Robust two-dimensional superconductivity and vortex system in Bi2Te3/FeTe heterostructures

The discovery of two-dimensional superconductivity in Bi2Te3/FeTe heterostructures provides a new platform for the search of Majorana fermions in condensed matter systems. Since Majorana fermions are expected to reside at the core of the vortices, a close examination of the vortex dynamics in superconducting interface is of paramount importance. Here, we report the robustness of the interfacial superconductivity and 2D vortex dynamics in four as-grown and aged Bi2Te3/FeTe heterostructure with different Bi2Te3 epilayer thickness (3, 5, 7, 14 nm). After two years’ air exposure, superconductivity remains robust even when the thickness of Bi2Te3 epilayer is down to 3 nm. Meanwhile, a new feature at ~13 K is induced in the aged samples, and the high field studies reveal its relevance to superconductivity. The resistance of all as-grown and aged heterostructures, just below the superconducting transition temperature follows the Arrhenius relation, indicating the thermally activated flux flow behavior at the interface of Bi2Te3 and FeTe. Moreover, the activation energy exhibits a logarithmic dependence on the magnetic field, providing a compelling evidence for the 2D vortex dynamics in this novel system. The weak disorder associated with aging-induced Te vacancies is possibly responsible for these observed phenomena.

Scientific RepoRts | 6:26168 | DOI: 10.1038/srep26168 heterostructures remain superconducting but with a broader transition region. A new feature appears at ~13 K after two years, and its relevance to superconductivity is further revealed by high field studies. The resistance of the Bi 2 Te 3 /FeTe heterostructure just below the transition temperature follows the Arrhenius relation, which we attribute to thermally activated flux flow (TAFF) behavior. The activation energy exhibits a logarithmic dependence on the applied magnetic field, indicating the existence of a 2D vortex system. Figure 1(a) presents the normalized temperature dependent resistances R(T) of Bi 2 Te 3 (7 nm)/FeTe in both as-grown and after-two-years measurements. Before the normalization, the normal state resistance of all after-two-years samples is generally higher: using R(18 K) as a benchmark, it is 12-64% larger compared with the as-grown samples. Since the formation of Te vacancies is always observed in the Bi 2 Te 3 and FeTe after long-term exposure to air [35][36][37] , it provides an explanation for the aging induced resistance increase here. Despite the increase in resistance, superconductivity is still robust after two years' air exposure, although the transition regime becomes broader and the zero-resistance temperature T zero drops. Therefore, the weak disorder from the Te vacancies is not completely detrimental to superconductivity; instead it provides an interesting avenue for investigating the vortex dynamics, which will be discussed later. Compared with the as-grown result, in Bi 2 Te 3 (7 nm)/FeTe the temperature of the maximum resistance, T max , shifts from 12.4 K to 13 K and the resistance exhibits a two-step drop below T max in the after-two-years case. To provide a clearer view on these results, dR/dT curves are plotted in Fig. 1(b). As can be seen, in the after-two-years case, a shoulder appears at around 11-13 K, corresponding to the first slow resistance drop in the R(T) curve. As temperature further decreases, a sharp transition starts. We define the starting point of the sharp resistance drop as T mid in after-two-years R(T) result, as shown in Fig. 1(b). Therefore, compared with the as-grown result, it demonstrates that an additional new feature appears at around 13 K in after-two-years case.

Results and Discussion
To learn more about the observation of the new feature, we further measure R(T) of after-two-years heterostructures with different Bi 2 Te 3 layer thicknesses. Compared with the as-grown results in Fig. 1(c) and its inset, a broader superconducting transition and a two-step resistance drop are observed in all after-two-years heterostructures even with the Bi 2 Te 3 layer down to 3 nm as shown in Fig. 1(d) and its inset. Furthermore, from the dR/dT curves in the inset of Fig. 1(d), T max shows an increase after two years and locates at ~13 K for all samples, manifesting that the new feature is indeed induced by the aging effect. Meanwhile, relative to the full superconducting transition, the shoulder is weakened as the Bi 2 Te 3 thickness decreases as shown in the inset of Fig. 1(c,d), which indicates that the new feature around 13 K is probably relevant to the interfacial superconductivity of the heterostructure.  To further investigate the aging effect on the superconducting transition of Bi 2 Te 3 /FeTe heterostructure, the temperature dependent resistances in different magnetic fields are studied. Fig. 2(a,b) show the as-grown and after-two-years R(T) results of Bi 2 Te 3 (14 nm)/FeTe in different magnetic fields applied perpendicular to the ab plane, respectively. With an increasing magnetic field, T max , T mid and T zero gradually shift to lower temperature together as superconductivity is suppressed. Similar behavior is also observed in the parallel fields. From the R(T) curves in different magnetic fields, the corresponding upper critical fields H max , H mid and H zero in both as-grown and after-two-years cases can be obtained, and the H -T phase diagrams of Bi 2 Te 3 (7 nm)/FeTe and Bi 2 Te 3 (14 nm)/ FeTe are plotted in Fig. 3(a,b), respectively. For both samples, the phase diagram clearly exhibits the anisotropy between the parallel and perpendicular field for both as-grown and after-two-years cases. Meanwhile, the anisotropy ratio ⊥ H H / c c 2 // 2 of the after-two-years sample shows a decrease, especially for H zero , comparing with the as-grown one. For both field directions, the as-grown H max locates between the after-two-years H max and H mid , and all three curves show the same variation trend as magnetic field changes. It further manifests that the new feature at 13 K, i.e., the after-two-years H max , are relevant to the interfacial superconductivity of the heterostructure. In the study of BiS 2 -based superconductor LaO 0.5 F 0.5 BiS 2 , two-step drop of R(T) in different magnetic fields was also observed 38 . Since the LaO 0.5 F 0.5 BiS 2 sample was polycrystalline, the origin of two anisotropic upper critical fields was attributed to the anisotropy of the grains in different directions 38 . However, this scenario cannot be applied easily to our heterostructures, since they are all composed of single crystallined films. In addition, the anisotropic behavior of upper critical fields in our heterostructures can be largely suppressed and affected by the annealing process in N 2 atmosphere, at the expense of lowering the superconductivity transition temperature (see Supplementary information).
Comparing with type-I superconductors, our Bi 2 Te 3 /FeTe heterostructure samples show a relatively broad superconducting transition regime (> 3 K) in magnetic fields even for the as-grown samples. This means the mixed states exist in the transition regime and vortex dynamics studies will be important and can provide useful information about the interfacial superconducting behavior. Thermally activated flux flow (TAFF) describes the motion of vortices due to the activation over some energy barriers, e.g. pinning centers [39][40][41] . It was widely studied in 3D iron-based superconductors, such as β-FeSe single crystal 41  Recently, TAFF was also reported in novel 2D superconductors, such as FeSe single layer 47 and exfoliated NbSe 2 48 , where in the latter case the TAFF behavior was reported to come from the unbinding of vortex-antivortex pairs. According to the TAFF theory, the resistivity ρ in the TAFF region follows the Arrhenius relation [39][40][41] Fig. 4. For both as-grown and after-two-years cases, the temperature dependent resistances of two samples in different perpendicular fields are plotted on ln ρ(T) − 1/T axes in Fig. 4(a,b,d,e), respectively. As can be seen, all curves exhibit good linear behaviors at low temperature region, manifesting that they follow the Arrhenius relation very well. All fitting lines in different fields cross to one point, whose corresponding temperature T m should be equal to the T c of the system. For the as-grown case, T m of Bi 2 Te3(7 nm)/FeTe and Bi 2 Te 3 (14 nm)/FeTe are obtained as 11.6 K and 10.2 K, which are close to their T max = 12.4 K and 11.4 K, respectively. However, for after-two-years results (c.f. Fig. 4(b,e)), T m of Bi 2 Te 3 (7 nm)/ FeTe and Bi 2 Te 3 (14 nm)/FeTe are obtained as 9 K and 8.7 K, which are closer to their T mid of ~ 11 K than T max of ~ 13 K. This indicates that as-grown samples fall into the TAFF region much faster than the after-two-years samples when the superconducting transition commences. This slower approach to the TAFF region in the after-two-years samples, to a large extent, is affected by the new feature around 13 K, although the origin of this new feature remains unclear.
From the linear fitting of ln ρ(T, H) − 1/T curves, the activation energy U(H) can be obtained from the slope value. Figure 4(c,f) displays U at different magnetic fields for Bi 2 Te 3 (7 nm)/FeTe and Bi 2 Te 3 (14 nm)/FeTe, respectively. For the as-grown samples (triangular symbols in Fig. 4(c,f)), U exhibits a logarithmic dependence on the magnetic field, U = U 0 ln(H 0 /H), with H 0 ≈ H c2 , as observed in other 2D systems [48][49][50] . This observation of a 2D vortex system is consistent with the earlier report of the Berezinsky-Kosterlitz-Thouless transition in the Bi 2 Te 3 / FeTe interface 33,51 . For both Bi 2 Te 3 (7 nm)/FeTe and Bi 2 Te 3 (14 nm)/FeTe samples, the fitted value of H 0 decreases after two years' air exposure as displayed in Fig. 4(c,f), which shows a good agreement with the result of upper critical field H zero in Fig. 3. The energy prefactor where d is the superconducting layer thickness, λ is the penetration depth and Ξ is a numerical factor which depends on the nature of the energy barrier 50 . In the aged samples, U shows an overall decrease, implying that the aging weakens the vortex pinning behavior or enhances the flux flow of the system. Interestingly, the logarithmic dependence of U on H remains valid, albeit with a lower U 0 (circular symbols in Fig. 4(c,f)). Therefore, the 2D nature of the vortex system remains robust in the aged heterostructures. Assuming that the dominant thermal activation mechanism remains the same in the aged samples, the drop in U 0 compared with the as-grown samples can be attributed to an increase in λ. Empirically, λ(0) ≈ 1.05× 10 −3 (ρ 0 /T c ) 1/2 , where ρ 0 is the residual resistivity of the normal state and λ(0) is the zero temperature limit of the penetration depth 52 . Further assuming that the temperature dependences of λ(T) and ρ(T) do not vary strongly with age, we can estimate , ′ U U / 0 0 is estimated to be ~0.50, in reasonable agreement with the observed ratio of ~0.38. Following the same procedure for Bi 2 Te 3 (14 nm)/FeTe, ′ U U / 0 0 is estimated to be ~0.52 whereas the observed ratio is also ~0.38. One possible scenario responsible for the logarithmic magnetic field dependence of U is the nucleation and the subsequent motion of the dislocation pairs associated with the vortex lattice. In this model, U is primarily the energy cost of nucleating the pair 49,50 . In the aged samples, the lowering of U can be associated with the relative ease of nucleating the dislocation pairs. Since exposing Bi 2 Te 3 and FeTe to air inevitably promotes the formation of Te vacancies [35][36][37] , the excess vacancies thus lower the energy barrier required to nucleate dislocation pairs. In addition, these vacancies introduce weak disorder to the material system, thereby resulting in a lower superconducting transition temperature and a higher normal state resistance; these trends are fully consistent with experimental observation in all aged Bi 2 Te 3 /FeTe heterostructures.

Conclusion
In conclusion, we study the superconducting properties of as-grown and aged Bi 2 Te 3 /FeTe heterostructures. Superconductivity is robust after two years' air exposure, even when the thickness of the Bi 2 Te 3 layer is down to 3 nm. Comparing with the upper critical fields of the as-grown measurements, a new feature around 13 K induced by the aging effect is demonstrated to be relevant to the interfacial superconductivity. The resistance of the Bi 2 Te 3 / FeTe heterostructures below the superconducting transition temperature obeys the Arrhenius relation, which demonstrates the TAFF behaviour. The activation energy U(H) follows a logarithmic dependence on the applied magnetic field in the as-grown samples, indicating that the vortex system is two-dimensional. The logarithmic dependence remains valid in the aged samples, although U(H) becomes lower at all magnetic fields studied, leading to the conclusion that the 2D vortex system in Bi 2 Te 3 /FeTe heterostructures is robust.

Methods
The Bi 2 Te 3 /FeTe heterostructure samples used in the experiment were grown by molecular beam epitaxy on a (111) semi-insulating GaAs substrate with an undoped 50 nm-thick ZnSe buffer layer. A 140 nm-thick FeTe layer was first deposited onto the ZnSe buffer, followed by a growth of the Bi 2 Te 3 layer on the FeTe layer via van der Waals expitaxy. The thicknesses of the Bi 2 Te 3 epilayer were 3 nm, 5 nm, 7 nm and 14 nm for four different wafers, respectively. Detailed structural characterizations can be found in the early work 33 . Silver paste and aluminum wires were employed to serve as the electrical contacts, after the wafers were cut into 2 mm × 6 mm strips by a diamond scribe. After the first round measurements on the as-grown heterostructures, all samples were exposed to the air atmosphere at room temperature for two years. To avoid the complication from the sample dependence, all four samples, i.e. Bi 2 Te 3 (3 nm)/FeTe, Bi 2 Te 3 (5 nm)/FeTe, Bi 2 Te 3 (7 nm)/FeTe, and Bi 2 Te 3 (14 nm)/FeTe, which were measured in the second round after two years, are exactly the same strips as the ones used in the first round. All transport measurements were conducted in a Quantum Design physical property measurement system with a 14-Tesla superconducting magnet and a base temperature of 2 K.