scanning tunnelling microscopy (STM) 29-34 and x-ray diffraction 24,25,35 techniques. The STM studies generally find uniaxial charge ordering structures. Furthermore, differences in charge modulations between the bulk and  surface have been pointed out 34 . Our bulk-sensitive results on Ir 0.95 Pt 0.05 Te 2 indicate that the pressure-induced charge order is connected to the short-axis direction only. Therefore, the most simple explanation is uniaxial Ir 3+ -Ir 3+ dimer formation along the short lattice parameter axis as illustrated in Fig. 3(b). For such a structure, an electronic gap is expected only along the reciprocal short lattice parameter axis. However since the crystals are inevitably twinned along three different directions, it can be challenging to observe with angle resolved photoemission spectroscopy (ARPES) experiments, in particular when factoring in the complex electronic band structure [36][37][38] . A suppression of the spectral weight (near the Fermi level) is observed with ARPES and optical experiments. This observation is at odd with a conventional charge density wave and hence taken as evidence of novel type of charge ordering 36,38,39 . Superconductivity and Charge order. Finally, we discuss the relation between unidirectional charge order and superconductivity. From our pressure-dependent x-ray and resistivity experiments, we show that a lowering of the crystal symmetry has no impact on superconductivity [see Figs 1(e) and 4(b)]. Upon entering into the charge ordered phase, the superconducting transition however, broadens dramatically. While the initial superconducting onset remains fairly constant, the onset of zero resistance (within the detection limit) undergoes dramatic changes. In fact as a function of pressure, the system quickly reaches a regime where zero resistance is not observed within the measured temperature window [see Fig. 1(e)]. The same trend is found at ambient pressure when lowering the Pt content [see Fig. 1(d) and (f)]. Hence there seems to be a correlation between the occurrence of the charge order and a broadening of the superconducting transition. On general grounds, such a broadening can have different explanations. (1) Chemical or electronic inhomogeneities can smear the transition.
(2) Granular superconductivity is also characterised by broad transitions. (3) Low-dimensional superconductivity is known to introduce two temperature scales. In particular, for two-dimensional superconductivity, an exponential resistive drop, approximately described by ρ ∝ − ( ) being a second superconducting temperature scale. This Kosterlitz -Thouless transition 40,41 , scenario finds its relevance in Ir 1−x Pt x Te 2 , since charge order is shown to generate two dimensional walls of low density-of-states 24,25,[42][43][44] . It is therefore not inconceivable that superconductivity is suppressed inside these walls. Hence there exists a possible physical mechanism for two-dimensional superconductivity in Ir 1− x Pt x Te 2 . Further experimental evidence supporting this scenario would be of great interest. Based on the experimental evidence presented here, it is difficult to prove the Kosterlitz -Thouless scenario. Nor can we completely exclude inhomogeneities or grain boundaries. Chemical inhomogeneity is very unlikely to be the cause, since it should not be influenced by hydrostatic pressure. Inhomogeneous pressure can also be excluded as the broadening is found also at ambient pressure [see Fig. 1(d)]. Intrinsic electronic inhomogeneity could be tuned by both pressure and chemical substitution. However, one would expect that inhomogeneity generates more modest correlation length of the charge order. Experimentally, however, long range (resolution limited) charge order reflections are observed. The domain formation makes the granular superconducting scenario more plausible. We notice, however, that the pressure induced crystal domain formation initially have no influence on superconductivity. Explaining our data in terms of granular superconductivity is therefore not straightforward.

Conclusion
In summary, we have presented a combined resistivity and x-ray diffraction study of Ir 1−x Pt x Te 2 as a function of Pt substitution and hydrostatic pressure. Just below the critical composition x c ~ 0.045 charge order with a (1/5, 0, 1/5) wave vector is found. The same modulation appears in Ir 0.95 Pt 0.05 Te 2 upon application of hydrostatic pressures beyond p c2 ~ 16 kbar. Based on these observations a charge ordering phase diagram is constructed. Application of pressure furthermore revealed a lattice symmetry lowering transition appearing before the charge ordering. We thus conclude that the charge ordering in Ir 1−x Pt x Te 2 is lattice driven. Finally, we discussed the relation between charge order and superconductivity.

Methods
Single crystals of Ir 1−x Pt x Te 2 were grown using a self-flux technique 39 . Piston-type pressure cells 45 with Daphne oil as pressure medium were used to reach ~18 kbar and 23 kbar, for x-ray diffraction and resistivity experiments respectively. The hydrostatic pressure was estimated from the orthorhombicity of La 1.85 Ba 0.125 CuO 4 at 60 K 46 and the resistive superconducting transition of lead. The electrical resistivity was measured by a conventional four-probe method using a physical property measurement system (Quantum Design PPMS-14T) and hard x-ray diffraction (100 keV) experiments were carried out with the triple-axis instrument at beamline P07 at PETRA III, DESY. Although Ir 1−x Pt x Te 2 at certain temperatures and pressures displays crystal structure twinning, the momentum Q = (h, k, l) is presented in hexagonal notation with a ≈ b ≈ 3.95 Å and c ≈ 5.38 Å. Crystallographic projections were produced using the VESTA software 47 .
The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.