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Caption : fig. s1 xps of ar 2p3/2-2p1/2  peaks after implantation of atomic ar in the cu(110) sample (black), after consequent annealing at 1050k for 5 min (red), and after final annealing at 1100k for 20 min (blue).    

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Caption : fig. s2 stm images of the cu(001) surface  (50 x50 nm2) at the intermediate stage of sample fabrication: (a) – after deposition of fe and annealing at 620k. due to annealing, fe forms flat nanoislands of 2 to 3 ml thick (a few of them are encircled) embedded into two or three near-surface layers of the surface.  the incorporation of fe pushes  cu towards the surface, resulting in a developed stepped structure on the surface; (b) – after capping the nanoislands with 32 ml (about 6 nm) of cu and light annealing.  a sub-atomic corrugation of the terraces appears above the buried fe nanoislands.  

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Caption : fig. s3. (a – c) sts maps 30x30 nm2of cu(001) surface with embedded subsurface fe nanoclusters: (a) and (b) the same sample with nanoclusters buried 6 nm below the surface and scanned with two different bias voltages; (c) sts maps of the sample with fe nanoclusters buried at 25 nm. (d – f) examples of oscillating conductance measured with the samples with fe nanoclusters embedded at depths: (d) – 4 nm, (e) – 6 nm, and (f) – 9 nm. the encircled spot on (a) and (b) indicates the location where the plot (e) has been measured.  

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Caption : fig. s4. (a) – stm image of fe(001) epitaxial layer ; (b) – normalized surface conductance in three different locations of the sample showing the oscillatory behaviour due to qw states.    

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Caption : fig. s5. (a) – stm image of bi nanoisland on the fe(001) surface; (b) – stm image of  the surface on the top of bi nanoisland; (c) – cross-section of bi nanoisland on the top of bi nanoisland ; (d) – normalized surface conductance with the oscillations induced by qw states.