Interfacial superconductivity in a bi-collinear antiferromagnetically ordered FeTe monolayer on a topological insulator

The discovery of high-temperature superconductivity in Fe-based compounds triggered numerous investigations on the interplay between superconductivity and magnetism, and on the enhancement of transition temperatures through interface effects. It is widely believed that the emergence of optimal superconductivity is intimately linked to the suppression of long-range antiferromagnetic (AFM) order, although the exact microscopic picture remains elusive because of the lack of atomically resolved data. Here we present spin-polarized scanning tunnelling spectroscopy of ultrathin FeTe1−xSex (x=0, 0.5) films on bulk topological insulators. Surprisingly, we find an energy gap at the Fermi level, indicating superconducting correlations up to Tc∼6 K for one unit cell FeTe grown on Bi2Te3, in contrast to the non-superconducting bulk FeTe. The gap spatially coexists with bi-collinear AFM order. This finding opens perspectives for theoretical studies of competing orders in Fe-based superconductors and for experimental investigations of exotic phases in superconducting layers on topological insulators.

T opological insulators (TIs) and interfacial superconductors (SCs) are both topics of intense current interest in modern condensed matter physics 1,2 . The combination of both materials is expected to reveal novel physics such as, for example, Majorana Fermions arising in heterostructures of TIs and s-wave SCs by including magnetic fields 3 . Most experimental studies of such heterostructures have concentrated on TI films grown on superconducting bulk substrates 4 . Alternatively, SC/TI heterostructures could be realized by growing superconducting films on top of pristine bulk TIs.
In the past years, studies of Fe-based SCs and their electronic and magnetic properties have been one of the major research fields in condensed matter physics 5,6 . The recent finding that the superconducting transition temperature T c can be pushed above 100 K in an FeSe unit cell (UC) thin film grown epitaxially on SrTiO 3 (refs 7-9) spurred numerous investigations aiming at an exact understanding of how the superconductivity in transition metal mono-and dichalcogenides evolves from bulk to ultrathin films. Bulk FeSe crystals exhibit a T c of no higher than 8 K (ref. 10). The significant interfacial enhancement of T c in UC FeSe on SrTiO 3 as well as in similar systems, such as FeSe on BaTiO 3 (ref. 11) and FeTe 1 À x Se x on SrTiO 3 12 , leads to a revival of the idea that tailoring the electron pairing by interfacing a SC with another material can be used to achieve high-temperature SC 1 . Interestingly, SC can even emerge by interfacing two insulators 13 or a TI (Bi 2 Te 3 ) with a non-SC Fe-chalcogenide (FeTe) 14,15 . It is therefore of great importance to understand how different substrates affect the electronic, spin-dependent and superconducting properties of single-layer Fe-based SCs. The latter studies 14,15 raised the fundamental question of what happens to the bi-collinear antiferromagnetic (AFM) structure of FeTe (ref. 16) once an interfacial SC state is established in contact with Bi 2 Te 3 . In the work of He et al. 14 , it was proposed that the topological surface state may dope the FeTe and suppress the long-range AFM order at the interface, thereby inducing the observed interfacial SC.
By a low-temperature spin-polarized scanning tunnelling spectroscopy (SP-STS) investigation of the correlation between the film structure, the local electronic, superconducting and spindependent properties, we show here that, in contrast to this assumption, the energy gap at the Fermi level in UC thin FeTe films epitaxially grown on Bi 2 Te 3 (111) can spatially coexist on the atomic scale with long-range bi-collinear AFM order.

Results
Structural properties of FeTe 1 À x Se x thin films. We have prepared ultrathin epitaxial FeTe films on Bi 2 Te 3 single crystals by in situ deposition of Fe on the TI substrates under ultrahigh vacuum (UHV) conditions, followed by an in situ annealing treatment (see Methods section). Figure 1a depicts a constantcurrent scanning tunnelling microscopy (STM) topographic image of such a film with FeTe islands of different thicknesses, together with regions of the bare substrate. We distinguish between these different areas based on the measured step heights and differences in the observed atomic-scale surface structures. The line profile displayed in Fig. 1b taken across three different terraces separated by two steps reveals a step height h (a-b) of hB0.65±0.05 nm, roughly equal to the c axis lattice constant (0.62 nm) of bulk FeTe, while the right step b-c is considerably smaller (hB0.35±0.05 nm). The smaller step results from an FeTe UC being embedded in the topmost quintuple layer of the substrate, most probably as sketched in Fig. 1b. Figure 1e presents an atomically resolved STM topographic image of the substrate area (Bi 2 Te 3 ), which reveals the hexagonal close-packed atomic lattice (see inset Fast Fourier transform (FFT) image) of top Te atoms with a spacing of B0.44 nm. A topographic STM image of the top UC layer of FeTe, with an atomic contrast determined by the topmost chalcogenide (Te) layer (Fig. 1f), reveals that the a axis of the FeTe is aligned parallel to one of the closed packed directions of the substrate Te atoms. The period of the atomic lattice along the a axis direction is B0.38 nm, which is consistent  with the Te-Te atomic distance on the surface of bulk FeTe (ref. 17). The period along the b axis is slightly smaller (a/ bB1.04), which might be partly attributed to the transition into the orthorhombic/monoclinic phase, known for bulk FeTe 18 , but could be enhanced by uniaxial strain as a result of the heteroepitaxial growth. This holds for the embedded UC FeTe as well as for thicker layers ( Supplementary Fig. 1). However, there is no overall periodic height modulation of the UC FeTe layers, and only in some areas of the thinnest islands irregular wrinkles are observed. This indicates a rather weak interaction of the FeTe layer with the substrate, in contrast to what has been observed for FeSe grown on Bi 2 Se 3 (ref. 19). The Fourier transform of the topographic image (inset of Fig. 1f) clearly shows the peaks associated with the almost square Te atomic lattice, with the spots along the a direction (q Te a ) slightly more intense than those along the b direction (q Te b ; ref. 16). Despite the different lattice symmetries (sixfold for Bi 2 Te 3 and fourfold for FeTe) with respect to the c axis directions and the relatively large lattice mismatch, the heteroepitaxial growth is of very high quality, resulting in an atomically sharp and defect-free interface. In contrast to the surface of bulk FeTe (ref. 16), the surfaces of our ultrathin FeTe films do not show any excess Fe atoms, indicating a stoichiometric FeTe layer.
Although the focus of the present study is on the single layer of FeTe on Bi 2 Te 3 (111), ultrathin FeTe 1 À x Se x (x ¼ 0.5) films grown on the ternary TI Bi 2 Te 1.8 Se 1.2 (111) serve as an important reference system 20 . In the corresponding bulk system, FeTe exhibits a bi-collinear AFM order, while superconductivity can be induced and substantially enhanced up to 15 K with partial substitution of Se for Te at x ¼ 0. 5 (ref. 12). It is therefore particularly interesting to investigate how the superconducting state develops from a magnetically ordered state with Se substitution in the thin-film system we studied here.
High-quality, one UC thin FeTe 0.5 Se 0.5 films (Supplementary Fig. 2) with well-defined stoichiometry were epitaxially grown on Bi 2 Te 1.8 Se 1.2 (111) substrates using a similar preparation method as for the FeTe films. Atomically resolved topographic STM images of the cleaved Bi 2 Te 1.8 Se 1.2 substrate surface (Fig. 1g) show Se and Te atoms in the topmost layer of the surface appearing with slightly darker and brighter contrast, respectively, with a frequency in accordance with the stoichiometry 21 . A typical topographic STM image of a one UC thin FeTe 0.5 Se 0.5 film grown on top ( Fig. 1h) reveals an ordered square lattice of Se/Te atoms with about half of the atoms appearing brighter (52%, Te sites) while the other half appears darker (48%, Se sites), with a height difference of 65 ± 15 pm, close to the value found for similarly doped FeTe 1 À x Se x samples 12,22 .
Characterization of superconducting properties. To characterize the electronic structure of these films, STS measurements of the differential tunnelling conductance (dI/dU) as a function of the applied bias voltage were performed, reflecting the sample's local density of states. Figure 2a shows single tunnelling spectra measured on the one UC thin FeTe 0.5 Se 0.5 film and on the Bi 2 Te 1.8 Se 1.2 substrate at a temperature of T ¼ 1.1 K. The FeTe 0.5 Se 0.5 film exhibits an overall U-shaped dI/dU spectrum with an almost vanishing conductance value at the Fermi level (E F ) and an energy gap of D ¼ 2.5 meV, defined by half the distance between the two sharp coherence peaks in Fig. 2a. This measured gap value is of the same order of magnitude as measured on the surface of the corresponding superconducting bulk material 23 . In order to determine the critical temperature T c of our FeTe 0.5 Se 0.5 films, we performed temperature-dependent measurements of dI/dU from 1.1 to 11 K (see Fig. 2b). As expected, the observed energy gap in dI/dU becomes shallower with increasing temperature and eventually disappears at B11 K. The energy gap values for different temperatures (shown in Fig. 2c) were extracted from fits of the background-corrected and symmetrized dI/dU spectra (for data processing see Supplementary Fig. 3) employing the Dynes density of states, , with the density of states in the normal state at the Fermi energy N n (E F ) and the real part <, where the parameter G accounts for the lifetime broadening of the quasiparticles 24 . The fitting of the temperature dependence of the gap in the framework of the Bardeen-Cooper-Schrieffer (BCS) theory 25 yields an energy gap at 0 K of D 0 ¼ 2.0 meV and an extracted T c ¼ 11 K, similar to the values that have been extracted from STS on the corresponding superconducting bulk materials 23,26 . The temperature dependence of the dI/dU spectra as well as the derived T c value provide strong evidence that the observed gap feature arises from superconductivity in the ultrathin FeTe 0.5 Se 0.5 film grown on Bi 2 Te 1.8 Se 1.2 . Now we turn to the investigation of the electronic and magnetic structure of ultrathin FeTe films grown on Bi 2 Te 3 . Figure 2d shows a series of spatially averaged dI/dU spectra measured at T ¼ 1.1 K on the Bi 2 Te 3 substrate as well as on ultrathin FeTe films of different thicknesses. For both embedded UC and top UC FeTe layers a reduced dI/dU at E F with diffuse peaks at energies of ±1 to ±2 meV are found with a gap width and occurrence of the peaks varying with position ( Supplementary Fig. 4). A gap of this size and temperature dependence (shown below) has not been observed at the surface of bulk FeTe (refs 27,28) or for FeTe single layers grown on SrTiO 3 (ref. 12). The Fermi-level gap gradually vanishes for increased thicknesses of FeTe layers on Bi 2 Te 3 . For example, two UC thin FeTe films show a gap with a significantly reduced depth at E F . This behaviour suggests that the FeTe/Bi 2 Te 3 interface plays a significant role for the observed gap structure. In order to reveal the origin of the energy gap in one UC thin FeTe films grown on Bi 2 Te 3 , we thoroughly investigated the temperature and field dependence of the dI/dU spectra. Figure 2e shows a series of background-corrected and symmetrized temperature-dependent dI/dU spectra for top UC FeTe on Bi 2 Te 3 . The tunnelling spectrum at T ¼ 1.1 K exhibits a pair of diffuse peaks at UB2 meV together with a gap region of reduced local density of states at E F . We observe that the gap depth and peak height in dI/dU decrease with increasing temperature and finally vanish above T ¼ 6 K, very reminiscent of a superconducting transition. In order to test this hypothesis, the temperature-dependent spectra were fitted to a Dynes density of states (Fig. 2e). Here we note that a considerable lifetime broadening G had to be assumed ( Supplementary Fig. 5). The temperature dependence of the fitted energy gap values (Fig. 2f) resembles that of a superconducting phase transition (cf. Fig. 2c). Kondo correlations, which were shown to cause dip features at E F for heavy Fermion systems 29 and might be present on the Fe lattice as well, are ruled out, as they would show a different temperature dependency of the gap depth ( Supplementary Fig. 6). In addition, unlike under-doped cuprates, where a pseudogap phase appears above T c (ref. 30), the gap in our tunnelling spectroscopy data always closes at T c B6 K, thereby ruling out the presence of a pseudogap state. The spectral features therefore strongly suggest superconducting correlations of the UC FeTe layer. In order to extract the corresponding T c , we fit the temperature dependence of the gap in the framework of the BCS theory (Fig. 2f), resulting in T c B6.5 K. Together with the zero temperature gap value of D 0 ¼ 1.05 meV extrapolated from the BCS fit we deduce a ratio of 2D 0 /k B T c B3.8 for one UC thin FeTe on Bi 2 Te 3 , which is comparable to the value of 4.2 we determine for the FeTe 0.5 Se 0.5 thin film on Bi 2 Te 1.8 Se 1.2 , but somewhat larger than typical values of 2.5-3.2 for bulk FeTe 1 À x Se x samples 23,26 . We note that the embedded UC of FeTe also shows a similar temperature-dependent behaviour ( Supplementary Fig. 7). Our results are consistent with the transport measurements of Fe 1 þ x Te films grown on Bi 2 Te 3 (ref. 15) where evidence for superconductivity with a T c B12 K was reported. We do not observe any significant effect on the energy gap in a magnetic field up to B ¼ 2.8 T applied perpendicular to the sample plane ( Supplementary Fig. 8). This suggests that the robustness of the pairing with respect to an external magnetic field is similarly strong as for other Fe-based superconducting thin films 7 , and an identical effect has been observed in magnetotransport measurements of a Bi 2 Te 3 /FeTe heterostructure 14,15 .
Spatial variation of superconducting correlation. Having established clear evidence for superconducting correlations in single UC FeTe layers grown on Bi 2 Te 3 below 6 K, we now focus in more detail on the spatial behaviour of these correlations at the lateral interface of the FeTe layer and the Bi 2 Te 3 substrate. In particular, we measured the spatial variation of tunnelling spectra across a step edge from the embedded UC FeTe layer to the Bi 2 Te 3 substrate (Fig. 3a,b). The resulting tunnelling spectra across the interface along the line shown in Fig. 3a obtained at T ¼ 1.1 K (Fig. 3c) again show the presence of the gap due to superconducting correlations on top of the FeTe layer, which vanishes on the TI substrate. To quantify the decay length of the superconducting correlations in our heterostructure system, we have fitted the spatial dependence of the gap area with an exponential decay function (Fig. 3d), resulting in a decay length of about x ¼ 8.9 Å at T ¼ 1.1 K. This decay length is a measure for the coherence length of the Cooper pairs 31,32 , which is obviously similarly small as, for example, in bulk FeTe 0. 6   In order to check this assumption, we simultaneously characterized the local superconducting correlations and the atomic-scale spin structure of the ultrathin FeTe films grown on Bi 2 Te 3 by SP-STS 33 . By using a spin-polarized bulk Cr tip 34 , we excluded the disturbing influence of a local magnetic stray field on the sample while being sensitive to its out-of-plane surface spin component. Figure 4a represents the spin-resolved constant-current image of a single UC thin embedded FeTe layer on Bi 2 Te 3 as obtained in an external magnetic field of B ¼ þ 1 T applied perpendicular to the sample surface. The SP-STM image shows a clear stripe-like pattern, superimposed on the square atomic lattice of surface Te atoms, which is significantly different from the STM topography obtained with a non-magnetic PtIr tip as presented in Fig. 1f. The Fourier transform (inset of Fig. 4a) of the SP-STM image reveals an additional pair of peaks along the a direction with a wave vector q AFM ¼ 1/2 q Te a that is half as long as that of the atomic lattice Bragg peaks. This unidirectional modulation with a characteristic periodicity of l ¼ 2a ¼ 7.5 Å (see Fig. 4e) has been attributed to a direct observation of bi-collinear AFM order of the Fe atoms below the surface of bulk Fe 1 þ y Te using SP-STM 16 . To confirm the magnetic origin of the observed superstructure with twice the atomic lattice periodicity, we performed an SP-STM measurement at the same location with an oppositely aligned effective spin at the Cr tip's front end by reversing the magnetic field to B ¼ À 1 T (see Fig. 4b). Now, the 2a superstructure reveals a phase shift (indicated by an arrow) of one atomic lattice unit as expected for a magnetic origin of the contrast. The maximum spin contrast appears between every second Fe lattice site along a diagonal of the surface UC being located between two neighbouring Te sites. This can be explained by the fact that spin-polarized tunnelling primarily results from the 3d states of Fe being located below the top Te layer. It is also clearly visible from the line profiles of Fig. 4e along the a direction, which were extracted from Fig. 4a,b, and by the 2a periodicity along the a direction in the out-of-plane spinpolarization distribution of the FeTe layer (Fig. 4c) obtained by subtracting the SP-STM images of Fig. 4a,b. These observations prove that single UC FeTe films on Bi 2 Te 3 exhibit a bi-collinear AFM structure, similar to the one known for bulk FeTe (ref. 16), but with a non-vanishing out-of-plane surface spin component 35 . Note that the same bi-collinear AFM structure was also observed for the thicker islands in our samples (Supplementary Fig. 9). To our knowledge, this is the first direct real-space observation of magnetic order in an Fe-chalcogenide compound at the single UC thickness limit.
The observed coexistence of magnetic order in UC FeTe, which is similar to the one found at the surface of the corresponding bulk material 16 , and superconducting correlations, which are not present in bulk FeTe, is quite surprising. In order to find a mutual relationship between magnetic order and superconductivity, we performed SP-STM experiments as a function of temperature from 1 to 10 K. Representative SP-STM images and corresponding FFT data obtained at temperatures T ¼ 1, 6 and 10 K are shown in Fig. 5a-f. The position of the surface area is the same in all three SP-STM data sets. The spin contrast is clearly reflected by the superstructure with twice the atomic lattice periodicity, and in the corresponding FFT data by the spots at wave vector q AFM ¼ 1/2 q Te a . Most notably, the spin structure does not change and the intensity of the spin contrast is almost the same for all three temperatures shown here. Similar SP-STM images at other temperatures have been taken in order to quantify the temperature evolution of the spin contrast via the ratio of FFT intensities of the q AFM spots to the Bragg spots at q Te a . Figure 5g shows this evolution together with the evolution of the superconducting energy gap taken from Fig. 2f. The comparison clearly demonstrates that the bi-collinear AFM order is largely unaffected by the disappearance of the superconducting correlations. Therefore, our experimental results do not provide any evidence that one kind of order emerges at the expense of the other, nor does the data provide any indication for a microscopic phase separation into regions with superconducting and magnetic order. Our findings for single UC thin FeTe layers on Bi 2 Te 3 therefore challenge the common belief that optimal superconducting pairing sets in when long-range AFM order is suppressed in the parent compound.

Discussion
In summary, we have explored the electronic and magnetic structure in a new class of systems, that is, heterostructures consisting of ultrathin Fe-chalcogenide layers of the type FeTe 1 À x Se x (x ¼ 0, 0.5) on Bi-based TI substrates. We observe fully developed U-shaped superconducting gaps in FeTe 0.5 Se 0.5 layers of one UC thickness with a transition temperature of T c B11 K, close to the one of the corresponding bulk system (T c B14.5 K). For FeTe/Bi 2 Te 3 heterostructures, our atomic-scale spin-resolved tunnelling spectroscopy measurements provide evidence for the coexistence of superconducting correlations with T c B6.5 K and bi-collinear AFM order in the one UC FeTe films. Although the coexistence of static magnetic order and superconductivity was observed earlier by spatially averaging techniques in several systems such as Fe-pnictides 36,37 , heavy fermion compounds 38 and Fe-chalcogenides 39 , the exact microscopic picture of the coexistence still remained unclear because of a lack of spatially resolved data 40 . Here we can compare the wavelength of the AFM order of l ¼ 2a ¼ 7.5 Å with the size of the Cooper pairs, inferred from the coherence length, of x ¼ 8.9 Å, giving x/lB1.2. The electron distance in the pairs is rather small, which is typical for Fe-based SCs, and apparently just large enough such that the effective Zeeman field induced by the AFM order cancels out along the length of the Cooper pair. The relative sizes of l and x therefore might be crucial for the coexistence of pairing and longrange AFM order in this material. Our surprising findings may stimulate further theoretical studies on the relationship between superconductivity and AFM order in Fe-based SCs. We finally note that the leakage of the gap into the TI substrate across the FeTe-Bi 2 Te 3 interface (Fig. 3c) indicates the presence of superconducting correlations in the TI material close to the interface. The atomic sharpness of this interface suggests that the topological surface state of the TI substrate stays intact as also shown recently by photoemission experiments for the case of a FeSe-Bi 2 Se 3 heterostructure 41 . The FeTe-Bi 2 Te 3 interface therefore provides an ideal platform to study the interesting physics of Dirac fermions interacting with Cooper pairs.

Methods
Samples. Bulk TI single crystals of Bi 2 Te 3 and Bi 2 Te 1.8 Se 1.2 used in this study as substrates were synthesized using a Stockbarger method and have been well characterized using angle-resolved photoemission spectroscopy, powder X-ray diffraction, inductively coupled plasma atomic-emission spectroscopy and potential Seebeck microprobe measurements 21,42 . For all substrates the Dirac point is located energetically below the Fermi level indicating n doping. Fe-chalcogenide film preparation and characterization were carried out in a UHV system with a base pressure below 1 Â 10 À 10 mbar. The TI crystals were cleaved in situ under UHV conditions and high-quality FeTe 1 À x Se x (x ¼ 0, 0.5) thin films were prepared by depositing 0.5-1 ML Fe at 300 K on-top of Bi 2 Te 3 and Bi 2 Te 1.8 Se 1.2 substrates, respectively, using molecular beam epitaxy, followed by annealing up to a maximum temperature of 315°C for 15 min. Fe deposited on Bi 2 Te 3 reacts with the substrate upon annealing, most likely via a substitutional process of Bi by Fe (ref. 43), leading to a high-quality defect-free FeTe film.
Experimental techniques. All STM/STS experiments were performed with an STM in UHV at temperatures between 1.1 and 14 K (ref. 24). A magnetic field B of up to 3 T can be applied perpendicular to the sample surface. Topography images were obtained in constant-current mode with stabilization current I s and bias voltage U applied to the sample. STS data were obtained using a lock-in technique to record the differential tunnelling conductance dI/dU by adding an AC modulation voltage U mod (given in r.m.s.) to the bias voltage, after stabilizing the tip at I s and U, switching off the feedback, and ramping the applied bias U. We used cut PtIr or electrochemically etched W tips (both in situ flashed) for spin-averaged imaging and spectroscopy measurements. For spin-resolved measurements, we used bulk Cr tips, which were prepared by electrochemical etching followed by a high-voltage field emission treatment using W(110) or Ta(001) as a substrate.
Data availability. The authors declare that the main data supporting the findings of this study are available within the article and its Supplementary Information files. Extra data are available from the corresponding author upon request.