Many-body electronic structure and Kondo properties of cobalt-porphyrin molecules

We use a combination of first-principles many-body methods and the numerical renormalization-group technique to study the Kondo regime of cobalt-porphyrin compounds adsorbed on a Cu(111) surface. We find the Kondo temperature to be highly sensitive to both molecule charging and distance to the surface, which can explain the variations observed in recent scanning-tunneling-spectroscopy measurements. We discuss the importance of many-body effects in the molecular electronic structure controlling this phenomenon and suggest scenarios where enhanced temperatures can be achieved in experiments.

Figure 1

Energy of electronic orbitals of TBrPP-Co in gas phase, obtained from first-principles GW calculations. The calculated Coulomb energy cost $U$ for double occupation of the $d_{3z^2-1}$ orbital is also indicated. Orbitals in the middle and right columns have projection on $\text{Co}3d$ atomic orbitals indicated. The “HOMO” and “LUMO” labels refer, respectively, to occupied and unoccupied orbitals in the nonmagnetic TBrPP. The Fermi energy $E_F$ indicated is an estimate of the actual Fermi energy of adsorbed TBrPP-Co on copper (see text).

Figure 2

(Color online) (a) Probability distribution of GW molecular orbitals HOMO-1, HOMO, LUMO, and $d_{3z^2-1}$ on a plane perpendicular to the plane of the porphyrin ring and crossing neighbor atoms N–Co–N. Probability is highest at the center of the regions enclosed by dark “halos”. The lowest amplitude background was replaced with white and therefore the extent of the outer dark “halos” is somewhat arbitrary. The TBrPP-Co molecule is shown in front view (e) and side view (f) A single cobalt atom is coupled to four nitrogen atoms at the center of a porphyrin ring. Four bromophenyl groups are symmetrically connected to the porphyrin unit, with the bromine atoms located at the end corners.

Figure 3

(Color online) Accumulated density of orbital $i$ (see Eq. (2)) for orbitals $d_{3z^2-1}$, HOMO-1, HOMO, and LUMO of TBrPP-Co in gas phase. Thick lines with filled symbols show the accumulated density calculated within the GW approximation. Thin lines with “$+$“ signs show the corresponding accumulated densities calculated within DFT-GGA. The inset shows the ratio between integrals $I_d$ and $I_{\text{HOMO}}$ obtained both with GW (thick line) and DFT-GGA (dashed line). The subsequent NRG calculations were done using the GW $I_d/I_{\text{HOMO}}$ ratio.

Figure 4

(Color online) (a) Kondo temperature $T_K$ (obtained from NRG calculations with GW-based parameters) versus (b) $E_d-E_F$ and molecule-surface distance $D$.

Figure 5

(Color online) Molecular DOS system for different molecular charging [(a)–(c) $D=3\text{Å}$] and molecule-surface distances [(d)–(f) $E_M-E_F=1.1\text{eV}$]. A Kondo resonance at the Fermi energy and the HOMO and LUMO orbitals are shown. The width variation in the Kondo resonance $\left(\sim T_K\right)$ is consistent with the results in Fig. 4.