Superconducting ferecrystals: turbostratically disordered atomic-scale layered (PbSe)1.14(NbSe2)n thin films

Hybrid electronic heterostructure films of semi- and superconducting layers possess very different properties from their bulk counterparts. Here, we demonstrate superconductivity in ferecrystals: turbostratically disordered atomic-scale layered structures of single-, bi- and trilayers of NbSe2 separated by PbSe layers. The turbostratic (orientation) disorder between individual layers does not destroy superconductivity. Our method of fabricating artificial sequences of atomic-scale 2D layers, structurally independent of their neighbours in the growth direction, opens up new possibilities of stacking arbitrary numbers of hybrid layers which are not available otherwise, because epitaxial strain is avoided. The observation of superconductivity and systematic Tc changes with nanostructure make this synthesis approach of particular interest for realizing hybrid systems in the search of 2D superconductivity and the design of novel electronic heterostructures.

Supplementary Figure S1 shows HAADF-STEM overview images of ferecrystals (PbSe) 1.14 (NbSe 2 ) n with n = 1 and 3. Grain boundaries are visible. The grain size is estimated as 5 nm -50 nm. The total film thickness agrees with the film thickness obtained by XRR. Figure S2. Thickness of the repeat units. The repeat unit thicknesses of (PbSe) 1.14 (NbSe 2 ) n ferecrystals and MLCs 4-6 have been determined by XRD. A linear fit obtained for the ferecrystals is shown. Figure 2, the c-lattice parameter increases linearly with n and a linear fit of c(n) yields an increase of the film thickness by NbSe 2 = 6.36(1) Å for the addition of one NbSe 2 layer obtained from the slope and a thickness of PbSe = 6.06(2) Å of the PbSe bilayer, obtained as the intercept at n = 0. These thicknesses are roughly in agreement with those of NbSe 2 monolayers in bulk NbSe 2 which are 6.27(2) Å thick 1 and with atomic bilayers in bulk PbSe, which are reported 6.1213 Å or 6.117 Å thick 2,3 . Similarly, the fit of c(n) for the corresponding MLCs leads to

Evaluation of in-plane XRD scans
The in-plane XRD scans (main text, Figure 2c) contain peaks, which can be indexed as Bragg reflections (hk0) from individual NbSe 2 and PbSe layers assuming crystal structures equal to the respective bulk structures of NbSe 2 (hexagonal in-plane unit cell) and PbSe (square in-plane unit cell), with the c-axes parallel to the stacking direction in the ferecrystals. Structure models of a monolayer NbSe 2 and an atomic bilayer of PbSe projected onto the layer plane are shown schematically in Figure  2d. The resulting a-and b-parameters for ferecrystals and MLCs are listed in the main text Table 1. For ferecrystals, bulk NbSe 2 and bulk PbSe NbSe 2 = √3 NbSe 2 (hexagonal in-plane unit cell) and PbSe = PbSe (square in-plane unit cell). In contrast, in MLCs the crystal structures distort in order to achieve lattice matching along the b-axes. Therefore, the NbSe 2 and PbSe layers in MLCs show rectangular in-plane unit cells 7,8 .
Supplementary Figure S3. X-ray diffraction data as a function of annealing temperature for (PbSe) 1.14 (NbSe 2 ) 3 ferecrystal. The optimum annealing temperature was found to be 450 °C. Silicon substrate peaks are indicated by (*), aluminium stage peaks are present are indicated by (#).

Hall measurements
Supplementary Fig. S4(a) shows the magnetic field dependence of the Hall voltages V H of the (PbSe) 1.14 (NbSe 2 ) n ferecrystals at T = 10 K, multiplied by the total sample thickness t. The inset shows a schematic of the measurement setup. The measurements were performed using a lock-in amplifier (DSP 7265) with currents I rms = 5 μA. The current I was applied between two contacts at two opposite arms of the cross-shaped sample and the voltage V m was measured between the contacts at the other two arms during slow (0.
A macroscopic difference between the MLC and the ferecrystal samples compared in Figure 5b of the main text is their total film thickness. The total thickness of the ferecrystals is about 40 nm, thereof 20 nm of NbSe 2 layers for n = 1, whereas the total thickness of the analogous MLCs is at least several micrometers 4,5,10 . However, the film thickness dependence of the transition temperature of 2H-NbSe 2 suggests that this should not play a major role: T c of a 10 nm thin NbSe 2 flake is reported to be 5.7 K to 6.7 K 11,12 almost reaching the bulk value. Instead, the transition temperatures of the MLCs and ferecrystals are much lower than this, indicating that the total film thickness even in the case of superconductive coupling between the NbSe 2 layers does not predominantly determine T c .
Possible reasons for the differences in T c of the ferecrystals in comparison to the MLCs are differences in the polytype and stoichiometry of their NbSe 2 layers. However, the HAADF-STEM images of the ferecrystals show a trigonal prismatic coordination of the Nb atoms by Se atoms in accordance with the coordination reported for NbSe 2 layers in MLCs (PbSe) 1+x (NbSe 2 ) n and in 2H-NbSe 2 , the most common polytype of NbSe 2 4,5,10,13,14 . In contrast, for the NbSe 2 layers in the ferecrystals (SnSe) 1+ NbSe 2 ) n indications for a mixture of a trigonal prismatic and an octahedral coordination have been reported 15 . NbSe 2 polytypes containing a mixture of trigonal prismatic and octahedral coordination, e.g. 4H-NbSe 2 , have been reported to show a lower transition temperature to superconductivity (T c < 6.5 K 16,17 ) than the polytype 2H-NbSe 2 (T c = 7 K 16-18 ), which contains only trigonal prismatic coordination. Deviations from T c = 7 K in NbSe 2 are also reported to be in connection with a non-stoichiometry, due to interstitial Nb atoms in NbSe 2 , i.e. Nb 1+y Se 2 , and T c is reported to decrease from 7 K for y = 0 to approximately 5.5 K for y = 0.02 13,16 . However, there were no indications for interstitial atoms in the gaps between the ferecrystal layers in the HAADF-STEM images and in the XRD-scans obtained in this work. Therefore, a deviation in polytype or nonstoichiometry does not seem to be a probable explanation for the lower T c of the ferecrystals in comparison to the MLCs.