Orbital signatures of Fano-Kondo line shapes in STM adatom spectroscopy

We investigate the orbital origin of the Fano-Kondo line shapes measured in STM spectroscopy of magnetic adatoms on metal substrates. To this end we calculate the low-bias tunnel spectra of a Co adatom on the (001) and (111) Cu surfaces with our density functional theory-based ab initio transport scheme augmented by local correlations. In order to associate different $d$ orbitals with different Fano line shapes we only correlate individual $3d$ orbitals instead of the full Co $3d$ shell. We find that Kondo peaks arising in different $d$ levels indeed give rise to different Fano features in the conductance spectra. Hence, the shape of measured Fano features allows us to draw some conclusions about the orbital responsible for the Kondo resonance, although the actual shape is also influenced by temperature, effective interaction, and charge fluctuations. Comparison with a simplified model shows that line shapes are mostly the result of interference between tunneling paths through the correlated $d$ orbital and the $sp$-type orbitals on the Co atom. Very importantly, the amplitudes of the Fano features vary strongly among orbitals, with the $3z^2$ orbital featuring by far the largest amplitude due to its strong direct coupling to the $s$-type conduction electrons.

Figure 1

Schematic drawing of an STM tip probing a magnetic atom on a metal substrate. The system is separated into three parts: the device region D (gray/yellow) contains the magnetic atom (dark gray/red) hosting the $d$ orbital giving rise to the Kondo peak, and parts of the substrate and STM tip. T and S (light gray/blue) are the bulk electrodes connected to the STM tip and substrate, respectively.

Figure 2

Comparison of Fano-Frota and Fano-Lorentz line shapes for different values of the $q$ parameter but for identical amplitudes and half-widths.

Figure 3

Fano-Lorentz (FL) and Fano-Frota (FF) fits of the impurity spectral function ${\rho }_d\left(\omega \right)$ (left) and the transmission function $T\left(\omega \right)$ (right) for $z^2$-orbital, Co@Cu(001), $U=2$ eV and ${\epsilon }_d=-1.0$ eV. See Sec. 4a for details.

Figure 4

Left, geometry of the Co atom deposited on a Cu(001) surface; dark gray/red, Co; gray/yellow, Cu; light gray/blue, Bethe lattice. Right, imaginary part of the hybridization function for the Co $3d$ shell.

Figure 5

Impurity spectral functions for the $z^2$ orbital of $\mathrm{Co}@\mathrm{Cu}$(001) for different Anderson impurity model parameters $U,{\epsilon }_d$.

Figure 6

Transmission functions for different $d$ orbitals of $\mathrm{Co}@\text{Cu}$(001). Coulomb repulsion $U=2$ eV, and energy level ${\epsilon }_d=-1$ eV (approximate particle-hole symmetry). The red continuous curves show the calculated transmission, the black dashed curves Fano-Frota fits. The transmission background has been subtracted [59].

Figure 7

Transmission functions for different $d$ orbitals of $\mathrm{Co}@\text{Cu}$(001). Coulomb repulsion $U=3$ eV vary occupation by shifting ${\epsilon }_d$. The red continuous curves show the calculated transmission, the black dashed curves Fano-Frota fits. The transmission background has been subtracted [59].

Figure 8

Left: Geometry of the Co atom deposited on a Cu(111) surface; dark gray/red, Co; gray/yellow, Cu; light gray/blue, Bethe lattice. Right: Imaginary part of the hybridization function of the Co $3d$ shell.

Figure 9

Transmission functions for different $d$ orbitals of $\mathrm{Co}@\text{Cu}$(111). Coulomb repulsion $U=2$ eV, ${\epsilon }_d=-1.0$ eV. The red continuous curves show the calculated transmission, the black dashed curves Fano-Frota fits. The transmission background has been subtracted [59].

Figure 10

Transmission functions for different $d$ orbitals of $\mathrm{Co}@\text{Cu}$(111). Coulomb repulsion $U=3$ eV vary occupation by shifting ${\epsilon }_d$. The red continuous curves show the calculated transmission, the black dashed curves Fano-Frota fits. The transmission background has been subtracted [59].

Figure 11

Temperature dependence of two different line shapes for $\mathrm{Co}@\mathrm{Cu}$(111), $xz,U=3$ eV, ${\epsilon }_d=-1.5$ eV, and ${\epsilon }_d=-2.2$ eV, respectively. Top: Transmission. Bottom: $q$ parameter; the lines are a guide for the eye.

Figure 12

Sketch of the simplified model. The effective atom A is described by the correlated $d$ level and one conduction electron level $c$, in contact with the surface and the tip.

Figure 13

Transmissions calculated ab initio with the ANT.G package (see Sec. 4) and for the simplified model; $\mathrm{Co}@\mathrm{Cu}$(001), $U=2$ eV, ${\epsilon }_d=-1$ eV. The transmission functions are rescaled and offset for better visibility.

Figure 14

Transmissions calculated ab initio with the ANT.G package (see Sec. 4) and for the simplified model; $\mathrm{Co}@\mathrm{Cu}$(111), $U=2$ eV, ${\epsilon }_d=-1$ eV. The transmission functions are rescaled and offset for better visibility.