**5.3. Proximity-induced superconductivities in Bi inclusions/bismuth chalcogenide thin films**

Recent studies have shown a two-dimensional interface state between TIs and superconductors resulting from the superconducting proximity effect that supports Majorana fermions [76, 77]. Majorana fermions, novel particles which are their own antiparticles, can potentially be applied to topological quantum computing, which has motivated intense interest in TIs [53].

**Figure 12.** (a) Temperature-dependent normalized *ab* resistivities (*ρ/ρ*300 K) between 1.8 and 300 K of 46- and 200-nmthick Bi2Te3 films. Upper inset: an EDS mapping image of a typical Bi-rich cluster. Lower inset: zoomed-in view of the *ρ/ρ*300 K in the low temperature range. (b) *ρ*(*T*) in 1.75–6.0 K of the 200 nm film at various *H||c* from 0 to 1 T. Inset: the onset *Tc* of the two superconducting transitions as a function of magnetic field. (c) Auger electron spectroscopy (AES) elemental depth profiling of a non-superconducting (46-nm-thick) and a superconducting (200-nm-thick) Bi2Te3 films. (d and e) The size distribution of Bi-rich clusters and Bi nanoclusters inside the clusters. (f) Schematics of the surface characteristics and a suggested superconducting mechanism in the Bi2Te3 films [53].

Koren et al. observed the local superconductivity in Bi2Te2Se and Bi2Se3 films below 2–3 K, which was naturally induced by small amounts of superconducting Bi inclusions or precipitations on the surface [78]. Moreover, Le et al. reported superconductivity at an onset critical temperature of approximately 3.1 K in a topological insulator 200-nm-thick Bi2Te3 thin film grown by pulsed laser deposition [53]. Indeed, **Figure 12a** shows the normalized resistivity *ρ/ ρ*300 K of a 46-nm-thick Bi2Te3 film (S1) and a 200-nm-thick Bi2Te3 film (S2) as functions of temperatures (*T*) from 1.8 to 300 K. Both films show a decrease in resistivity (*ρ*) with decreasing *T* in the range of 20–300 K, implying that the films exhibit weak metallic properties commonly seen in narrow band-gap semiconductors with high carrier concentrations [53]. Below 20 K (**Figure 12a**, the lower inset), the *ρ/ρ*300 K of S1 shows a gentle upturn because of the weak localization of electrons [7], whereas the *ρ/ρ*300 K of S2 reaches a plateau before dropping slightly at *Tc1* ≈ 5.8 K and then sharply at *Tc2* ≈ 3.1 K. **Figure 12b** further shows the *H*||c-dependent *ρ*(*T*) of S2 in the low *T* regime, where *H*||c is the applied magnetic field along the *c*-axis of the film. At *H*||c = 0, *<sup>ρ</sup>* drops abruptly by 8% below 2 but does not go down to zero, even at *T* = 1.8 K. This nonzero *ρ* at low *T* indicates that the superconducting volume ratio is not 100%. The inset in **Figure 12b** shows that the 2 (1 ) decreases from 3.1 (5.8) to 1.8 (5.4) K with increasing *H||c* from 0 to 0.2 T, strongly indicating that both transitions are superconducting in nature.

The detailed investigations of S2 strongly suggest the existence of superconducting Bi nanoclusters on the surface that induce the *Tc1* ~ 5.8 K. EDS lateral elemental mapping revealed that the distributions of Te and Bi were not uniform, and many Bi-rich (47–54 at.%) clusters were visible (green color), as shown in the upper inset in **Figure 12a**, differing substantially from the uniform distribution and cluster-free surface observed in film S1. The size distribution and the most probable size of Bi-rich clusters are in the range of 400–2400 nm and 560–772 nm, respectively. Intriguingly, a closer inspection reveals that Bi-rich clusters are composed by some Bi nanoclusters (or nanograins) with a size of 20–62 nm.

The Bi-rich environment on the film surface is confirmed by AES analysis (**Figure 12c**) [53]. This is because the vapor pressure of Te (at *T*<sup>S</sup> = 300°C) is approximately 105 times higher than that of Bi, and therefore, more Te atoms are re-evaporated from the 300°C substrates [79]. The loss of Te is more severe in film S2 than in film S1 (14.3% in S2 and 4.5% in S1 at depth *Z* = 0, **Figure 12c**) because of the six times longer deposition time of S2 (60 min) compared to S1 (10 min). In addition, the nonstoichiometric effect is strongly depth-dependent (**Figure 12c**). The Te/Bi ratio gradually increases toward the stoichiometric ratio of 3/2 in 200-nm-thick films or slightly exceeds it (Te-rich) in 46-nm-thick films when the depth (*Z*) of the films increases. Under such a sufficiently high surface concentration of Bi atoms, the Bi clusters precipitate and segregate readily on the S2 surface to minimize overall free energy, as long as the substrate temperature of 300°C is higher than the 271°C melting point of Bi, as demonstrated in **Figure 12f**. Notably, the Bi clusters can only be observed in highly Bi-rich (14.3% at *Z* = 0) films (S2) and not in low Bi-rich (4.5% at *Z* = 0) films (S1), suggesting a critical Bi-rich concentration for Bi precipitation (separating a Bi phase) in a Bi2Te3 film [53]. The *Tc1* at ~5.8 K found in our samples should be induced by the superconducting transition of the Bi nanoclusters, which is closely consistent with the *T*<sup>c</sup> of 6.3 K for the surface Bi islands observed in Bi2Te2Se films [78]. The tiny resistivity drop at *Tc1 =* 5.8 K (by approximately 0.5%, **Figure 12b**) indicates that the amount of superconducting Bi nanoclusters in S2 is likely small and, therefore, the Josephson coupling between these islands is extremely weak. Since the superconductivity of Bi nanoclusters survived until *H||c* = 1.0 T (**Figure 12b**), the critical field of Bi nanoclusters is in between 0.3 and 1.0 T. This section demonstrates that natural defects generated during PLD growths, namely superconducting Bi nanoclusters or Bi inclusions, can substantially induce nonsuperconducting TI thin films (i.e., Bi2Te3, Bi2Se3, and Bi2Te2Se) into superconducting states at low temperatures.
