Theory of Differential Conductance of Co on Cu(111) Including Co $s$ and $d$ Orbitals, and Surface and Bulk Cu States

We revisit the theory of the Kondo effect observed by a scanning-tunneling microscope (STM) for transition-metal atoms (TMAs) on noble-metal surfaces, including $d$ and $s$ orbitals of the TMA, surface and bulk conduction states of the metal, and their hopping to the tip of the STM. Fitting the experimentally observed STM differential conductance for Co on Cu(111) including both the Kondo feature near the Fermi energy and the resonance below the surface band, we conclude that the STM senses mainly the Co $s$ orbital and that the Kondo antiresonance is due to interference between states with electrons in the $s$ orbital and a localized $d$ orbital mediated by the conduction states.

Figure 1

Sketch of the system. The Co atom is described by a noninteracting level $a$ representing an $s$ orbital and a $d$ level intraorbital Coulomb repulsion $U$. Both levels hop to the bulk and surface conduction states.

Figure 2

Spectral density for a given spin of the $d$-orbital as a function of energy for ${ϵ}_d=-0.8\mathrm{eV}$, $U=1.6\mathrm{eV}$, ${ϵ}_a=0$, 33 eV, $V_b^d=-0.50\mathrm{eV}$, $V_s^d=0.62\mathrm{eV}$, $V_b^a=-1.41\mathrm{eV}$, and $V_s^a=-1.46\mathrm{eV}$ at $T=4\mathrm{K}$. The inset shows details of the Kondo peak near $\omega =0$.

Figure 3

Spectral density for a given spin of the Co $s$ orbital as a function of energy for the same parameters as Fig. 2. The inset shows details of the peak near $\omega =0$.

Figure 4

Differential conductance as a function of voltage. Black solid line: experimental $dI/dV$ for Co/Cu(111). Orange solid line: $t_a=-0.978$, $t_d=-0.175$, $t_s=-0.1$, and $t_b=-0.04$. Green dashed line: $t_a=-0.959$, $t_d=-0.192$, $t_s=-0.2$, and $t_b=-0.08$. Blue dashed-dot line: $t_a=-0.925$, $t_d=-0.185$, $t_s=-0.31$, and $t_b=-0.12$. The inset displays the Kondo dip.

Figure 5

Same as Fig. 4 for $V_s^d=-1.36\mathrm{eV}$, $t_a=-0.67$, $t_d=-0.24$, $t_s=-0.67$, and $t_b=0.20$. The inset shows the Kondo dip at low energies.