Abstract
FeTe monolayer islands situated on a topological insulator Bi2Te3 (0001) surface were recently reported to exhibit the opening of an energy gap below temperatures T ~ 6 K, which could be due to a superconducting phase transition. In this work, we present a magnetic field dependent transport study proving that this gap is indeed of superconducting origin. Upon cooling, several drops in resistance are observed in the temperature range between 6 K and 2 K, indicating multiple transitions. Using the Ginzburg-Landau theory, we show that the critical magnetic field of the dominant high-temperature transition at ~ 6 K is governed by orbital Cooper pair breaking in larger FeTe islands, large enough to exceed the superconductive coherence length \(\xi\). At smaller island sizes, transitions at lower temperatures < 6 K become more prominent, showing significantly increased critical fields dominated by paramagnetic pair breaking. The multiphase superconducting behaviour is in line with an observed wide distribution of FeTe islands width 5–100 nm and seems to reflect disorder effects at the interface to Bi2Te3. The proof of local superconductivity makes the FeTe interface to the topological insulator Bi2Te3 substrate a potential host of topological superconductivity.
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Introduction
Interfaces between superconductors and topological insulators (TIs) are predicted to show interesting physics arising from a trivial to non-trivial topology transition, where topological superconductivity (SC) may be realised1.
The 2008 discovered iron-chalcogenide superconductor family FeSe1-xTex and respective well-understood Bi-chalcogenide TIs Bi2Se3 and Bi2Te3 are a promising material combination to study such physics. Both have a simple van der Waals crystal structure consisting of stacked triple (Ch-Fe-Ch) and quintuple (Ch-Bi-Ch-Bi-Ch) atomic layer units (Ch = Te, Se), respectively. In the case of FeCh, one triple layer corresponds to one unit cell (UC) of the respective bulk crystal structure. Throughout the work, 1 UC FeCh will be denoted as a monolayer (ML). FeSe is particularly interesting as its superconducting properties are shown to be highly susceptible to interface effects. The bulk FeSe critical temperature of Tc = 8 K2 was shown to increase up to 100 K when a single FeSe monolayer (ML) is grown on insulating SrTiO33. In contrast to FeSe, the parent compound FeTe is at first glance less promising as it is known to exhibit a bi-collinear antiferromagnetic (AFM) order below T ~ 70 K and remains non-superconducting in the bulk4.
Surprisingly, recent studies of interfaces between FeSe and Bi2Se3 turned out not to show SC, while the combination of FeTe and Bi2Te3 does. First transport experiments through epitaxially grown n-layer thick Bi2Te3 on bulk-like FeTe (n-Bi2Te3/bulk-FeTe heterostructures) reported values of Tc, which depend on the number of Bi2Te3 layers and their lateral dimension and reach a maximum Tc = 12 K at n = 75,6,7,8. The superconducting phase is tentatively assigned to unconventional SC triggered by interface-induced charge transfer from FeTe into Bi2Te3 topological surface states9,10, which—at the same time—is believed to destroy the FeTe AFM order close to the interface11. Recently, however, Qin et al. reported SC even for n = 111 with similar values Tc ≈ 12 K, which suggests topology not to play a role, as Bi2Te3 develops its non-trivial TI properties only at thicknesses n ≥ 212. As a complementary approach, inverted (n-FeTe/bulk Bi2Te3) heterostructures were investigated by scanning tunnelling spectroscopy (STS). In this geometry, TI properties of Bi2Te3 can be considered intact, and the FeTe magnetic state is directly accessible via spin-polarised scanning tunnelling microscopy (SP-STM). As highlighted recently by Qin et al.13, although SC is expected to emerge at the interface between Bi2Te3 and FeTe, the mechanism for SC might be fundamentally different in the inverted approach for single layer FeTe grown on Bi2Te3. Indeed, considerable differences are observed. For 1 ML FeTe (n = 1), an energy gap in the local density of states (LDOS) was observed in local STS at temperatures below T ~ 6 K, considerably lower than the SC transitions Tc ~ 12 K in (n-Bi2Te3/bulk-FeTe) systems14. This gap is moreover reported to coexist with FeTe bi-collinear AFM order. A trend towards a lower Tc in the inverted approach were recently observed in transport measurements through FeTe1-ySey monolayers on Bi2Te3 when y is reduced from 0.25 to 0.115. The disappearance of the gap at much lower temperatures could point to different superconductive properties in (n-FeTe/bulk Bi2Te3), but a possible pseudo-gap phase reported, e.g., in high-Tc SCs16 was so far not ruled out. For a proof of a true superconducting phase, magnetic field dependent studies, e.g. by transport methods, would be needed to extract also characteristic critical fields Bc versus temperature.
In this work, we present a field-dependent transport study on (n-FeTe/bulk Bi2Te3) systems, proving a superconducting phase and thus their potential as a host for topological SC. In-plane transport was measured in heterostructures consisting of Si-capped 1–2 ML thick FeTe (FeSe) layers, which were grown ontop molecular beam epitaxy (MBE) fabricated Bi2Te3(0001) (Bi2Se3(0001)) substrates. The observed transport properties suggest the presence of a non-continuous superconducting state in (n-FeTe/bulk Bi2Te3) samples, where the measuring current is flowing through the Bi2Te3 substrate between non-percolative superconducting areas of different sizes, causing finite resistance even in the superconducting state. Separated areas are inherently defined by the formation of 60°-rotated tetragonal FeTe island domains on Bi2Te3 visible in dark field electron microscopy. At small FeTe coverages of 1 ML, these areas can be extremely small, falling below the superconducting coherence length, which we see as an onset of the paramagnetic Cooper pair breaking regime. Increasing the FeTe coverage to ~2 ML, the superconducting phase in FeTe/Bi2Te3(0001) becomes more stable with higher critical temperatures of ~6 K. Respective critical fields of Bc ~ 2 T are attributed to orbital breaking of Cooper pairs with a coherence length \(\xi \left(0\right)\) of tens of nm, which match the average scale of FeTe island widths.
Results and discussion
Sample fabrication and x-ray photoemission spectroscopy characterisation
For our transport studies, we grew FeCh (Ch = Te,Se) layers on respective Bi2Ch3(0001) surfaces under ultra-high vacuum conditions, following a two-step Fe-deposition and subsequent thermal annealing procedure [see Methods section]. The growth procedure was first described by Cavallin et al. and Manna et al. for bulk Bi-chalcogenide TIs14,17. In order to achieve a higher sensitivity to ultrathin FeCh (Ch = Te,Se) layer properties in transport measurements, we here use 300 nm thin MBE-grown Bi2Ch3(0001) films, which reduces lateral shunt currents through the substrate and fosters a step-edge induced nucleation and growth process of FeCh monolayer islands18. Deposited Fe amounts were chosen equivalent to coverages of one and two MLs of FeCh (denoted as “1 ML” and “2 ML” FeCh samples henceforth). For ex situ transport methods, an amorphous Si cap layer was finally added in situ to protect the interface from deterioration in air.
During the different steps of in situ sample preparation, surfaces were thoroughly characterised by x-ray and ultraviolet photoemission spectroscopy. In surface sensitive x-ray photoemission spectroscopy (XPS), the formation of FeCh on Bi2Ch3(0001) can be traced by the appearance of characteristic chemical shifts in Ch and Bi core levels (CLs)18,19. Figure 1 summarises CL spectra before and after FeCh growth, as well as after Si capping. Te 4d and Se 3d CL contributions originating from the FeTe and FeSe phase (denoted as TeFe and SeFe in Fig. 1b, j) are shifted by 0.5 eV and 1.0 eV to higher binding energies (BEs) with respect to those from initial Bi2Te3 and Bi2Se3 substrate (denoted as Tei and Sei in Fig. 1a, i).
The intensity ratios (TeFe/Tei) and (SeFe/Sei) of respective components in CLs moreover reflect the FeCh coverage on Bi2Ch3 and can be referenced to previously reported XPS data of 1 ML FeCh (thickness 6.3 Å for FeTe and 5.5 Å for FeSe) ontop of Bi2Ch318. A shifted Bi 5d CL component at BE ~ 24 eV indicates a partial chemical reaction of Bi2Ch3 in line with the reported growth of FeTe as top and embedded islands on Bi2Te320. Fe 2p CL shapes in Fig. 1g, o look similar for FeTe and FeSe and are dominated by asymmetric Doniach-Sunjic components (labelled FeDS) typical for a metallic character of the layer. Contaminations, e.g., from carbon and oxygen, were negligible at all stages of growth.
Study of the electronic band structure
We characterised the electronic band structure and Fermi surface topology of our samples by angle-resolved photoemission spectroscopy (ARPES) techniques. Figure 2 compares ARPES data of 1 ML FeTe (a, b) and 1 ML FeSe (e, f) on Bi2Te3(0001) and Bi2Se3(0001), respectively. As references we show ARPES data of in-situ cleaved single-crystalline bulk Fe1.02Te (c, d) and FeSe0.5Te0.5 (g, h) counterparts under the same experimental conditions.
The ARPES Fermi surfaces and LEED patterns of the FeCh MLs (Fig. 2a, e) exhibit the characteristic 12-fold symmetric (kx, ky)-space pattern in line with the previously reported formation of three equally prominent 60°-rotated tetragonal FeTe and FeSe island domains (D1, D2, and D3 hereafter) on the hexagonal Bi2Te3(0001) and Bi2Se3(0001) surface symmetry18,21. Dark-field microscopy imaging in Fig. 3a reveals D1, D2, and D3 domain widths in the range of 5–100 nm, which we approximate by a normal distribution of (50 ± 20) nm.
Exemplary, the Brillouin zones (BZs) of one domain (D1) and respective \(\bar{{\rm{X}}}\) and \(\bar{{\rm{M}}}\) points are sketched in the ARPES Fermi surfaces in Fig. 2a, e. Respective bulk BZs are sketched in Fig. 2 c, g, assuming bulk lattice constants \(\bar{\Gamma }\)-\(\bar{{\rm{X}}}\) = 0.84 Å-1 (a’ = π/3.75 Å) and \(\bar{\Gamma }\)-\(\bar{{\rm{X}}}\) = 0.82 Å-1 (a’ = π/3.82 Å), respectively. The Fermi surfaces of the bulk reference samples in Fig. 2c, g correspond to their tetragonal phase at temperatures well above any known AFM phase transitions in bulk FeSexTe1-x systems ( ~ 70 K for FeTe) or tetragonal-to-orthorhombic structural transition in bulk FeSe systems ( ~ 90 K)2. Both Fermi surfaces exhibit a point-like intensity at \(\bar{\Gamma }\) and a tetragonal cross-shaped intensity distribution due to higher intensities along \(\bar{\Gamma }\)-\(\bar{{\rm{X}}}\) directions with respect to \(\bar{\Gamma }\)-\(\bar{{\rm{M}}}\). A broad ARPES intensity at \(\bar{{\rm{M}}}\) is visible in FeSeTe (Fig. 2g), while in FeTe (Fig. 2c) it is suppressed, all in agreement with earlier reports at photon energies ~ 20 eV and T ≥ 120 K22,23. The 12-fold azimuthal modulation of the Fermi surface intensity for 1 ML FeTe and 1 ML FeSe at |kǁ| ~ 1.2 Å-1 (Fig. 2a, e) is in line with a superposition of larger intensities along \(\bar{\Gamma }\)-\(\bar{{\rm{X}}}\) directions for each 60°-rotated domain D1, D2, and D3.
Figure 2 (bottom row) compares (kǁ , E) cuts through 1 ML FeTe and 1 ML FeSe (Fig. 2b, f) as well as bulk FeTe and FeSeTe (Fig. 2d, h). For 1 ML FeTe and 1 ML FeSe \(\bar{{\rm{X}}}\,\)- \(\bar{\Gamma }\) - \(\bar{{\rm{X}}}\) cuts through the BZ of D1 are shown (see vertical lines in Fig. 2a, e). While for single-crystal bulk samples, high-symmetry cuts \(\bar{\Gamma }\)-\(\bar{{\rm{X}}}\) and \(\bar{\Gamma }\)-\(\bar{{\rm{M}}}\) in Fig. 2d, h are well-defined in their BZs, respective cuts through D1 in 1 ML FeTe and FeSe contain equal contributions also from the 60°-rotated domains D2 and D3. ARPES intensities, therefore, appear averaged, and contain a mixture of bands observed in the respective bulk case along \(\bar{\Gamma }\)-\(\bar{{\rm{X}}}\) and \(\bar{\Gamma }\)-\(\bar{{\rm{M}}}\) directions, e.g. bands indicated T1-T3 [for FeTe] and S1-S3 [for FeSe]. Close to the Fermi surface, bulk and 1 ML data are comparable in the range |kǁ| ≤ 0.7 Å-1. FeSe shows a broad bow-tie-shaped ω-band at 0.25 eV (see label in Fig. 2f) observed also, e.g., for superconductive 1 ML thin FeSe on oxide surfaces24 and a suppressed intensity at higher BEs between 0.5 eV and 1.0 eV22. FeTe on the other hand exhibits the well-known fork-like bands around \(\bar{\Gamma }\)23, dispersing steeply from the Fermi level to BEs of 1.5 eV with relatively constant intensity. In contrast to 1 ML FeTe, the point-like intensity at \(\bar{\Gamma }\) is missing in case of 1 ML FeSe. At higher BEs [1.5 – 2.5] eV broad and strongly dispersing bands appear close to |kǁ| ~ 0.5 Å-1 along \(\bar{\Gamma }\)-\(\bar{{\rm{X}}}\) and \(\bar{\Gamma }\)-\(\bar{{\rm{M}}}\) directions (see white brackets in Fig. 2b, f), as reported earlier in refs. 22,23.
It is important to note that after 1 ML FeCh growth, characteristic band structure features of Bi2Ch3(0001), such as the topological surface state and prominent downwards dispersing bulk bands starting at ~ 2 eV around \(\bar{\Gamma }\) have disappeared (Supplementary Fig. 1a, b and ref. 18). In its initial decapped state, Bi2Te3 and Bi2Se3 both show the typical intrinsically n-doped behaviour of bismuth chalcogenides (see Supplementary Fig. 1). It confirms the high areal coverage of the Bi2Ch3(0001) surface by FeCh island domains, in line with our microscopy results in Fig. 3a. We remark that the FeCh coverage dissolves upon annealing to temperatures ≥400 °C, where the reappearance of the bare Bi2Ch3(0001) band structure is observed (see Supplementary Fig. 1c). At these temperatures, the Bi2Ch3(0001) step-edge assisted nucleation and growth mode of FeCh monolayers (see ref. 18) seems to break down. This is connected to a general loss of surface order evidenced also by the absence of the Bi2Ch3(0001) topological surface state at \(\bar{\Gamma }\).
For ex situ transport measurements, the pre-characterised FeCh/Bi2Ch3(0001) surfaces were finally protected by an amorphous Si cap of several nanometre thickness, deposited in situ under UHV conditions at room temperature (see also methods section). In order to monitor the influence of the Si on the ultrathin FeCh layer properties, XPS was once more done at an early stage of the cap deposition process, when the Si thickness was comparable to the XPS probing depth of ~ 10 Å. Te 4d, Se 3d, and Bi 5d CLs show slight uniform broadening upon Si deposition (see Fig. 1c, k, as well as Fig. 1f, n). Fe 2p CL line shapes in Fig. 1h, p appear sharper and more symmetric, pointing towards a less metallic character of Fe in the presence of the Si interface.
Field-dependent superconductive transport through FeTe layers on Bi2Te3(0001)
Low-temperature superconducting transport measurements Si-cap/FeTe/Bi2Te3(0001) and Si-cap/FeSe/Bi2Se3(0001) heterostructures were realised by 50 μm silver wire electrodes, which were attached to the Si-capped samples via indium droplets as sketched in Fig. 3a. The sample resistances have been determined from the voltage responses (U+ / U−) at low bias currents (5 nA to 10 μA) through the leads (I+ / I−). External magnetic fields were applied perpendicular to the sample plane. We refer the reader to the methods section for further details.
Figure 3 shows the temperature-dependent lateral electrical resistances R(T) measured in zero field on Si-capped 1 ML FeTe/Bi2Te3 (Fig. 3b-black symbols), 2 ML FeTe/Bi2Te3 (Fig. 3b—green symbols) and FeSe/Bi2Se3 (Fig. 3c—black symbols) heterostructures. For comparison, we added a typical R(T) curve of pure Bi2Se3 in Fig. 3c (red symbols). Looking at this data at lowest temperatures, the inset of Fig. 3c shows a slight increase of the resistance below 6 K for FeSe/Bi2Se3 and, much weaker, for Bi2Se3. For Bi2Se3, recent works attribute this rise to increasing electron-electron interactions in the TSS of Bi2Se3 at low temperatures25. All R(T) curves in Fig. 3 reveal very similar metallic temperature dependencies down to about 6 K with a residual-resistance ratio RRR ~ 2 and saturation below 30 K. At T ~ 6 K, a sharp 10% drop in resistance is visible in 2 ML FeTe/Bi2Te3, which is followed by a more continuous decrease below 3 K (see the inset in Fig. 3b). In the 1 ML FeTe/Bi2Te3 case, the drop at T ~ 6 K (see vertical red line in the inset Fig. 3b) is significantly smaller, while the transition below 3 K now appears as two rather sharp drops at T = 2.8 K and T = 2.4 K (total drop amounts to 1%, leveling off at a finite resistance ~ 4.01 ῼ). The transition temperatures are best visible on logarithmic temperature scales in Fig. 4a, b. Respective R(T) data of the FeSe/Bi2Se3 heterostructure shows no sudden drops and approximately follows the curve measured on a pure Bi2Se3 sample. Comparing the resistance data obtained on our heterostructures with that of pure Bi2Se3, we can conclude that the order of resistance values of our heterostructures are mainly determined by the respective Bi2Ch3 (Ch = Te, Se) substrate26.
The multiple drops of the resistances observed in 1 ML FeTe/Bi2Te3 and 2 ML FeTe/Bi2Te3 heterostructures at low temperatures point towards the presence of non-percolative low resistance phases formed at the interfaces FeTe/Bi2Te3 or FeTe/Si. We ruled out a significant role of the FeTe/Si interface for SC, e.g., due to silicide formation27,28, by measuring Si-capped bulk FeTe reference samples where no drops in resistance were observed at temperatures below 40 K (Supplementary Fig. 3). Instead, the resistance drops in our data around 6 K confirms the abovementioned STS studies on FeTe/Bi2Te3 in the absence of a Si-interface. Local STS on monolayer FeTe reported the formation of energy gaps at critical temperatures Tc = 6.5 K and Tc = 7.5 K for “top” an “embedded” island types, respectively14. Our observed additional transitions in the temperature range 2-3 K were not reported in STS works at respective temperatures and suggest the existence of even further superconducting phases on a local scale.
To prove the superconducting origin of the observed low-temperature drops in the R(T) curves for FeTe/Bi2Te3 heterostructures, we studied their magnetic field dependence. R(T) curves, measured at different fixed magnetic fields B⊥ are shown in Fig. 4, for 1 ML (Fig. 4b) and for 2 ML FeTe heterostructures (Fig. 4e). The drops of the R(T) curves are shifting to lower temperatures with increased magnetic fields, indicative of SC transitions in both cases. Despite the evidence for SC, both sample resistances, however, remain finite down to 1.8 K. The effect of magnetoresistance is negligible in the 1 ML sample, where a small magnetic field of 130 mT was applied (Fig. 4b and Supplementary Fig. 4b). For 2 ML, at much higher fields, a slight shift is visible at 6 K (Fig. 4e) due to magnetoresistance in the normal phase.
Finite values of the resistances below the critical temperature are typical for samples where only small amounts of the material is superconducting and measuring currents are flowing through non-percolative superconducting islands/phases. This is in line with microscopy results in Fig. 3a, where (50 ± 20) nm wide FeTe islands with D1, D2, and D3 orientations seem to be below the percolation limit. We note that also in the case of (n-Bi2Te3/bulk-FeTe) heterostructures, a finite resistance is reported when the Bi2Te3 coverage reaches the limit n = 1-2, where the percolation limit is expected5. In our case, as discussed above, the multiple zero-field resistive transitions at different temperatures (inset Fig. 3b) evidence that these non-percolated islands have varying superconducting properties.
B-T phase diagrams of 1 ML and 2 ML FeTe samples can be derived from the measured field-dependent transport properties. The value of the critical temperature Tc(B) at a fixed magnetic field has been determined from the resistive transitions shown in (Fig. 4b, e). As determination criteria, we used the classical method, where the critical temperature Tc is evaluated at different percentual values of the total resistance step ΔR = (RS – RN) between the normal state resistance (RN) and the superconducting (RS) state. Since our samples did not show zero resistance below the transition temperatures, we considered the plateaus at RS = 4.01 ῼ for 1 ML sample and at RS = 0.756 ῼ for 2 ML sample as the resistance in the superconducting state as indicated in Fig. 4a, d.
Figure 4c shows the B-T phase diagram of the 1 ML sample for the two well-defined transitions below 3 K. Field-dependent Tc(B) values determined at different percentual levels 10%, 25%, 50%, 75%, and 90% of ΔR are plotted in colours specified in the legend. For clarity, 25%, 50%, and 75% levels are indicated exemplary as horizontal lines in Fig. 4b, e. Points labelled in pink symbols (10% ΔR), green (25% ΔR), and red (50% ΔR), representing mainly the phase with the lowest Tc2 ~ 2.4 K, reveal a rapid increase in the slopes near below Tc2 (for 10% ΔR the slope is shown as black dashed line in Fig. 4c). Above magnetic fields B ~ 60 mT (horizontal blue dashed line), an evident change in their curvature is visible. When the Tc values are determined at higher 75% ΔR and 90% ΔR values, the resulting Tc(B) curves correspond to the Tc1 = 2.8 K phase. Even though these curves are closer to a linear dependence, the change in curvature above B = 60 mT towards steep slopes is evident (see the black arrow in Fig. 4c). It strongly suggests that the low-temperature phase with Tc2 ~ 2.4 K has a significantly higher critical magnetic field than the phase with Tc1 ~ 2.8 K.
A different behaviour is observed in the respective B-T phase diagram of the 2 ML sample shown in Fig. 4f. Here, Tc(B) curves are quasi-linear for all percentual values 10%, 25%, 50%, 75%, and 90% of ΔR with critical temperatures of ~ 5.5 - 6 K. We comment that we have compensated for the above-mentioned small magnetoresistance effect by shifting the R(T) data in finite fields (Fig. 4e) to match the zero-field data in the normal phase at 6 K. The different linear slopes indicate different Bc values, which reflects the strongly smeared resistive transitions in Fig. 4e in the presence of multiphase superconductivity. The small variation of Tc values between 5.5 K and 6 K derived by linear extrapolation strongly suggests that in transport properties the phase with Tc1 = 5.8 K dominates. We were able to confirm the properties of this superconductive phase independently by magnetic susceptibility measurements giving a consistent critical temperature Tc = 5.8 K for the 2 ML sample (see Supplementary Figure 2).
Discussion of the pair breaking mechanism in FeTe and multiphase superconductivity
In the following, we discuss the B-T phase diagrams of 1 ML and 2 ML samples in the framework of the Ginzburg-Landau theory for type-II superconductors29, considering that Cooper pairs forming the superconducting condensate can be destroyed by orbital or Pauli paramagnetic pair breaking effects.
In the case of orbital pair breaking, the Cooper pairs are broken by superconducting screening currents at the upper critical magnetic field Bc2(0), defined as
where Θ0 = 2.07 × 10−15 Tm2 is the magnetic flux quantum and \(\xi \left(0\right)\) is the superconducting coherence length at T = 0. For FeSe such critical fields are, e.g., about ~ 7 T30.
Following the Werthamer-Helfand-Hohenberg (WHH) theory 31, the upper critical magnetic field increases linearly with decreasing temperature and saturates at temperatures close to zero. The saturated value Bc2(0) can be estimated from the linear critical field determined from the extrapolation of the linear temperature dependence down to zero in accordance with the expression \({B}_{c2}(0)=-0.69{T}_{C}{|d{B}_{c2}/{dT}|}_{{T}_{C}}\).
When SC is suppressed through a Pauli paramagnetic pair-breaking mechanism, the Zeeman splitting energy of the electronic spins exceeds the superconducting energy gap and destroys the Cooper pair spin ground state. In this case, Bc2 is recognised as the Pauli-limiting field, defined as
where g ∼2 represents the Landé factor, μB the Bohr magneton, and Δ the value of the superconducting energy gap at zero temperature. The value of \({B}_{c}^{P}\)(0) can be estimated in the Clogston limit as \({B}^{P}\left[T\right]\simeq 1.8{T}_{c}\,\left[{\rm{K}}\right]\)32. The Pauli limiting critical magnetic field reveals a typical square-root temperature dependence \({B}_{c}^{P}\propto {\left(1-T/{T}_{C}\right)}^{1/2}\) at temperatures near Tc.
Which of the pair-breaking mechanisms dominate the suppression of SC in the presence of an applied magnetic field depends on the lateral sample size with respect to the direction of the field. The orbital effects dominate in bulk 3D samples or wide thin films in perpendicular magnetic fields. In the case of nanoscale samples, when the magnetic field is applied in a direction where the sample dimension is smaller than the coherence length \(\xi\), the pair breaking is realised via paramagnetic Zeeman spin-splitting. This is the case in e.g. for ultra-thin films (thickness < \(\xi\)) in the parallel field or superconducting nanostructures (with dimension < \(\xi\)).
In the following, we will show that the B-T phase diagrams of 1 ML and 2 ML FeTe samples suggest coverage-dependent contributions from both orbital and paramagnetic pair breaking mechanisms. The different curvatures of the Bc(T) curves of the 1 ML sample derived from different determination criteria (Fig. 4c) indicate the appearance of different pair breaking in the same sample. The huge slope of the Bc(T) curves (black dashed line) and the evidently higher critical magnetic field of the low-temperature phase with Tc2 = 2.4 K strongly suggest the presence of paramagnetic suppression of SC in this phase. On the other hand, the quasi-linear Bc(T) dependencies responsible for the phase with Tc1 = 2.8 K indicate orbital pair breaking, with much lower Bc ~ 260 mT (solid black line). The change in curvature of all Bc(T) curves between 60 mT and 100 mT (emphasised by arrows at the end of pink and orange curves), visible regardless of the determination criteria (10–90% ΔR), is due to the flow of measuring current through both phases. Above 150 mT the low temperature phase (Tc2 = 2.4 K) with higher (Pauli-limited) critical fields dominates (open black arrow). The observation of both orbital and paramagnetic pair breaking effects in one non-percolative sample is possible only if the sample consists of separate superconducting islands of different widths, of which a large number have sizes smaller than the coherence length.
For the case of orbital pair breaking, the critical field Bc(0) ~ 260 mT allows to estimate an in-plane coherence length of \(\xi \left(0\right)\) = 36 nm in the 1 ML case, which indeed only cuts a part of our typical island width distribution of (50 ± 20) nm.
For the 2 ML FeTe sample, the B-T phase diagram in Fig. 4f reveals quasi-linear dependences in all Bc(T) curves determined at different determination criteria (10–90% ΔR) and all measured temperatures. Here, the linear slopes change with determination criteria (10–90% ΔR) but converge into the same value Tc,1 ~ 5.8 K. For the highest slope, we can estimate the value of the zero temperature critical field Bc(0) of 1600 mT again by a WHH fit (solid black line in Fig. 4f). This value is far below the Clogston limit of Pauli pair breaking, which would predict critical fields of approximately 10 T for a superconductor with Tc = 5.8 K. It confirms the orbital pair breaking mechanism at Tc,1 in the 2 ML case, consistent with the observed linear behaviour of Bc(T). The corresponding coherence length for the critical field 1600 mT corresponds to\(\,\xi \left(0\right)\) = 14 nm, which is close to the low end of the typical distributions of (50 ± 20) nm. We comment here that for (n-Bi2Te3/bulk-FeTe) heterostructures with n = 7 considerably smaller values of\(\,\xi \left(0\right)\) = 5.2 nm were found5, which underlines the possible inequivalence in interface physics of the two approaches.
From the above discussion of field-dependent transport measurements and respective B-T phase diagrams we can conclude the presence of non-percolative multiphase SC in our FeTe/Bi2Te3 heterostructures. The multiphase character of the superconducting state in 1 ML and 2 ML samples becomes visible as multiple transitions with different pair-breaking mechanisms, starting at temperatures Tc ≈ 6 K and continuing below 3 K.
The high-temperature transition at 6 K is most intense at higher FeTe coverages 2 ML and respective critical fields reveal orbital pair-breaking character. This transition compares well to the reported formation of an energy gap at temperatures Tc = 6.5 K locally measured by STS in zero field on extended several tens of nanometre wide FeTe monolayer islands on Bi2Te314. This work’s proof of the true superconducting nature of the reported energy gap makes the material system a candidate for the search for topological superconductivity.
Transitions below 3 K, not reported so far, become well-defined at lower FeTe coverages of 1 ML. The temperature dependence of the critical magnetic field of the lowest transition at Tc2 = 2.4 K shows evident multiphase character and a huge increase in Bc near below Tc2. We attribute this increase to the presence of paramagnetic pair breaking in extremely small superconducting FeTe islands with lateral dimensions smaller than the coherence length.
The lateral dimensional effects of individual superconducting islands can cause not only different pair-breaking mechanisms and different values of the local critical magnetic field Bc, but also different Tc values. As the dimension of the islands decrease, the mean free path of the charge carriers forming its Cooper pairs decreases, which induces an increase in the electron-electron interaction. This reduces the electronic shielding, enhancing the Coulomb interaction, and leads to suppression of the amplitude of the superconducting wavefunction. Therefore, as the size of a superconducting nanostructure decreases, we can observe a gradual suppression of the energy gap as well as the critical temperature Tc33.
Variations in local Tc can, moreover, be caused by local variations in FeTe/Bi2Te3 interface properties such as “top” (FeTe van der Waals growth ontop of Bi2Te3) and “embedded” (chemical reaction with underlying Bi2Te3 during FeTe growth) monolayer island types14, the nucleation of double-layer FeTe islands even in the nominal 1 ML coverage case20, or the recently observed 2×8 and 1×2 superlattices in the case of van-der-Waals grown FeTe13.
Despite the shown unprecedented quantitative values of critical magnetic fields and our interpretation of Cooper pair breaking mechanisms in the framework of Ginzburg-Landau theory, the cause of absence of superconductivity in FeSe/Bi2Se334 and the origin of superconductivity in FeTe/Bi2Se39,10,13,35 remain fundamental open questions.
Methods
Sample preparation under UHV conditions
All samples studied in this work were entirely fabricated under UHV conditions (base pressure p = 5×10-11 mbar) to ensure clean materials and interfaces. FeCh (Ch = Te, Se) layers were grown on respective Bi2Ch3(0001) surfaces following a procedure described first by Cavallin et al. and Manna et al.14,17 for bulk Bi2Ch3 substrates. Here, we use 300 nm thin MBE-grown Bi2Ch3(0001) films on insulating BaF2(111) as substrates. In comparison to bulk surfaces, the choice of MBE-grown Bi2Ch3(0001) film substrates fosters a more homogeneous step-flow growth of FeCh monolayers nucleated at densely distributed Bi2Ch3(0001) step-edges18. Clean Bi2Te3(0001) and Bi2Se3(0001) surfaces were achieved under UHV conditions after the removal of protective (Te, Se) cap layers as described, e.g., in ref. 18.
Fe amounts equivalent to coverages of one, and two monolayers were deposited at room temperature from a calibrated Omicron evaporator. Fe fluxes from an Omicron evaporator were calibrated by comparing Fe 2p core level XPS intensities with those of Bi as well as Te or Se. Typical evaporator settings (IFil = 1.6 A, U = 710 V, Iem = 10 mA) resulted in fluxes of ~ 35 nA. Fe coverage estimations by XPS were cross-referenced to STM data of respective Fe growth on clean Au(111).
After Fe deposition, FeTe and FeSe layers form during a 30 min annealing step at temperatures 250 °C and 300 °C, respectively. For ex situ transport methods, an amorphous Si cap layer was finally added in situ to protect the interface from deterioration in air. Si-capping layers were deposited at room temperature from a Si evaporator at 20 cm sample distance at maximum pressures of 1 × 10-9 mbar during deposition.
Photoemission spectroscopy
k-PEEM measurements with laboratory light sources were done at room temperature using an Omicron NanoESCA system. The photoemission spectrometer is based on a PEEM column and an imaging double hemispherical energy filter. XPS is done with monochromatised Al Kα radiation. Energy-dependent k-space mapping was performed using a helium discharge lamp at hv = 21.2 eV with an analyser kinetic energy resolution ΔE = 0.2 eV. An overview of the used techniques can be found in ref. 36.
Fitting of core level spectra from XPS and UPS experiments was done in the program KolXPD [https://www.kolibrik.net/kolxpd]. Bi 5d, Te 4d, and Se 3d were fitted by spin–orbit split Voigt doublets. A Shirley background is assumed in all cases. For Fe 2p spectra, the leading edges are fitted by Doniach–Šunjic profiles.
Low-temperature transport measurements
The samples were glued on a standard Quantum Design Helium-3 puck for resistivity measurements with BF-6 glue. Samples were electrically separated from the Helium-3 puck by capacitor paper. Electric contacts were created by 50 μm silver wires, which were attached to the sample via indium droplets. The droplet was heated at 180 ◦C for several seconds by gently pressing the soldering tip to the sample surface. This approach ensures good contact through the protective Si layer. Contacts were arranged on the samples in four-point configurations with contact distances of ~1 mm.
The electrical ex-situ transport measurements were realised in a Quantum Design Physical Properties Measurement System (PPMS) using the AC Transport option in the temperature range from 300 K to 0.4 K in external magnetic fields oriented perpendicular to the plane of the sample and with a minimum current value of I = 0.01 mA.
Control measurements were performed with the Resistivity option to exclude possible electric current heating effects at the lowest temperatures with the AC Transport option. The resistivity option allows measuring with a minimum electric current of 5 nA.
Susceptibility measurements
DC susceptibility measurements were performed in Quantum Design Magnetic Properties Measurement Systems (MPMS3) in the temperature range from 1.8 K to 10 K in several constant magnetic fields. The sample was attached to a plastic straw, and the magnetic field was applied perpendicular to the sample plane.
Data availability
Data available on request from the authors.
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Acknowledgements
We thank Prof. M. Bremholm from Aarhus University for the growth of single crystalline bulk FeTe reference samples supported by VILLUM FONDEN via the Centre of Excellence for Dirac Materials (Grant No. 11744). This work was supported by the Czech Science Foundation (Project No. GA22-04408S) and through the project Quantum Materials for Applications in Sustainable Technologies (QM4ST), funded as project No. CZ.02.01.01/00/22_008/0004572 by Programme Johannes Amos Commenius, call Excellent Research. P.Sz. was supported by APVV-18-0358 project, European Microkelvin Platform, EU ERDF (European regional development fund) Grant No. VA SR ITMS2014 + 313011W856 and VEGA 1/0743/19. G.S. acknowledges support by the Austrian Science Funds (FWF) (Projects P30960-N27 and I4493-N) and LIT-2022-11-SEE-131 of the University of Linz. V.T. was also supported by the Slovak Research and Development Agency Projects numbers APVV-18-0197, APVV-20-0425 and APVV-22-0172.
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V. Tkáč, S. Vorobiov, and P. Baloh contributed with electrical sample contacting and transport measurements. M. Vondráček and J. Honolka contributed with sample growth, XPS/ARPES measurements, and manuscript writing. K. Carva performed DFT calculations. P. Szabó contributed with data analysis and manuscript writing. G. Springholz and Ph. Hofmann provided MBE-grown Bi2Te3 films and bulk Bi2Te3, respectively.
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Tkáč, V., Vorobiov, S., Baloh, P. et al. Multiphase superconductivity at the interface between ultrathin FeTe islands and Bi2Te3. npj 2D Mater Appl 8, 52 (2024). https://doi.org/10.1038/s41699-024-00480-x
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DOI: https://doi.org/10.1038/s41699-024-00480-x