Decoupling of Lattice and Orbital Degrees of Freedom in an Iron-Pnictide Superconductor

The interplay of structural and electronic phases in iron-based superconductors is a central theme in the search for the superconducting pairing mechanism. While electronic nematicity, defined as the breaking of four-fold symmetry triggered by electronic degrees of freedom, is competing with superconductivity, the effect of purely structural orthorhombic order is unexplored. Here, using x-ray diffraction (XRD), we reveal a new structural orthorhombic phase with an exceptionally high onset temperature ($T_\mathrm{ort} \sim 250$ K), which coexists with superconductivity ($T_\mathrm{c} = 25$ K), in an electron-doped iron-pnictide superconductor far from the underdoped region. Furthermore, our angle-resolved photoemission spectroscopy (ARPES) measurements demonstrate the absence of electronic nematic order as the driving mechanism, in contrast to other underdoped iron pnictides where nematicity is commonly found. Our results establish a new, high temperature phase in the phase diagram of iron-pnictide superconductors and impose strong constraints for the modeling of their superconducting pairing mechanism.

The interplay of structural and electronic phases in iron-based superconductors is a central theme in the search for the superconducting pairing mechanism. While electronic nematicity, defined as the breaking of four-fold symmetry triggered by electronic degrees of freedom, is competing with superconductivity 1,2 , the effect of purely structural orthorhombic order is unexplored. Here, using x-ray diffraction (XRD), we reveal a new structural orthorhombic phase with an exceptionally high onset temperature (T ort ∼ 250 K), which coexists with superconductivity (T c = 25 K), in an electron-doped ironpnictide superconductor far from the underdoped region. Furthermore, our angle-resolved photoemission spectroscopy (ARPES) measurements demonstrate the absence of electronic nematic order as the driving mechanism, in contrast to other underdoped iron pnictides where nematicity is commonly found. Our results establish a new, high temperature phase in the phase diagram of iron-pnictide superconductors and impose strong constraints for the modeling of their superconducting pairing mechanism.
Underdoped iron-pnictides commonly host a nematic state below T nem in which the four-fold rotational C 4 symmetry is spontaneously broken into C 2 symmetry in electron, spin and structural degrees of freedom 3 (see Figs. 1 a-b). Due to its close proximity to superconductivity and its putative quantum criticality 4-6 the nematic phase has been heavily investigated for elucidating a microscopic description of the superconducting pairing mechanism. Among other experiments, transport 7-9 and ARPES 10-15 studies provided compelling evidence that nematicity in underdoped iron-pnictides is triggered by electronic order, subsequently driving other degrees of freedom such as the lattice to break C 4 symmetry 2 . In ARPES the orbital order was directly revealed by the splitting of the d xz -d yz bands, which are degenerate in the high-temperature tetragonal phase (see Fig.  1 b). In some parent compounds, a band splitting of up to ∼ 60 meV was observed [10][11][12][13] , which is too large to be a trivial consequence of the small orthorhombicity of less than 1% (ref. 16). This led to the conclusion that electronic order is driving the nematic state in underdoped pnictides 17 , triggering a tetragonal-to-orthorhombic transition in the lattice degrees of freedom at the same temperature scale (T ort = T nem ). Importantly, XRD measurements of the orthorhombic distortion revealed that the electronically driven nematic phase is competing with superconductivity 2 . However, due to the strong coupling of electronic and lattice degrees of freedom, the competing channel (i.e. electronic or structural) is ambiguous.
Here, we report the observation of a new, purely structural orthorhombic phase in the electron-doped iron-pnictide superconductor Pr 4 Fe 2 As 2 Te 0.88 O 4 (PFATO, T c = 25 K) [18][19][20] . Our XRD study revealed that this phase has an exceptionally high onset temperature of T ort = 250 K. This is ∼ 50 K higher than the maximum T ort which has so far been observed in iron-based superconductors 3 .
Considering the high electron doping of 0.12 electrons per Fe, this observation is unexpected. Furthermore, we find that the lowtemperature structural orthorhombic order parameter δ is not suppressed below T c indicating a "friendly" coexistence of orthorhombicity with superconductivity. The structural (phononic) origin of this phase is further supported by our ARPES measurements which reveal the absence of orbital splitting down to lowest temperatures within the applied energy resolution. These properties are orthogonal to what has been found for the nematic phase in underdoped iron-pnictides and therefore indicate that this orthorhombic phase is new and distinct from previously described phases in iron-pnictides.
We directly reveal the tetragonal-to-orthorhombic phase transition in PFATO by XRD measurements of the (1,1,0) Bragg reflection. At room temperature, x-ray diffraction studies have previously shown that PFATO has a tetragonal I4/mmm structure with a large c-axis (29.86Å) lattice parameter 19 (see Fig. 1 c). As shown in Fig. 1 d-e, below T ort = 250 K, the (1,1,0) reflection (inset of Fig. 1 d) splits into two peaks along the transverse direction, evidencing the existence of orthorhombicity. The gradual (continuous) onset of the orthorhombic order parameter at T ort suggests a second-order phase transition 21 , congruent to what is found in parent compounds of iron-pnictides 3 and FeSe 22 . However, the onset temperature is ∼ 50 K higher than the highest structural arXiv:1910.01639v2 [cond-mat.supr-con] 28 Jul 2020 transition temperature in any other iron-pnictide parent compound 3 . In light of the rather high electron doping of Pr 4 Fe 2 As 2 Te 0.88 O 4 (0.12 electrons per Fe, see supplementary information), such a high onset temperature is surprising and indicates that this orthorhombic phase is different in nature from the electronic nematic phase in underdoped iron-pnictides.
By analysing the structural peak splitting 24 , we infer the orthorhombic order parameter Fig. 1 a). As shown in Fig. 1 f, δ gradually increases and plateaus below ∼ 50 K at 12×10 −4 . Importantly, δ retains its maximum value for all temperatures below T c (within error bars) indicating friendly coexistence with superconductivity (see inset of Fig. 1 f). This is in contrast to the strong phase competition between the electronically induced nematic phase of underdoped iron-pnictides in which nematicity gets suppressed below T c and C 4 rotational symmetry restores at low temperatures close to optimal doping 2 . It has been suggested that the suppression of orthorhombicity in the electronic nematic phase is indirect and arises due to the competition for the same electronic states between magnetism and superconductivity 1 . This suggests that orthorhombicity in Pr 4 Fe 2 As 2 Te 0.88 O 4 is not triggered by electronic degrees of freedom which compete with superconductivity.
In order to reveal rotational symmetry breaking in the electronic degrees of freedom, we performed highresolution ARPES measurements on twinned samples. At this point it is worth noting that due to the very small sample size of ≤ 50 × 50µm 2 usual methods such as in-plane resistivity anisotropy on detwinned samples are not feasible. However, as ARPES directly accesses the electronic structure in momentum space it presents a suitable technique to measure the electronic nematic order parameter on twinned samples by resolving the d xz -d yz orbital splitting 10 .  to the very large c-axis lattice constant we don't expect any significant out-of-plane dispersion, as suggested by our DFT calculations (see supplementary Fig. S1 a-b).
Electronic nematicity manifests as an energy splitting of the d xz and d yz orbitals, as sketched in Figs. 1 b and  3 b. In the following, we disentangle the bands of different orbital character by using light polarisation analysis on a twinned sample (Figs. 3 c-n, supplementary Fig.  S2-S7). Using π and σ polarised light we observe two electron-like bands around M 1 , which we identify as the d xy band (blue) and a superposition of the d xz and d yz bands (see Figs. 3 c-f). Past reports on the electronically driven nematic phase in iron pnictides have shown that the nematic order parameter is largest at the M point 14 .
Our curvature plots (Fig. 3 e,f) show that neither of the two bands splits in energy or momentum direction. A cut through M 0 with circular polarised light is shown in Fig. 3 g. We observe the d xz -d yz hole-like band at binding energy of E B ∼ −100 meV. Similarly to the two electron-like bands, this band is also not energy-split within our experimental resolution (see Methods), as seen in the curvature and second derivative plots (Fig. 3 h  In iron-pnictides, the structural orthorhombicity in the nematic phase is suppressed below T c (see Ref. 2), indicating a competition between superconductivity and electronic nematicity. Therefore, it is important to check if superconductivity is suppressing any possible band splitting in Pr 4 Fe 2 As 2 Te 0.88 O 4 . We recorded the temperature dependence of the bands at the M and Γ point up to 56 K (∼ 2 × T c , see supplementary Fig. S6 and S7) and observe that the d xz -d yz bands remain degenerate up to highest measured temperatures at both high-symmetry points (Γ and M).
We summarize our multifold high-resolution ARPES study on a twinned Pr 4 Fe 2 As 2 Te 0.88 O 4 sample in Fig. 3 a. For comparison, Fig. 3 b depicts the expected band structure of a twinned sample with a low-temperature electronic nematic phase (see supplementary Fig. S2  p), which is distinct from our observations. To further exclude that the here observed orthorhombic phase is driven by electronic degrees of freedom, we estimate the expected nematic order parameter (δ nem ) by comparing the low-temperature structural orthorhombic order parameter of Pr 4 Fe 2 As 2 Te 0.88 O 4 , δ ∼ 12 × 10 −4 to other iron-pnictides. We find that Ba(Fe 1−x Co x ) 2 As 2 , (x ∼ 0.05) shows a similar δ (see Ref. well detectable in our measurements. On the other hand, it has been suggested that δ nem generally scales with the orthorhombic transition temperature in the electronic nematic phase 17 . This would set the expected band splitting in Pr 4 Fe 2 As 2 Te 0.88 O 4 to > 100 meV. Our experiments definitely exclude such a splitting. The absence of the d xz -d yz splitting (see Fig. 3) suggests that the structural orthorhombicity is not driven by electronic nematicity in Pr 4 Fe 2 As 2 Te 0.88 O 4 .
In combination our XRD and ARPES study on the iron-based superconductor PFATO provide strong evidence for a new phase in the iron-pnictide phase diagram.
The direct comparison between Pr 4 Fe 2 As 2 Te 0.88 O 4 and the widely studied Ba(Fe 1−x Co x ) 2 As 2 system (Fig. 4) highlights the difference between the electronic nematic phase and the here discussed structural orthorhombic phase from the perspective of the doping dependence. The phase transition of the electronic nematic phase has its highest T nem at the parent compound which is then decaying once electrons are doped into the system. Furthermore, it is closely accompanied by a spin-density wave (SDW) phase which follows a similar doping-dependence. So far, a magnetic transition has not been found in Pr 4 Fe 2 As 2 Te 0.88 O 4 18-20 , but could possibly be stabilised under pressure, similar to bulk FeSe 25 . Furthermore, the absence of SDW order could be explained by the poorly fulfilled nesting condition, due to the absence of the holelike Fermi surface around Γ (see Fig. 2 a). From this standpoint it is hard to imagine that the orthorhombic phase of 12 % electron-doped PFATO has a similar doping dependence and is of the same origin as the nematic phase.
PFATO therefore presents an iron pnictide with a purely structural phase transition right on top of the superconducting dome. The structural phase transition is likely driven by phonon modes which make this system highly interesting for studying the influence of lattice vibrations on the superconducting pairing mechanism. Our observation therefore calls for further experimental and theoretical investigations in order to understand the interplay between this structural instability and superconductivity.