Multiple scattering theory for superconducting heterostructures

We generalize the screened Korringa-Kohn-Rostoker method for solving the corresponding Kohn-Sham-Bogoliubov–de Gennes equations for surfaces and interfaces. As an application of the theory, we study the quasiparticle spectrum of Au overlayers on a Nb(100) host. We find that within the superconducting gap region, the quasiparticle spectrum consists of Andreev bound states with a dispersion which is closely connected to the underlying electronic structure of the overlayer. We also find that the spectrum has a strongly $k$-dependent induced gap. The properties of the gap are discussed in relation to the thickness of the overlayer, and it is shown that certain states do not participate in the Andreev scattering process.

Figure 1

DOS (arbitrary units) of bulk Nb ($E_F=0.713$ Ry) in the case of ${\overline{\Delta }}_{Nb}=0$ Ry (left panel) and ${\overline{\Delta }}_{Nb}=0.01$ Ry (right panel). The blue line corresponds to the density of electronlike states and the red line corresponds to the density of holelike states.

Figure 2

Contour plot of the BSF (normal-state band structure) from the “middle” of the Au layers for different thicknesses of the Au: 3 Au layers (top left panel), 9 Au layers (top right panel), 24 Au layers (bottom left panel), and 93 Au layers (bottom right panel).

Figure 3

Contour plot of the BSF (normal-state band structure) for different layers. In the interface region, there are 6 Nb layers, 9 Au layers, and 3 vacuum layers.

Figure 4

Contour plot of the BSF (quasiparticle spectrum calculated from BdG equations) from the “middle” of the Au layers for different thicknesses of the Au: 3 Au layers (top left panel), 9 Au layers (top right panel), 24 Au layers (bottom left panel), and 93 Au layers (bottom right panel).

Figure 5

Contour plot of the BSF (quasiparticle spectrum calculated from BdG equations) for different layers in the system consisting of 6 Nb layers, 9 Au layers, and 3 empty sphere layers.

Figure 6

Induced gap on the Au layers as a function of the thickness of the Au, extracted from results similar to that shown in Fig. 4.

Figure 7

Contour plot of the BSF in the $k_y=0$ direction corresponding to the last layer of Au. The Au sample consisted of 9 layers. The quasiparticle spectrum was calculated from the BdG equations. ${\overline{\Delta }}_{Nb}=0$ Ry is used on the left panel and ${\overline{\Delta }}_{Nb}=0.05$ Ry is used on the right panel.