Studies on the origin of the interfacial superconductivity of Sb₂Te₃/Fe_1+yTe heterostructures

Significance

Interfacial superconductivity (SC) is found in the Sb₂Te₃/FeTe heterostructure system, of which neither the Sb₂Te₃ topological insulator (TI) nor the FeTe parent compound of iron chalcogenides is superconducting. We have systematically studied some factors that are responsible for inducing the 2-dimensional SC, including the spin fluctuation of antiferromagnetic ordering in Fe_1+yTe layer and the thickness of Sb₂Te₃. These findings help us understand the mechanism of the unconventional SC at the interface of TI/FeTe heterostructures. TI/FeTe heterostructures will provide a new platform for trapping and controlling Majorana fermions.

Abstract

The recent discovery of the interfacial superconductivity (SC) of the Bi₂Te₃/Fe_1+yTe heterostructure has attracted extensive studies due to its potential as a novel platform for trapping and controlling Majorana fermions. Here we present studies of another topological insulator (TI)/Fe_1+yTe heterostructure, Sb₂Te₃/Fe_1+yTe, which also has an interfacial 2-dimensional SC. The results of transport measurements support that reduction of the excess Fe concentration of the Fe_1+yTe layer not only increases the fluctuation of its antiferromagnetic (AFM) order but also enhances the quality of the SC of this heterostructure system. On the other hand, the interfacial SC of this heterostructure was found to have a wider-ranging TI-layer thickness dependence than that of the Bi₂Te₃/Fe_1+yTe heterostructure, which is believed to be attributed to the much higher bulk conductivity of Sb₂Te₃ that enhances indirect coupling between its top and bottom topological surface states (TSSs). Our results provide evidence of the interplay among the AFM order, itinerant carries from the TSSs, and the induced interfacial SC of the TI/Fe_1+yTe heterostructure system.

Three-dimensional topological insulators (3D TIs) with extraordinary electronic states have attracted intense research interest in recent years due to their unusual electronic band structures (1–4). In an ideal 3D TI, bulk states feature an energy gap like an ordinary insulator, while surface states are characterized by a linear Dirac-like dispersion energy band with spin texture locked helically to momentum, resulting in metallic topological surface states (TSSs). The most studied 3D TIs include Bi₂Se₃, Bi₂Te₃, and Sb₂Te₃ binary compounds that have a rhombohedral structure in which the unit cell consists of 3 quintuple layers (QL) bonded by van der Waals (vdW) force. Heterostructures containing a 3D TI are extensively studied because they are expected to produce novel phenomena that may not arise from heterostructures composed of conventional materials. For example, topological superconductivity (SC) has been theoretically predicted to be induced on the surface of TI-superconductor heterostructure via a proximity effect, which may provide a platform to host non-Abelian Majorana fermions (5, 6). Interestingly, our group recently discovered a 2-dimensional (2D) SC at the interface of 2 nonsuperconducting materials (7, 8), Fe_1+yTe, a parent compound of iron-based superconductors, and Bi₂Te₃, a 3D TI, and later we reported further studies on this heterostructure such as the superconducting proximity effect (9), current-induced depairing (10), anisotropic magnetic responses (11), and vortex dynamics (12, 13). Due to the complexity of this heterostructure, revealing the underlying mechanism of its induced 2D SC with a theoretical approach is very unlikely. Recently, experimental studies using angle-resolved photoemission spectroscopy (ARPES) (14) and ultraviolet photoemission spectroscopy (15) reported that the Fe_1+yTe layer in this heterostructure involved hole doping through a transfer of electrons into the Bi₂Te₃ layer. However, confirmation of this claim requires further studies to provide evidence about the linkage between the charge transfer and the behavior of the observed 2D SC.

The 2D SC of the Bi₂Te₃/Fe_1+yTe heterostructure is likely induced on the Fe_1+yTe layer, as described in several previous works (9, 15). The studies on how some physical parameters involved in this heterostructure could modify the physical property of the Fe_1+yTe layer and its 2D SC may provide hints to achieve a better understanding of the underlying mechanism of the induced SC. One of the most interesting issues in iron-based superconductors is the interplay between magnetism and SC. A synthetized bulk Fe_1+yTe crystal usually favors excess Fe atoms in interstitial sites, which could affect its magnetic order and electronic topological Lifshitz transitions (16) as in doped iron-based superconductors (17). Koz et al. (18) previously reported that below 70 K, for bulk Fe_1+yTe with 0.04 < y < 0.11, the spin direction of Fe atoms is oriented along the diagonal of the Fe–Fe square lattice, forming a bicollinear commensurate antiferromagnetic (AFM) structure, followed by a mixed phase for 0.11 < y < 0.13 and then an incommensurate AFM magnetic order for 0.13 < y < 0.15 as y increases. They also observed that the commensurate AFM transition temperature for bulk Fe_1+yTe increases as the concentration of excess Fe decreases down to y = 0.04. Studies on superconducting iron chalcogenide ternary Fe_1.02Te_1-xSe_x (19) and iron pnictides such as ReFeAsO_1-xF_x (Re = rare earth element) (20) showed that AFM order is antagonistic to SC that generally occurs after the magnetic order was suppressed by varying chemical doping concentration, even though they can coexist in a certain composition range (21, 22).

In this study, we demonstrate that 2D SC also appears in another TI/Fe_1+yTe system, the Sb₂Te₃/Fe_1+yTe heterostructure. We have systematically studied how the quality of the 2D SC of this heterostructure depends on the fluctuation of the AFM order of the Fe_1+yTe layer and the thickness of the Sb₂Te₃ layer. Particularly, the results from the former study provide a deeper understanding on the correlation between SC and AFM in this heterostructure, while the results from the latter study support that the TSSs may be involved in the induction of SC. Based on these experimental observations, we propose a possible origin of the induced interfacial SC.

Results

Structural Characterizations of the Sb₂Te₃/Fe_1+yTe Heterostructure.

Reflection high-energy electron diffraction (RHEED) patterns were captured after the growth of Fe_1+yTe and Sb₂Te₃ layers. Fig. 1 A and B display the RHEED patterns of tetragonal Fe_1+yTe when the incident electron beam is along the Fe_1+yTe [100] and $\left[1\overline{1}0\right]$ axis with the sample rotation angle at φ = 0° and φ = 45°, respectively. The diffraction streaks are marked by short lines and denoted by 2D Miller indices. The streaky patterns of Fe_1+yTe display a 90° rotational symmetry, as expected from the tetragonal structure of Fe_1+yTe. In contrast, the RHEED pattern of Sb₂Te₃ at rotation angle φ = 0° shown in Fig. 1C has 2 sets of streaks. The spacing ratio of the wider and narrower set of streaks is approximately $\sqrt{3}$, and their 2D Miller indices are marked correspondingly. As the sample rotates, the diffraction pattern of Sb₂Te₃ repeats at every 30°, which can be explained by the fact that the as-grown Sb₂Te₃ layer consists of 2 hexagonal lattices twisted by 90°. This is attributed to the 4-fold symmetry of the bottom Fe_1+yTe lattice and the 6-fold symmetry of the top Sb₂Te₃ lattice with respect to the growth direction. The details will be addressed in the next paragraph where the results of cross-sectional scanning transmission electron microscopy (STEM) imaging are presented.

Fig. 1.

Structural analysis of a Sb₂Te₃/Fe_1+yTe heterostructure. RHEED patterns of Fe_1+yTe taken when the electron beam is along the (A) [100] and (B) $\left[1\overline{1}0\right]$ direction. (C) RHEED pattern of Sb₂Te₃ taken when the electron beam is along the [100] direction of Fe_1+yTe. The short lines in A–C denote 2D Miller indices of the observed diffraction streaks. (D–F) Three cross-sectional STEM-HAADF images of the heterostructure taken at different locations of one TEM specimen with the zone axis along the [100] direction of Fe_1+yTe. (G and H) Schematic drawings of top and side views of the atomic arrangement of domains D and E, respectively. (I and J) Schematic drawings of top and side views of the other 2 domains that have identical side-view atomic arrangement corresponding to the STEM-HAADF image shown in F. The red and blue arrows marked in G–J indicate the crystalline axes $\left[10\overline{1}0\right]$ and $\left[01\overline{1}0\right]$ of Sb₂Te₃, respectively. They are conventionally written as a and b axes for a hexagonal lattice.

The epitaxial growth of bismuth and antimony chalcogenides on substrates that have 6-fold symmetry, such as Al₂O₃(0001) (23), Si(111) (24), BaF₂(111) (25, 26), InP(111) (27), and GaAs(111) (28), usually results in 2 mirror-symmetric twin domains due to the fact that there are 2 stacking sequences (ABCAB and ACBAC) along the [0001] direction for one QL of these chalcogenides. In order to investigate whether such twin domains exist in Sb₂Te₃ grown on Fe_1+yTe that has 4-fold symmetry and how they are developed into a different symmetry observed by RHEED as described above, high-resolution spherical-aberration-corrected STEM imaging was performed on an Sb₂Te₃(27 QL)/Fe_1+yTe(60 nm) heterostructure (one QL of Sb₂Te₃ is approximately equal to $10.2\mathrm{\AA }$), which was expected to provide more visualized and finer structural analysis at atomic scale than what can be achieved by RHEED. Cross-sectional high-angle annular dark field (HAADF) STEM images of this heterostructure observed at different locations of one TEM specimen with the zone axis along the [100] direction of Fe_1+yTe are displayed in Fig. 1 D–F. As can be seen, Fig. 1 D and E display the atomic arrangement of Te-Sb-Te-Sb-Te QL stacking in ABCAB and ACBCB sequence with the $\left[11\overline{2}0\right]$ direction (Fig. 1D) and $\left[\overline{1}\overline{1}20\right]$ direction of Sb₂Te₃ (Fig. 1E) aligned with the [100] direction of Fe_1+yTe, respectively. In Fig. 1 G and H, schematic drawings with both top-view and side-view modes for these 2 stacking sequences are displayed. As mentioned earlier, the Sb₂Te₃ layer was grown on Fe_1+yTe(001) that has a 4-fold symmetry, and thus it is expected that one can find 2 other domains that are laterally twisted by 90° from each of the 2 domains schematically drawn in Fig. 1 G and H. Fig. 1 I and J show the corresponding drawings of these expected domains. One can see that these 2 domains have identical side-view atomic arrangement when the viewing zone axis is along the [100] direction of Fe_1+yTe. In fact, we did observe such an atomic arrangement among our STEM images, and one typical example is shown in Fig. 1F. These observations indeed provide evidence that the Sb₂Te₃ layer consists of 2 hexagonal lattices twisted by 90°. It is worth pointing out that the 4 different domains mentioned above can be generated through azimuthal rotation of a domain having a stacking sequence either shown in Fig. 1 G and H, then laterally twisted by 90°, 180°, and 270°. This can be visualized by starting with the domain in Fig. 1G, then Fig. 1 I, H, and J are the resulting domains when it is twisted by 90°, 180°, and 270°, respectively. It is also worth mentioning that all of the STEM-HAADF images shown in Fig. 1 D–F enjoy a sharp and defect-free interface, which can be attributed to the vdW bonding nature between Sb₂Te₃ and Fe_1+yTe. Based on these images, the lattice parameters of the Fe_1+yTe unit cell at the interface are determined to be $a=3.88\mathrm{\AA }$ and $c=6.24\mathrm{\AA }$, and those of Sb₂Te₃ are $a=4.24\mathrm{\AA }$ and $c=30.54\mathrm{\AA }$, which are close to their reported bulk values. High-resolution X-ray diffraction studies (SI Appendix, Fig. S1) support that all of the 4 domains of Sb₂Te₃ likely orient with their c-axes along the growth direction (29).

Two-Dimensional SC.

Fig. 2 A and B show the temperature-dependent resistance of the Sb₂Te₃(27 QL)/Fe_1+yTe heterostructure measured under different magnetic fields in directions perpendicular $\left(H\right)$ and parallel $\left(H_{//}\right)$ to the interface, respectively (29). At zero applied magnetic field, resistance starts to drop at an onset temperature $T_C^{onset}$ of 12.3 K and zero-resistance state happens at 3.1 K. Fig. 2 A and B display a large anisotropy regarding the direction of the applied magnetic field since the transitions significantly broaden as $H_{\perp }$ increases, while such a broadening is much weaker as $H_{\mathrm{/}/}$ increases to the same magnitudes, indicating the SC is likely in 2D. Its further confirmation could be obtained by studying the temperature dependence of the upper critical magnetic field ${\mu }_0{H}_{c2}$ of the observed SC. Here, we define the critical superconducting transition temperature $T_C$ as the resistance drops to 50% of the normal-state value at 15 K. The out-of-plane upper critical magnetic field and in-plane upper critical field are denoted as ${\mu }_0{H}_{c2}^{\perp }$ and ${\mu }_0{H}_{c2}^{//}$, respectively. Fig. 2C shows the temperature dependence of the upper critical field ${\mu }_0{H}_{C2}\left(T\right)$ for the Sb₂Te₃(27 QL)/Fe_1+yTe heterostructure in directions parallel $\left(H_{\mathrm{/}/}\right)$ and perpendicular $\left(H_{\perp }\right)$ to the interface (29), where the x axis denotes the $T_C$ values at different applied magnetic field. It is well known that 2D SC is governed by Ginzburg–Landau (GL) theory (30) with the temperature dependences of the upper critical magnetic fields expressed by

$${\mu }_0{H}_{c2}^{\perp }=\frac{{\mathrm{\Phi }}_0}{2\pi {\xi }_{GL}^2\left(0\right)}\left(1-\frac{T}{T_C\left(0\right)}\right)$$ [1]

$${\mu }_0{H}_{c2}^{//}=\frac{{\mathrm{\Phi }}_0\sqrt{12}}{2\pi {\xi }_{GL}\left(0\right)d_{SC}}{\left(1-\frac{T}{T_C\left(0\right)}\right)}^{\frac{1}{2}},$$ [2]

where ${\mathrm{\Phi }}_0$ is the magnetic flux quantum, ${\xi }_{GL}\left(0\right)$ the zero-temperature GL in-plane coherence length, $d_{SC}$ the temperature-independent SC thickness, and $T_C\left(0\right)$ the critical temperature at zero magnetic field. Our data shown in Fig. 2C indeed can be well fitted by this theory in both parallel and perpendicular directions; the solid curves in this figure result from the best fitting with ${\xi }_{GL}\left(0\right)=4.1\pm 0.2\hspace{0.17em}\mathrm{nm}$ and $d_{SC}=3.9\pm 0.2\hspace{0.17em}\mathrm{nm}$. It is important to point out that neither a pure Fe_1+yTe nor a pure Sb₂Te₃ thin film grown under similar conditions exhibits SC (SI Appendix, Fig. S2), further supporting that the observed SC in the Sb₂Te₃/Fe_1+yTe heterostructure occurs at its interface.

Fig. 2.

Two-dimensional SC nature of the Sb₂Te₃(27QL)/Fe_1+yTe heterostructure. Resistance as a function of temperature under (A) out-of-plane and (B) in-plane magnetic field up to 12 T. (C) Temperature dependence of the upper critical field ${\mu }_0{H}_{c2}^{\perp }$ and ${\mu }_0{H}_{c2}^{//}$. Solid curves are obtained by fitting with the theoretical 2D GL equations. (D) Temperature dependence of resistance with a fitted curve based on the BKT model, yielding $T_{\text{BKT}}=3.68\mathrm{K}$. (Inset) ${\left[\mathrm{d}lnR/\mathrm{d}T\right]}^{-2/3}$ as a function of temperature with its linear part extrapolated to zero, yielding $T_{\text{BKT}}=3.64\hspace{0.17em}\mathrm{K}$. (E) V-I curves at various temperatures plotted on a logarithmic scale. The line with $\mathrm{\alpha }=1$ represents ohmic behavior while the line with $\mathrm{\alpha }=3$ corresponds to the BKT transition. (F) $\mathrm{\alpha }$ versus T extracted from fitting the data in E with power law $V\propto I^{\alpha }$, showing $\mathrm{\alpha }$ approaches 3 at $T_{\text{BKT}}=3.71\hspace{0.17em}\mathrm{K}$.

It is commonly accepted that the transport properties of a 2D SC system can be well described by the 2D Berezinskii–Kosterlitz–Thouless (BKT) theoretical model (31–33), in which vortex–antivortex pairs are formed and bound together below a critical temperature called the BKT temperature, $T_{BKT}$. At a temperature above $T_{BKT}$, vortex–antivortex pairs are thermally dissociated and free vortices give rise to a finite resistance. At a temperature just above $T_{BKT}$, the temperature-dependent resistance at zero magnetic field is predicted to be in the form of

$$\mathit{R}={\mathit{R}}_0\text{exp}\left(-\mathit{b}{\mathit{t}}^{-1/2}\right),$$ [3]

where ${\mathit{R}}_0$ and b are material-specific parameters and $\mathit{t}=\left(T/T_{BKT}\right)-1$ is the reduced temperature. The main panel of Fig. 2D shows the best fit using Eq. 3 for the temperature-dependent resistance at zero applied magnetic field of the heterostructure, yielding $T_{BKT}=3.68\hspace{0.17em}\mathrm{K}$. Fig. 2D, Inset shows the extrapolation of the linear part of ${\left(\text{dln}R/\text{d}T\right)}^{-2/3}$ to zero, yielding a consistent value of $T_{\text{BKT}}=3.64\hspace{0.17em}\mathrm{K}$ (29). Another important piece of evidence of BKT transition is obtained from fitting the voltage-current (V-I) curves on a log-log scale for a temperature range from 2 to 12 K near each critical current in its superconducting transition region with a $V\propto I^{\alpha \left(T\right)}$ power-law dependence, where $\mathrm{\alpha }$ equals 3 at $T_{BKT}$, as shown in Fig. 2E (29). Fig. 2F plots $\mathrm{\alpha }$ as a function of temperature from which $T_{BKT}$ is determined to be 3.71 K (29). The above analyses thus provide strong evidence for the 2D nature of the observed SC of the Sb₂Te₃/Fe_1+yTe heterostructure.

The Role of Fluctuation of the AFM Order.

Aiming at studying the interplay between the AFM order and SC, a group of Sb₂Te₃(24 QL)/Fe_1+yTe(60 nm) heterostructures named SF-1, -2, and -3 and 2 pure Fe_1+yTe(60 nm) thin films named F-1 and -2 were fabricated with various excess Fe concentrations. A combination of X-ray photoelectron spectroscopy (XPS) and spherical-aberration-corrected STEM was used to estimate the nominal y values of these samples. To achieve a more accurate analysis, a standard sample with known chemical composition is needed to derive the more reliable values of the relative sensitivity factors (RSFs) used in XPS analysis. These RSFs are further assumed to be constants for a certain variation of the sample matrix. We used sample SF-1 as such a standard sample and its y value was estimated by counting the number of interstitial Fe atoms in its spherical-aberration-corrected STEM images of its Fe_1+yTe layer. Fig. 3 shows one of the STEM-HAADF images that have the highest detected amount of interstitial Fe, in which the rectangular boxes contain the interstitial Fe atoms. Since fewer interstitial Fe atoms are seen in some of these images, we obtained the estimated y value of this sample as 0.004 by taking the average. The nominal y values of SF-2, SF-3, F-1, and F-2, as estimated using the peak areas of Fe and Te in their XPS spectra and the RSFs derived from the estimated y value of sample SF-1, are 0.021, 0.074, 0.042, and 0.09, respectively.

Fig. 3.

A cross-sectional STEM image of sample SF-1 taken in the Fe_1+yTe region. The red rectangles enclose the areas that have interstitial Fe atoms.

The normalized resistances as a function of temperature for samples F-1 and -2 are shown in Fig. 4A (29). Sample F-1 with fewer excess Fe concentration of the 2 samples shows a semiconducting behavior within the entire measured temperature range from 300 K to 2 K. Sample F-2 with more excess Fe shows a semiconducting-to-metallic transition at 47.3 K, which is known to be associated with the AFM phase transition. The spin fluctuation of the AFM order in Fe SCs was previously proposed to be corelated to their SC (34, 35). We believe that such fluctuation can be reflected by the distinctness of the AFM transition, that is, a less distinctive transition corresponds to higher spin fluctuation, which is consistent with the observations on the temperature-dependent resistivity curves of Fe_1.02(Te_1-xSe_x) alloys (19). Interstitial Fe atoms are believed to provide magnetic proximity coupling with the neighboring AFM spins [as we addressed in a previous study (9)] to reduce their fluctuation. The results shown in Fig. 4A indicate that the reduction of excess Fe concentration in Fe_1+yTe layer increases the fluctuation of this magnetic ordering, consistent with the previous findings from Bao et al. (35) using a spin polarized inelastic neutron spectrometer. Fig. 4B shows the temperature-dependent normalized resistances of samples SF-1, -2, and -3 (29). Samples SF-1 and SF-2 with less excess Fe than sample SF-3 show a semiconducting behavior as the temperature decreases from 300 K to just above the superconducting transition temperature, while SF-3 shows an AFM transition at 47.6 K. This correlation is consistent with that observed for the 2 pure Fe_1+yTe layers as shown in Fig. 4A. As can been seen in Fig. 4B, the onset temperatures of superconducting transition are 9.2 K, 8.9 K, and 8.7 K for SF-1, -2, and -3, respectively. These results indicate that the reduction of excess Fe concentration not only increases the spin fluctuation of the AFM order in the Fe_1+yTe layer but also enhances the quality of the SC of this heterostructure system. In fact, this provides important evidence that spin fluctuation of the AFM order in the F_1+yTe layer of the heterostructure is related to the induction of the observed 2D SC.

Fig. 4.

The interplay among the excess Fe concentration, magnetism, and SC. Normalized temperature-dependent resistance of (A) 2 pure Fe_1+yTe (60-nm) films named F-1 and F-2 and (B) a group of Sb₂Te₃ (24 QL)/Fe_1+yTe (60-nm) heterostructures named SF-1, SF-2, and SF-3 with various excess Fe concentration y. (B, Inset) A zoomed-in region at low temperature from 1 K to 15 K for displaying the contrast of the SC transition of these heterostructures.

Sb₂Te₃ Thickness Dependence on the Interfacial SC.

In the following, we will present the studies on the Sb₂Te₃ layer thickness dependence of the 2D SC of the Sb₂Te₃/Fe_1+yTe heterostructures with the aim of providing evidence that the TSSs of the Sb₂Te₃ layer are likely involved in the induction of the SC. A set of Sb₂Te₃/Fe_1+yTe(60 nm) heterostructures, each containing an Sb₂Te₃ layer with a different thickness, was fabricated for these studies. Fig. 5A shows the normalized temperature-dependent resistance R/R(T = 100 K) curves of Sb₂Te₃/Fe_1+yTe heterostructures with Sb₂Te₃ of 10, 15, 24, and 27 QL, which display SC with onset temperatures of 3.7, 6.6, 8.7, and 12.3 K, respectively, showing a trend that the onset temperature of SC increases with the Sb₂Te₃ thickness (29). To better illustrate the SC signature of the Sb₂Te₃(10 QL)/Fe_1+yTe sample with the thinnest Sb₂Te₃ layer among the 4 heterostructures, Fig. 5A, Inset shows the resistance versus temperature curve for this sample near the SC transition, which indeed displays a resistance drop at 3.7 K. Fig. 5B shows the zoomed-in normalized resistance curves for these heterostructure samples around their AFM transition temperatures, which are 48.2, 53.3, 47.6, and 53.3 K for Sb₂Te₃ thickness of 10, 15, 24, and 27 QL, respectively. The variation of the AFM transition temperatures of these heterostructures is caused by the small differences in the spin fluctuation of the AFM order of their Fe_1+yTe layers. As can be seen in Fig. 5B, Sb₂Te₃/Fe_1+yTe samples with 10-QL- and 24-QL-thick Sb₂Te₃ have very similar AFM transition temperatures, which indicates that the spin fluctuation in these 2 samples is nearly the same; however, the latter has a much higher onset SC temperature than the former. A similar circumstance also exists for the other 2 Sb₂Te₃/Fe_1+yTe heterostructures with 15 QL and 27 QL of Sb₂Te₃. Thus, the Sb₂Te₃ thickness dependence of the onset SC temperature revealed in Fig. 5A is a true property of these heterostructures. In SI Appendix, we describe an approach to fabricate 2 heterostructures with Sb₂Te₃ layers of different thicknesses grown on a single Fe_1+yTe layer with a high spin fluctuation. The results of their SC characteristics (SI Appendix, Fig. S3) indeed provide further confirmation of this Sb₂Te₃ thickness dependence.

Fig. 5.

The influences of Sb₂Te₃ thickness on the SC of Sb₂Te₃/Fe_1+yTe heterostructures. (A) Normalized resistance as a function of temperature for Sb₂Te₃/Fe_1+yTe heterostructures with varying thicknesses of the Sb₂Te₃ thin films of 10, 15, 24, and 27 QL. (Inset) The resistance at low temperature for the Sb₂Te₃/Fe_1+yTe sample with 10 QL Sb₂Te₃ layer for clarifying the signature of its SC. (B) Normalized resistance for these 4 heterostructures in a zoomed-in region around the AFM transition. The arrows mark the AFM transition temperatures. The data plotted in A and B with colors in red, yellow, green, and blue are for Sb₂Te₃/Fe_1+yTe heterostructures with the thickness of the top Sb₂Te₃ layer of 10, 15, 24, and 27 QL, respectively.

Spin–Orbit Coupling Alone Cannot Induce the Observed SC.

In the following, we will briefly address the studies of another factor that was thought to be the underlying cause of the 2D SC in the TI/Fe_1+yTe heterostructure system. It is related to an obvious and straightforward theoretical hypothesis that the strong spin–orbit coupling (SOC) of TI materials could itself induce the 2D SC. One can test this hypothesis experimentally by studying the transport properties of a Fe_1+yTe heterostructure with a top layer possessing strong SOC but it is not a TI. We chose elemental Sb and Bi thin films as the replacement for the TI layers for the following reasons. The difference between A₂B₃-type TI compounds and Sb is that the former compounds have a bulk energy gap with TSSs confined at the surfaces, while the latter is a semimetal (36, 37) and thus its TSSs penetrate to the entire interior of the film (38). On the other hand, due to an even stronger SOC in Bi (which is stronger than that of both Bi₂Te₃ and Sb₂Te₃), its surface bands inverse twice along $\overline{\mathrm{\Gamma }}\overline{M}$ and return to the valence band, making Bi a semimetal with topologically trivial surface states (39) [except that ultrathin Bi films are a 2D TI (40)]. Thus, it is expected that both Sb/Fe_1+yTe and Bi/Fe_1+yTe heterostructures can be used to test if SOC alone could induce interfacial SC in Fe_1+yTe. SI Appendix, Fig. S4 displays the temperature-dependent resistance curves of 3 heterostructures, Sb(10 nm)/Fe_1+yTe, Bi(13 nm)/Fe_1+yTe, and Sb₂Te₃(18 QL)/Fe_1+yTe. As shown in this figure, the AFM transition temperatures for these 3 heterostructures are 54.8, 55.8, and 61.3 K, respectively, indicating that the AFM order of the Sb₂Te₃/Fe_1+yTe heterostructure is stronger (equivalent to weaker spin fluctuation) than that of both the Sb/Fe_1+yTe and Bi/Fe_1+yTe heterostructures. The Sb₂Te₃/Fe_1+yTe heterostructure is superconducting as expected; however, neither the Sb/Fe_1+yTe nor the Bi/Fe_1+yTe heterostructure displays SC and they only show an up-turn in resistance at low temperature instead (SI Appendix, Fig. S4). These results indicate that SOC alone is not able to induce the interfacial SC observed in TI/Fe_1+yTe heterostructures.

Discussions

We believe that the observed Sb₂Te₃ thickness dependence on the SC quality of the heterostructure system described earlier can be linked to the evolution of the TSSs at the interface in the following ways. The degree of integrity (totality) of the TSSs at the interface increases with the Sb₂Te₃ thickness, which likely corresponds to higher SC quality of the heterostructure system. For thin Sb₂Te₃ layers, the 2 factors that can affect the degree of integrity of the interfacial TSSs are direct coupling and indirect coupling between the top and bottom TSSs. In direct coupling, the wave functions of the top and bottom TSSs are overlapped such that a small gap opens at the Dirac point, which reduces the integrity of the bottom TSSs. For Sb₂Te₃, the critical thickness for observing gapless TSSs is 4 QL, as demonstrated by scanning tunneling microscopy (41, 42) and ARPES (43). Since the observed Sb₂Te₃ thickness dependence in this study covers a thickness range from 10 to 27 QL, direct coupling should not play a key role in this dependence. Jiang et al. (44) previously reported that molecular beam epitaxy (MBE)-grown Sb₂Te₃ usually displays a p-type conductivity due to various intrinsic defects. We have also confirmed the p-type nature of our Sb₂Te₃ layers by conducting Hall measurements (SI Appendix, Fig. S2). This bulk conductivity was known to mediate a so-called indirect coupling between the top and bottom TSSs (45), which likely occurs even when the Sb₂Te₃ thickness is larger than the critical thickness of direct coupling. We believe this indirect coupling can also reduce the integrity of the TSSs at the interface of the heterostructure and the coupling is weakened as the TI thickness increases (46). Thus, indirect coupling is considered to be mainly responsible for the observed Sb₂Te₃ thickness dependence on the 2D SC of the heterostructure system. It is worth pointing out that such a TI-layer thickness dependence beyond the critical thickness for observing gapless TSSs of the Bi₂Te₃/Fe_1+yTe heterostructures is less obvious, as shown in our previous work (8). This can be explained by the big contrast between the estimated bulk carrier concentration of a Sb₂Te₃(25 QL) and that of a Bi₂Te₃(50 QL) thin film; the former is $1.63\times {10}^{22}{\text{cm}}^{-3}$ (SI Appendix, Fig. S2), while the latter is about 1.3 to $1.6\times {10}^{19}{\text{cm}}^{-3}$, as reported by us earlier (47). This big contrast implies that our Sb₂Te₃ thin film has a much higher bulk conductivity than Bi₂Te₃, leading to a stronger indirect coupling between the top and bottom TSSs for Sb₂Te₃ and, in consequence, a wider-ranging TI thickness dependence of the 2D SC as described above.

The fact that 2D SC of a Fe_1+yTe layer occurs only when it is covered with either Bi₂Te₃ or Sb₂Te₃ implies that a property of TI is likely involved in the induction of this SC. Since the TI layer in these heterostructures provides a source of itinerant carriers confined at the interface through the TSSs, it is possible that these itinerant carriers exhibit an unconventional pairing at the interface, leading to the observed interfacial SC. Recently, Yasuda et al. (48) observed a large nonreciprocal charge transport associated with the superconducting transition of Bi₂Te₃/FeTe, which is revealed to originate from the current-induced modulation of supercurrent density due to spin-momentum locking, indeed suggesting a close connection between SC and TSSs.

Below we briefly discuss the possible pairing mechanism of the 2D SC at the Sb₂Te₃/Fe_1+yTe interface. We believe the 2 key ingredients at the Sb₂Te₃/Fe_1+yTe interface are 1) 2D itinerant electrons induced by the TSSs of Sb₂Te₃ and 2) local spin moments with AFM ordering in Fe_1+yTe. The hybridization of the 2 ingredients, which are reminiscent of the Anderson lattice, was recently proposed to explain the strong superconducting pairing in strongly correlated materials where inhomogeneous magnetism could appear as in electron-doped FeSe (49) and in spin-striped nickelate (50); therefore, the possibility that spin order and SC could be intertwined cannot be ruled out. In fact, new spatial resolved methods show that the inhomogeneous charge-density-wave short-range order coexists with SC in cuprates (51). At the Sb₂Te₃/Fe_1+yTe interface, the fluctuation of the local moments of the AFM ordering in Fe_1+yTe is enhanced due to the hybridization with the itinerant electrons in TSSs. On the other hand, the enhanced fluctuating spin moments provide a driving force for the superconducting pairing of the itinerant electrons at the interface. The fact that SC transition temperature increases upon the increase of the fluctuation of the AFM order, as observed in this study, also implies that superconducting pairing benefits from the fluctuation of AFM order. Consequently, we propose that the superconducting pairing mediated by spin fluctuation enhanced by the hybridization of local spin moments in Fe_1+yTe and 2D itinerant electrons in the TSSs of Sb₂Te₃ is a possible mechanism of the SC observed in the Sb₂Te₃/Fe_1+yTe heterostructures. More quantitative experimental analysis and theoretical calculation are needed to confirm such a mechanism in future studies. We believe that the Sb₂Te₃/Fe_1+yTe heterostructures will provide a new platform not only for investigating the novel physics emerging from the interplay among SC, magnetism, and topological helical surface states but also for trapping and controlling Majorana fermions.

Methods

Sample Preparation.

All of the samples studied in this work were fabricated by a VG-V80H MBE system equipped with in situ RHEED. Sample synthesis was conducted using high-purity Sb₂Te₃ and ZnSe compound sources together with Fe and Te elemental sources. A ZnSe buffer layer (80 nm) was firstly deposited on the GaAs (001) n+ substrates to form a flat surface, followed by a deposition of Fe_1+yTe with a thickness of 60 nm and a Sb₂Te₃ layer. For the studies of the interstitial Fe concentration dependence, a set of Sb₂Te₃(24 QL)/Fe_1+yTe heterostructures and a set of pure Fe_1+yTe thin films with various amount of interstitial Fe in the Fe_1+yTe layer were fabricated by changing the temperature of Te effusion cell while keeping the temperatures of the Fe cell and substrate constant. Another set of Sb₂Te₃/Fe_1+yTe heterostructure samples were fabricated containing Sb₂Te₃ thin films with average thicknesses of 10, 15, 24, and 27 QL to study the Sb₂Te₃ thickness dependence of the 2D SC. All of the samples were capped with a Te protective layer (∼8 nm) to avoid oxidization.

Characterizations.

The thickness of each layer was determined by transmission electron microscope (TEM; JEOL 2010F). High-resolution spherical-aberration-corrected STEM images were carried out in a JEM-ARM200F TEM equipped with a probe corrector and a HAADF detector for finer crystal structure analysis. Sb₂Te₃/Fe_1+yTe heterosturctures were cut into long strips (with dimension $\sim 2\hspace{0.17em}\text{mm}\times 6\hspace{0.17em}\text{mm}$) and conventional 4-point electric contacts were made on the surface of each strip using silver paint as the contact material for performing ex situ electrical and magnetotransport measurements, which were carried out in a physical property measurement system equipped with a 14-T superconducting magnet. To determine the interstitial Fe concentration in the Fe_1+yTe layer, ex situ XPS measurements were performed by Kratos Axis Ultra DLD XPS equipped with a monochromatic Al kα X-ray source (photon energy 1,486.7 eV, 150 W), which was operated in hybrid lens mode with an energy step of 100.0 meV, a pass energy of 40 eV, and a large measuring area of $1\times 2\hspace{0.17em}\mathrm{m}{\mathrm{m}}^2$. Before acquiring a spectrum, Ar ion sputtering was performed to remove the upper layer(s) to reveal a pure surface of the Fe_1+yTe layer. The binding energy was calibrated with the C 1-s peak at 284.8 eV. The actual core-level peak areas were determined after applying Shirley background subtraction. High-resolution X-ray diffraction measurements were conducted using a PANalytical multipurpose diffractometer with an X’celerator detector (PANalytical X’Pert Pro) for crystalline characterizations.

Data Availability.

All data included in this study are available via the 4TU.Centre for Research Data https://researchdata.4tu.nl/en/ under the dataset identifier 18d09214-e75c-4846-bc53-73abe036f452.