Dirac-fermion-assisted interfacial superconductivity in epitaxial topological-insulator/iron-chalcogenide heterostructures

Over the last decade, the possibility of realizing topological superconductivity (TSC) has generated much excitement. TSC can be created in electronic systems where the topological and superconducting orders coexist, motivating the continued exploration of candidate material platforms to this end. Here, we use molecular beam epitaxy (MBE) to synthesize heterostructures that host emergent interfacial superconductivity when a non-superconducting antiferromagnet (FeTe) is interfaced with a topological insulator (TI) (Bi, Sb)2Te3. By performing in-vacuo angle-resolved photoemission spectroscopy (ARPES) and ex-situ electrical transport measurements, we find that the superconducting transition temperature and the upper critical magnetic field are suppressed when the chemical potential approaches the Dirac point. We provide evidence to show that the observed interfacial superconductivity and its chemical potential dependence is the result of the competition between the Ruderman-Kittel-Kasuya-Yosida-type ferromagnetic coupling mediated by Dirac surface states and antiferromagnetic exchange couplings that generate the bicollinear antiferromagnetic order in the FeTe layer.

Main text: Decoherence of a quantum state causes errors during the process of quantum computation and thus is the major obstacle to the realization of practical quantum computers.
Majorana zero modes (MZMs), which obey non-Abelian statistics, are arguably the most promising anyon platform towards fault-tolerant quantum computing since they are expected to be inherently robust against local perturbation and decoherence effects.MZMs are expected to be bound to vortex cores in the presence of topological superconductivity (TSC) and appear as a zeroenergy state inside the superconducting gap.The TSC phase can be created in hybrid structures where an electronic system with spin-split bands caused by strong spin-orbit coupling (SOC) is proximally coupled to a conventional s-wave superconductor [3][4][5] .This idea led to the fabrication of semiconductor nanowires covered with superconducting layers [6][7][8][9] and magnetic metallic wires on superconducting substrates 10,11 .So far, several experiments have reported evidence of MZM in 1D semiconducting nanowire/superconductor devices, such as unusual zero-bias conductance peak [6][7][8] and fractional AC Josephson effect 9 .However, there are serious concerns about the validity of such claims of MZMs in these devices [12][13][14] .These concerns provide new impetus to explore TSC in other systems.
Since topological insulators (TIs) possess strong SOC-induced inherent topological nontrivial band structures with inverted bulk conduction and valence bands, TIs provide a natural platform to pursue TSC.When a TI is coupled to a conventional s-wave superconductor through the proximity effect, TSC is expected to emerge 3 .Compared to the Rashba bands (i.e. the strong SOC-induced momentum-dependent band splitting) in 1D semiconducting nanowire systems 6,10,15,16 , TI films have two advantages: (i) The helical Dirac surface states of TIs lift the spin degeneracy, thus bypassing the SOC-plus-Zeeman splitting control needed in 1D nanowire systems 6 ; (ii) The bandgap of canonical TIs such as the Bi-chalcogenides is typically a few hundred meV (Refs. 17,18) as compared to the magnetic field-induced Zeeman splitting of ~1 meV in 1D nanowire systems [6][7][8] .A large gap provides more flexibility for the realization of the TSC phase.Moreover, TI/superconductor heterostructures allow surface-sensitive probes such as angleresolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy and spectroscopy (STM/S) to directly probe the surface states.Such heterostructures also allow established transport techniques to be deployed for the exploration of the putative Majorana physics 3 .An ideal TI-based TSC platform would be comprised of an epitaxial heterostructure wherein both TI and superconductor layers are synthesized by molecular beam epitaxy (MBE), thus allowing precise engineering of the TI/superconductor interface and the band structure.
However, there remains an important obstacle, specifically, the superconductivity in MBE-grown thin superconducting films usually disappears once a TI layer is grown on top, presumably due to the occurrence of charge transfer 19 .
An alternative approach is to exploit the emergent interfacial superconductivity that arises in certain TI/non-superconducting material heterostructures that fulfill the two essential ingredients of TSC, i.e. topological and superconducting orders 3 .Recently, interfacial superconductivity has been observed in Bi2Te3/FeTe and Sb2Te3/FeTe heterostructures with superconducting temperatures of Tc ~11.5 K and ~3.1 K, respectively 20,21 .In these two heterostructures, Bi2Te3 and Sb2Te3 are heavily electron-and hole-doped TI, respectively 17,22,23 , while FeTe is an antiferromagnetic iron chalcogenide that is non-superconducting without element doping 24,25 and/or tensile stress 26 .Notably, a proximity effect-induced superconducting gap has been demonstrated on the top surface of the Bi2Te3/FeTe heterostructure, setting the stage for the potential TSC phase 27 .Compared to bulk iron-based superconductors with a band topology such as FeTe0.55Se0.45(Ref. 28) and LiFeAs (Ref. 29), the (Bi,Sb)2Te3/FeTe heterostructures provide the tunability of chemical potential across a single Dirac cone, without resorting to introducing disorder or applying strain in the sample to tune for the TSC phase.
In this work, we use MBE to synthesize (Bi,Sb) 2 Te 3 /FeTe heterostructures with an atomically sharp interface, in which the chemical potential of the ternary TI (Bi,Sb)2Te3 can be tuned by varying the Bi/Sb ratio 30,31 .By performing in-vacuo ARPES and ex-situ electrical transport measurements, we find that interfacial superconductivity appears in all (Bi,Sb) 2 Te 3 /FeTe heterostructures that we studied and we find both the superconducting transition temperature and the upper critical magnetic field are suppressed when the chemical potential approaches the Dirac point.This observation indicates the correlation between massless Dirac electrons of the TI layer and the interfacial superconductivity in (Bi,Sb) 2 Te 3 /FeTe heterostructures.We show evidence that the chemical potential dependence of interfacial superconductivity is a result of the competition between bicollinear antiferromagnetic order in the FeTe layer and the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction mediated by surface Dirac electrons of the TI layer 32 .
All (Bi1-xSbx)2Te3/FeTe (0 ≤ x ≤ 1) bilayer heterostructures are synthesized in an MBE chamber (ScientaOmicron), which is connected to an ARPES chamber.The MBE growth is monitored using in-situ reflection high-energy electron diffraction (RHEED) (Supplementary Fig. 1).The in-vacuo ARPES measurements are carried out using a Scientia DA30L analyzer with unpolarized He-Iα light (∼21.2eV).Our MBE-grown (Bi1-xSbx)2Te3/FeTe films are characterized by scanning transmission electron microscopy (STEM) (Fig. 1 and Supplementary Figs. 2 to 5), atomic force microscopy (Supplementary Fig. 6), and ARPES (Fig. 2 and Supplementary Figs. 7 to 11) measurements.The electrical transport studies are performed on mechanically scratched sixterminal Hall bar devices (Supplementary Fig. 12) with the magnetic field applied perpendicular to the film plane.More details about the MBE growth, sample characterization, and electrical transport measurements can be found in Methods.
Neither (Bi,Sb)2Te3 nor FeTe crystals by themselves are superconductors.The (Bi,Sb)2Te3 lattice is built from quintuple layer (QLs) containing two Bi layers and three Te layers 30,31 , while the FeTe unit cell (UC) consists of one Fe layer and two Te layers (Fig. 1a).Although (Bi,Sb)2Te3 and FeTe have different lattice symmetry (hexagonal vs cubic, respectively), the van der Waals nature of both materials allows for epitaxial growth of (Bi,Sb)2Te3/FeTe heterostructures.To evaluate the changes of in-plane lattice constant in 8QL (Bi1-xSbx)2Te3 layer on 50UC FeTe heterostructures, we extract the line intensity distribution curve from their RHEED patterns (Supplementary Fig. 1a).The spacing distance d between the intensity peaks is inversely proportional to the lattice constant.We note that the d value of the FeTe layer is close to that of the Bi2Te3 layer because the in-plane lattice constant ratio between FeTe and Bi2Te3 is ~ √3: 2 (Ref. 33).With increasing x, the value of d expands, suggesting a gradual reduction of the lattice constant in the (Bi1-xSbx)2Te3 layer (Supplementary Figs.1g and 4).This will induce compressive stress if it exists in the FeTe layer.In Supplementary Fig. 5c, the d value of FeTe is smaller compared to that of Sb2Te3, which is a result of the in-plane lattice mismatch between Sb2Te3 and FeTe layers.The monotonic decrease of the in-plane lattice constant indicates a van der Waals epitaxy growth mode in our (Bi1-xSbx)2Te3/FeTe heterostructures.Moreover, we observe the twin domain feature with a rotation angle of ~30 o in these heterostructures (Supplementary Figs. 5 to   7), further verifying an epitaxial growth of the heterostructures between two materials with hexagonal and cubic lattice structures 33 .Figure 1b shows the cross-sectional STEM image of an 8 QL (Bi,Sb)2Te3/50 UC FeTe heterostructure.We see the QL and trilayer atomic structures of (Bi,Sb)2Te3 and FeTe, respectively.Moreover, a highly ordered and sharp interface is seen between (Bi,Sb)2Te3 and FeTe even with different lattice structures.Supplementary Figs. 2 to 4 show the corresponding energy dispersive spectroscopy (EDS) maps of Fe, Bi, Sb, and Te, which confirm the automatically sharp interfaces in our (Bi,Sb)2Te3/FeTe heterostructures.
We next perform transport measurements on 50 UC FeTe, 8 QL Bi 2 Te 3 /50 UC FeTe, and 8 QL Sb 2 Te 3 /50 UC FeTe heterostructures.The 50 UC FeTe sample shows a semiconducting-tometallic transition at T ~54 K.Such behavior in the R-T curve of FeTe has been associated with the paramagnetic-to-antiferromagnetic phase transition 21 .This magnetic ordering temperature is known as the Néel temperature TN (Fig. 1c).The spin fluctuation of the antiferromagnetic order has been proposed to be correlated to the superconductivity in Fe(Se,Te) single crystals 34 .For the 8 QL Bi 2 Te 3 /50 UC FeTe heterostructure (i.e. the x=0 sample), the onset Tc,onset and the zero resistance Tc,0 are ~13.6K and ~12.5 K, respectively (Fig. 1c).For our Sb2Te3/FeTe heterostructure (i.e. the x=1 sample), Tc,onset and Tc,0 are ~12.5 K and ~11.3 K, respectively (Fig. 1c).Compared to prior studies 20,21 , the higher Tc and much narrower superconducting transition windows observed here reveal that our MBE-grown Bi2Te3/FeTe and Sb2Te3/FeTe heterostructures are much more uniform and homogeneous.
To demonstrate the topological property of the (Bi1-xSbx)2Te3 layer, we perform in-vacuo ARPES measurements on a series of (Bi1-xSbx)2Te3/FeTe heterostructures with different x (Fig. 2 and Supplementary Figs. 9 and 10).The high quality of the FeTe layer is confirmed by observing a hole-type pocket near  point (Supplementary Fig. 8), consistent with prior studies 33 .In all (Bi1-xSbx)2Te3/FeTe heterostructures with 0 ≤ x ≤ 1, we observe linearly dispersed Dirac surface states at room temperature (Fig. 2 and Supplementary Fig. 9).We define the value of the Fermi momentum kF as the momentum at which the left branch of the Dirac surface states crosses the chemical potential.For the x = 0 sample, kF ~ -0.106 Å -1 and the Dirac point is buried in the bulk valence bands, ~245 meV below the chemical potential (Fig. 2a).A similar Fermi momentum kF is derived from ARPES band maps at low temperatures (Supplementary Fig. 11).With increasing x, the chemical potential moves downward and gradually approaches the Dirac point.Specifically, at kF ~ -0.082 Å -1 , -0.054 Å -1 , -0.025Å -1 , -0.015 Å -1 for the x=0.2, 0.4, 0.6, and 0.7 samples, respectively (Figs. 2b to 2e).For the x = 0.8 sample, the chemical potential almost crosses the Dirac point and kF ~ -0.005 Å -1 (Fig. 2f).With further increasing x, the chemical potential is below the Dirac point for the x = 1 sample and kF ~0.034 Å -1 (Fig. 2g).Therefore, our ARPES results show an electron-to hole-type crossover for the Dirac surface states in 8 QL (Bi1-xSbx)2Te3/50 UC FeTe heterostructures.In addition, we find that with increasing x, one bulk valence band moves upwards, while the other one moves downwards (Supplementary Fig. 10).
To examine the role of the Dirac electrons in the development of the interfacial superconductivity, we perform electrical transport measurements on these 8 QL (Bi1-xSbx)2Te3/50 UC FeTe heterostructures (Fig. 3).Figures 3a to 3h show R-T curves of eight different (Bi1-xSbx)2Te3/ FeTe heterostructures with different x under magnetic field 0H = 0 T and 0H = 9 T.
To determine the values of 0Hc2,⊥ of these (Bi1-xSbx)2Te3/FeTe heterostructures, we perform electrical transport measurements under high perpendicular magnetic fields.Figure 3i shows R-0H curves of six (Bi1-xSbx)2Te3/FeTe heterostructures at T = 1.5 K.We define the value of 0Hc2,⊥ as the magnetic field at which R drops to half of the normal resistance.For the x = 0 sample, 0Hc2,⊥ ~ 46.7 T, which is much larger than the value in a prior work 20 .With increasing x, the value of 0Hc2,⊥ first decreases and then increases.Specifically, we find 0Hc2,⊥ ~44.8 T, ~41.3 T, ~36.3 T, ~38.8 T, and 43 T for the x = 0.4, 0.7, 0.8, 0.95, and 1.0 samples, respectively.Therefore, 0Hc2,⊥ has a minimum near x = 0.8 (Fig. 3i).The sheet longitudinal resistance R also shows a maximum value near x = 0.8, confirming our ARPES results that the chemical potential meets the Dirac point of the TI layer near x = 0.8 (Fig. 2).Supplementary Fig. 12 shows the more pronounced dip features of 0Hc2,⊥ at 5K, 7K, and 9K.
To reveal the link between Dirac surface states and the formation of the interfacial superconductivity in (Bi1-xSbx)2Te3/FeTe heterostructures, we plot the values of kF, Tc,onset, Tc,0, and 0Hc2, ⊥ as a function of the Sb concentration x (Figs.4a to 4c).For x < 0.85, the negative kF indicates the n-type Dirac fermion in the TI layer, Tc,onset, Tc,0, and 0Hc2,⊥ decrease with increasing x.For x > 0.85, the positive kF indicates the p-type Dirac fermion in the TI layer, Tc,onset, Tc,0, and 0Hc2,⊥ increase with increasing x.The values of Tc,onset, Tc,0, and 0Hc2,⊥ show a minimum (Figs.4b and 4c) when the chemical potential approaches the Dirac point, indicating that the Dirac electrons of the TI layer participate in the formation of the interfacial superconductivity.On the other hand, the formation of coherent Cooper pairs with condensed Dirac electrons is a prerequisite for the appearance of the TSC phase and Majorana physics in the (Bi1-xSbx)2Te3/FeTe heterostructures.
In the following, we discuss the possible origins of the interfacial superconductivity and its chemical potential dependence in (Bi1-xSbx)2Te3/FeTe heterostructures.The dip observed in the   ~ phase diagram (Fig. 4b) is likely a result of two main effects: (i) the charge transfer effect between (Bi1-xSbx)2Te3 and FeTe layers, and (ii) the suppression of long-range antiferromagnetic order in the FeTe layer.First, both work functions in Bi2Te3 (~5.3 eV) and Sb2Te3 (~5.0 eV) are greater than that of FeTe (4.4~4.8 eV) (Ref. 27,35,36).This work function mismatch between (Bi1-xSbx)2Te 3 and FeTe is expected to cause a charge transfer, which may lead to the different energy levels for the Dirac points on the top and bottom [i.e. the (Bi1-xSbx)2Te3/FeTe interface] surfaces of (Bi1-xSbx)2Te3.As a consequence, the minimum value of Tc is anticipated to be observed away from the Bi/Sb ratio at which the chemical potential crosses the Dirac point on the top surface of (Bi1-xSbx)2Te 3.In our experiments, the chemical potential crosses the Dirac point at x=0.8 (Fig. 4a).
However, the minimum values of both Tc, onset and Tc,0 are observed at x=0.85 (Fig. 4b).This observation further implies that the presence of band bending in the (Bi1-xSbx)2Te3 layer.Prior studies 27,36 have claimed the occurrence of hole carrier transfer from Bi2Te3 to FeTe, which may give rise to interfacial superconductivity in the FeTe layer by screening out the strong Coulomb repulsion.However, in this doping effect hypothesis 37 , the   value of (Bi1-xSbx)2Te3/FeTe heterostructures is likely to be enhanced or suppressed monotonically by tuning  from 0 to 1.
This assumption certainly cannot be the entire explanation in creating the interfacial superconductivity because it is inconsistent with the observed dip in our   ~ phase diagram (Fig. 4b).
To understand the   dip, we examine the second hypothesis that the origin of interfacial superconductivity in (Bi1-xSbx)2Te3/FeTe heterostructures lies in the coupling with Dirac surface states that suppresses the long-range antiferromagnetic order of the FeTe layer.As noted above, our transport results indicate that the long-range antiferromagnetic order is weakened or even destroyed after the deposition of the (Bi1-xSbx)2Te3 layer (Fig. 1c and Supplementary Fig. 14).
Besides the charge transfer effect, we note that an RKKY magnetic exchange interaction in FeTe can be caused through its coupling to Dirac surface states near the interface 32,38 , which could renormalize the spin-spin interactions and tune the magnetic ground state in the FeTe layer.For example, the antiferromagnetic order of FeTe can be described by the  1 −  2 −  3 spin model, where  1,2,3 are the magnetic exchange interactions (Fig. 4d) and are all positive (i.e.antiferromagnetic) 39 .Once the FeTe layer is coupled to the (Bi1-xSbx)2Te3 layer, the local magnetic moments of Fe tend to be aligned to the spin direction of the Dirac surface states, leading to the RKKY interaction between different Fe magnetic moments.Prior studies 32,38,40,41 have shown that the Dirac surface states mediated RKKY interaction consists of Heisenberg-like, Ising-like, and Dzyaloshinskii-Moriya (DM)-like terms, all of which are not compatible with the bi-collinear antiferromagnetic order and can lead to strong magnetic fluctuations.Therefore, the RKKY interaction, in addition to the doping effect 27,36 , may weaken or even destroy the bi-collinear antiferromagnetic order in the FeTe layer, so superconductivity is expected to emerge.
Next, we show that the RKKY interaction also explains the chemical potential dependence of Tc observed in our experiments.As discussed in Refs. 32,38, when the chemical potential approaches the Dirac point, the oscillation feature of RKKY interaction becomes weaker or even disappears as   → 0 and Fermi wavelength   = 1   → ∞.Specifically, a correction to the spinspin interaction in the FeTe layer can be found,   ′ =   +   (    ), from the RKKY interaction (Methods), where   is the RKKY-induced interaction at two sites with the distance   ( = 1,2,3 label the nearest neighbor  1 =   , next nearest neighbor  2 = √2  , and the third nearest neighbor  3 = 2  ) and has a negative sign (i.e.ferromagnetic type).Prior studies 42- 45 have shown that that the dominant superconducting pairing is determined by the next nearestneighbor exchange coupling  2 ′ term, which gives rise to the spin-singlet  ± -wave pairing with the gap function form Δ( ⃗ ) = cos   cos   in iron chalcogenides (Fig. 4f and Methods) 46,47 .At the interface,  2 > 0 from the intrinsic antiferromagnetic contribution in the FeTe layer should be dominant over the correction of ferromagnetic   < 0, which comes from the proximity from Dirac surface states to magnetic moments in FeTe.Therefore, we expect  2 ′ constantly has a positive sign (antiferromagnetic).As the amplitude |  | increases first and then decreases with increasing Sb concentration x (Fig. 4e),  2 ′ is expected to first decrease and then increase accordingly.Consequently, the mean-field critical temperature   ∝  − 4 3 0  2 ′ (Methods), where  0 is the electron density of states, is expected to exhibit a non-monotonic behavior.We note that the parameters used in our theoretical calculations are extracted from our experiments.|  | is estimated to be ~1 meV for   → 0, which is comparable to the intrinsic  2 ~10 meV (Methods).To summarize, we synthesize a series of (Bi,Sb) 2 Te 3 /FeTe heterostructures and find that interfacial superconductivity appears in these heterostructures.By performing ARPES and electrical transport measurements, we find the superconducting temperature and the upper critical magnetic fields are suppressed when the chemical potential approaches the Dirac point.These observations reveal the correlation between the interfacial superconductivity and the Dirac surface states in the TI layer, indicating the Dirac electrons in the TI layer must play a role in the formation of the interfacial superconductivity.The dip in the Tc~x phase diagram can be understood as a consequence of the complex competition between the RKKY interaction and antiferromagnetic exchange coupling.Our experiments provide evidence for Dirac-fermion-assisted interfacial superconductivity in (Bi,Sb) 2 Te 3 /FeTe heterostructures and thus provide strong motivation for using this as a model material system for exploring Majorana physics and topological quantum computation.We also envision that extending (Bi,Sb)2Te3/FeTe bilayers to multilayers could provide a rich platform for the pursuit of other emergent topological phenomena, including Weyl superconductors 48 .

MBE growth
The (Bi1-xSbx)2Te3/FeTe heterostructures are synthesized in a commercial MBE system (ScientaOmicron) with a vacuum better than 2 × 10 −10 mbar.The insulating SrTiO3 (100) substrates are first soaked in ~80°C deionized water for 1.5 hours and then put in a diluted hydrochloric acid solution (~4.5% w/w) for 1 hour.These SrTiO3 (100) substrates are then annealed at ~974°C for 3 hours in a tube furnace with flowing high-purity oxygen gas.Through the above heat treatments, the SrTiO3(100) substrate surface becomes passivated and atomically flat, which becomes suitable for the MBE growth of the FeTe films.We next load the heat-treated SrTiO3 (100) substrates into our MBE chamber and outgas them at 600℃ for ~1 hour.High-purity Bi (99.9999%),Sb (99.9999%),Te (99.9999%), and Fe (99.995%) are evaporated from Knudsen effusion cells.The growth temperature is maintained at ~340 ℃ and ~ 210 ℃ for the MBE growth of the FeTe and (Bi,Sb)2Te3 layers, respectively.The growth rate is set to ~0.4 UC/min for the FeTe film, and ~0.2 QL/min for the (Bi,Sb)2Te3 layer, which is calibrated by measuring the thickness of the (Bi,Sb)2Te3/FeTe bilayer heterostructures using both STEM and atomic force microscopy measurements.Finally, to avoid possible contamination, a ~10 nm Te layer is deposited at room temperature on top of the bilayer heterostructures before their removal from the MBE chamber for ex-situ electrical transport measurements.

ADF-STEM measurements
The aberration-corrected ADF-STEM measurements are performed on an FEI Titan 3 G2 STEM operating at an accelerating voltage of 300 kV, with a probe convergence angle of 25~30 mrad, a probe current of 70~100 pA, and ADF detector angles of 42~253 mrad.More STEM images and EDS maps of (Bi,Sb)2Te3/FeTe heterostructures can be found in Supplementary Figs. 2 to 5.

ARPES measurements
We perform in-vacuo ARPES measurements in a chamber with a base vacuum better than 5 × 10 −11 mbar.After finishing the MBE growth, the (Bi,Sb)2Te3/FeTe bilayer heterostructures are transferred from the MBE chamber to the ARPES chamber.The energy analyzer DA30L (ScientaOmicron) is used.We use a helium-discharge lamp with a photon energy of ~21.2 eV.The energy and angle resolutions are set to ~10 meV and ~0.1º, respectively.We note that He Ⅰ  light with an energy of ~21 eV is sensitive to the sample surface 49 .

Electrical transport measurements
The (Bi,Sb)2Te3/FeTe bilayer heterostructures are scratched into a Hall bar geometry using a computer-controlled probe station.The Hall bar device size is ~ 1 mm × 0.5 mm (Supplementary Fig. 12).We made the electrical contacts by pressing tiny indium spheres on the Hall bar, and the presence of the indium contacts does not influence the interface-induced superconducting in (Bi1-xSbx)2Te 3/FeTe heterostructures (Supplementary Fig. 15).The electrical transport measurements are conducted using a Physical Property Measurement Systems (Quantum Design DynaCool 1.7 K, 9 T) and a capacitor-driven 65 T pulsed magnet at the National High Magnetic Field Laboratory (NHMFL), Los Alamos.The excitation current is ~1 A for all R-T measurements.
The Hall trace of the FeTe layer shows a nearly zero slope at low temperatures (Supplementary Figs.16 and 17), which indicates a significantly higher carrier density in the FeTe layer.
Consequently, the Hall trace of the (Bi1-xSbx)2Te3/FeTe heterostructure does not accurately reflect the carrier density (or the position of the chemical potential) in the (Bi1-xSbx)2Te3 layer (Supplementary Fig. 17).For the (Bi1-xSbx)2Te3 layer without the FeTe layer, a comprehensive analysis comparing kF derived from ARPES and Hall transport measurements has been carefully studied in our prior work 30 .Therefore, for the (Bi1-xSbx)2Te3/FeTe heterostructures used in this work, the kF value obtained from ARPES measurements is considered more reliable in reflecting the position of the chemical potential position of (Bi1-xSbx)2Te3.

X-ray diffraction reciprocal space mapping (RSM) measurements
We perform XRD reciprocal space mapping (RSM) measurements on Bi2Te3/FeTe and Sb2Te3/FeTe heterostructures, respectively (Supplementary Fig. 18).RSMs are collected on a 320 mm radius Panalytical X'Pert 3 MRD four circle X-ray diffractometer equipped with a line source For the 8 QL Bi2Te3/50 UC FeTe heterostructure, the out-of-plane Bi2Te3(0 0 15) and off-axis (0 1 5) reflections are measured (Supplementary Figs.18a and 18b), which are used to determine the in-plane and out-of-plane lattice constants.The calculated strain in the Bi2Te3 layer is ~ 1% inplane tensile strain, with no significant strain observed out of the plane.For the 8 QL Bi2Te3/50 UC FeTe heterostructure, a light strain is observed in the in-plane or out-of-plane directions (~ 0.3%) (Supplementary Figs.18d and 18e).The presence of a small strain in the (Bi1-xSbx)2Te3 layer grown on the FeTe layer implies no changes in the topological properties of (Bi1-xSbx)2Te3 (Refs. 50,51).Moreover, the twin domains with a 30 o rotation are further verified by φ scans of (Bi1-xSbx)2Te 3/50 UC FeTe heterostructures (Supplementary Figs.18c and 18f), which are consistent with our RHEED, atomic force microscopy, and ARPES measurements (Supplementary Figs. 1, 6,   and 7).

Surface Dirac electrons mediated RKKY interaction
We investigate the RKKY interaction within adjacent magnetic moments on the TI surface (Supplementary Fig. 19).The two magnetic moments are labeled by  1 and  2 (Supplementary Fig. 19a).The TI surface here can serve as the interface that is coupled with the FeTe layer.The magnetic moments likely have their origin in the extra iron impurities on the surface of the FeTe layer near the TI/FeTe interface.To simplify our theoretical model, we only consider the Dirac surface states of the TI layer (Supplementary Fig. 19b).This simplification is scientifically sound because the chemical potential is located within the bulk band gap as the Sb concentration x varies from 0 to 1.Moreover, unlike the oscillating RKKY interaction in a conventional metal, the RKKY of the TI/FeTe heterostructure shows a relatively strong ferromagnetic-type RKKY interaction, primarily induced by a small   .Here the   value of the surface Dirac electrons is much less than that of the TI bulk states.
Here  is the Fermi velocity of Dirac electrons, (  ,   ) is the momentum,   is the effective spin-spin interaction strength,  ⃗ 1,2 are the location of magnetic moments  1,2 , and   is the spin operator for the Dirac electrons in real space.
The RKKY interaction between  1 and  2 is given by where  0 is the in-plane area of the TI unit cell and   is the in-plane spatial distance between the two magnetic moments 32 .Note that the constant coefficient with Λ is the cutoff.In our calculations, we choose Λ = 120 which is sufficiently large because of the maximal     ~ 1.Here Γ is the phenomenological imaginary self-energy correction that describes the disorder broadening.The real part of self-energy provides corrections to the energy of Dirac points and the velocity of the Dirac surface states 52 .The RKKY interaction as a function of z at different self-energies is shown in Supplementary Fig. 19c.We find that Φ  () curves become monotonic when Γ ≥ 0.3.In the region with a larger Γ, the RKKY interaction is constantly ferromagnetic at a small .For a selected   = √2  for the next nearest neighbor sites, where   is the lattice constant of FeTe, we expect the RKKY interaction can reach a maximal value for   ~ 0 (Supplementary Fig. 19d).We plot When   is small, the ferromagnetic interaction strength is large for a small   .Only for a relatively large   , the intra-band scattering contribution   dominates the RKKY interaction strength.Therefore, the typical RKKY oscillations are observed in real space (the black curve in Supplementary Fig. 19d), similar to the RKKY behavior in a conventional metal.For a small   , the inter-band scattering contribution   dominates, which shows a strong ferromagnetic type RKKY interaction (the green curve in Supplementary Fig. 19d).
We employ the above method to calculate the strength of RKKY interaction in the (Bi,Sb)2Te3/FeTe heterostructure.  = √2  and self-energy Γ = 0.6 are used.The values of   are extracted from our ARPES data (Fig. 2).The estimated RKKY strength in (Bi,Sb)2Te3/FeTe heterostructures is shown in Fig. 4e.We also consider the weak x dependence of  that leads to error bars.  < 0 is negative, revealing a ferromagnetic-type RKKY interaction.When   is near the Dirac point, the inter-band contribution dominates, and a larger RKKY interaction   is achieved (Supplementary Fig. 19).Note that similar results are expected for smaller values of   .Below we list the parameters used in our theoretical calculations.For different Sb concentrations , the values of   are extracted from our ARPES band maps in Fig. 2  In FeTe, the value of   has been determined to be ~50 meV (Ref. 53).Therefore, we assume a comparable energy scale range of [10,100] meV for   and estimate the ferromagnetic-type RKKY strength   within the range of −[0.02, 1.9]  at   → 0. This value is in the order of 1 , which can greatly reduce the antiferromagnetic coupling in FeTe, whose energy scale can be estimated from the critical temperature of the bi-colinear AFM order (TN ~68 K) 54,55 .
Therefore, it can significantly affect   of the interface-induced superconductivity in our (Bi,Sb)2Te3/FeTe heterostructures.
As discussed in the main text, the ferromagnetic type RKKY interaction competes with the superconducting order near the TI/FeTe interface, which can lower Tc.
photoemission spectroscopy (ARPES) and ex-situ electrical transport measurements, we find

When 𝐽 2 ′
reaches a minimum when the chemical potential is near the Dirac point (kF~0), the superconducting pairing shows a dip in the   ~ phase diagram (Figs. 4b).Our experimental results thus suggest a mechanism of correlating the interfacial superconductivity with surface Dirac electrons in (Bi1-xSbx)2Te3/FeTe heterostructures through the chemical potential tuning of spin-spin interaction across the interface.Besides the above direct correction to short-range   in the atomic scale, the long-range ferromagnetic component of the RKKY interaction may also arise in the scale of the superconducting coherence length.As the spin-singlet pairing is incompatible with ferromagnetic coupling, this long-range ferromagnetic component of the RKKY interaction may further weaken the superconductivity when the chemical potential approaches the Dirac point.We note that the DM component of the RKKY interaction also remains for the chemical potential near the Dirac point, which can support skyrmion spin texture40 .A complete understanding of the influence of the complex RKKY interaction on the pairing symmetry and mechanism of the emergent interfacial superconductivity in (Bi1-xSbx)2Te3/FeTe heterostructures needs further theoretical and experimental studies.

[
Cu Kα1-2 (1.540598/1.544426Å)]X-ray tube operating at ~45 kV and ~40 mA.The incident beam path includes a 2×Ge(220) asymmetric hybrid Kα1 monochromator and a 1/4° divergence slit.A PIXcel3D 1×1 detector operating in frame-based mode is used to measure the RSMs.The lower and upper levels of the pulse height distribution are set at ~4.02 and ~11.27 keV, respectively.The heterostructures are aligned using the SrTiO3(002) reflection and the azimuthal angle for off-axis peaks is aligned using the φ scans.The in-plane lattice constant is determined by measuring the off-axis peaks in the symmetric geometry after tilting the sample in  because the reflections available for asymmetric scans had very low intensities.The 2 positions for reflections are measured by fitting a Lorentzian function to the data.
and are plotted in Fig.4a.Based on our ARPES band maps, we obtained the Fermi velocity  ≈ 3.5  ⋅ Å.The area  0 .84Å 2 and the distance   ≈ 5.34 Å.

, 2 2𝑚−2𝑒
where   ( ⃗ ,   ) = 1   −  ⃗ ⃗ ,  ℎ ( ⃗ ,   ) = 1   +  ⃗ ⃗ , and   = (2 + 1 )   is the Matsubara frequency of fermions.The form factor cos   cos   in the above  0 () comes from the attractive interaction   ⃗ , ⃗ ′ in the Hamiltonian   2 .With a simple parabolic dispersion   ⃗ =   for electron pockets, we can obtain  0 ()) with  0 the electron density on the Fermi energy,  = 0.57721 the Euler-Mascheroni constant and   is the large energy cutoff.Therefore, the linearized gap equation gives the mean-field   = 2 .As we expect,   decreases exponentially as  2 decreases (assuming  2 > 0).As we discussed in the main text, the decrease of  2 is caused by the RKKY interaction mediated by the surface Dirac electrons, which explains the Tc dip observed in our experiments.

Figures
Figures and figure captions:

Fig
Fig. 4| Dirac-fermion-assisted interfacial superconductivity in (Bi 1-x Sb x ) 2 Te 3 /FeTe Our theoretical calculations point out a possible macroscopic model to understand the superconducting   dip near the Dirac point of the TI layer.The  2 term for the antiferromagnetic interaction between next-nearest Fe atoms is renormalized as  2 ′ =  2 +   (    ) and thus alters by varying   .Though the sign of   is negative, which make  2 ′ smaller than  2 .But  2 ′ is still assumed to be positive, Therefore, our experimental and theoretical studies suggest that the Dirac electrons participate in interaction Hamiltonian, we can perform the mean field decomposition to derive the linearized gap equation 3 2  0 () = 1, where  0 () is the superconductivity susceptibility as defined below, to compute the mean-field superconducting critical temperature   .The superconductivity