First-principles quantum transport simulation of CuPc on Au(111) and Ag(111)

We investigate equilibrium and transport properties of a copper phthalocyanine (CuPc) molecule adsorbed on Au(111) and Ag(111) surfaces. The CuPc molecule has essentially three localized orbitals close to the Fermi energy resulting in strong local Coulomb repulsion not accounted for properly in density functional calculations. Hence, they require a proper many-body treatment within, e.g., the Anderson impurity model (AIM). The occupancy of these orbitals varies with the substrate on which CuPc is adsorbed. Starting from density functional theory calculations, we determine the parameters for the AIM embedded in a noninteracting environment that describes the residual orbitals of the entire system. While correlation effects in CuPc on Au(111) are already properly described by a single orbital AIM, for CuPc on Ag(111) the three orbital AIM problem can be simplified into a two orbital problem coupled to the localized spin of the third orbital. This results in a Kondo effect with a mixed character, displaying a symmetry between SU(2) and SU(4). The computed Kondo temperature is in good agreement with experimental values. To solve the impurity problem we use the recently developed fork tensor product state solver. To obtain transport properties, a scanning tunneling microscope (STM) tip is added to the CuPc molecule absorbed on the surface. We find that the transmission depends on the detailed position of the STM tip above the CuPc molecule in good agreement with differential conductance measurements.

Figure 1

An isolated CuPc molecule (a) and the position of the CuPc molecule on the Au(111) surface (b). The pictures are drawn with XCrySDen [26]. Color code: C atoms, yellow; H atoms, cyan; N atoms, gray; Cu atom, red; Au atoms, gold.

Figure 2

Two-dimensional cut through the central region for the simulation of the CuPc molecule sandwiched between an Au(111) substrate and the STM tip. The picture is drawn with XCrySDen [26].

Figure 3

The schematic representation of the transport region consisting of left (L) and right (R) lead and the extended molecule (EM), or rather the central region, with its subsystems: the extended region (ER), the interacting region (IR), and the Anderson impurity (AI).

Figure 4

Atom resolved DOS of CuPc on Au(111), (a) and (c), and Ag(111), (b) and (d), surface. (a) and (b) are the ones obtained in DFT-PBE and (c) and (d) include the interaction term in the CPT approximation. We used a $0^{+}$ of 0.04 for calculating the DOS and an additional convolution with a Gaussian to obtain a total broadening $\sigma$ of $0.2/\sqrt{2}$. The vertical lines indicate the HOMO (solid line), the position of the $2e_g$ orbitals (dashed lines), and $b_{1g}$ orbitals (dotted lines).

Figure 5

Matrix elements of the imaginary part of the hybridization ${\overline{\mathrm{\Delta }}}_{\text{AI}}$ for CuPc on Ag(111).

Figure 6

Spectral function of the Anderson impurity model of CuPc on Ag(111) for $J=0$ (gray line) and $J=25\mathrm{meV}$ (black line) separated in spin down (blue line) and spin up (red line).

Figure 7

The tip positions I (a) and II (b) of the STM tip (black sphere) on the molecule on the Ag(111) surface. The pictures are drawn with XCrySDen [26].

Figure 8

Transmission of CuPc on Ag(111) in tip position I. The vertical lines mark the position of the HOMO resonance (solid line), the Kondo resonance at $0\mathrm{eV}$ (dash-dotted line), and the positions of the Hubbard satellites (dashed lines).

Figure 9

Coherent transmission of the STM configuration in tip position I (left axis) and the DOS projected on the atomic orbitals of the tip and the surface layer and the surface DOS of a six-layer slab calculation (right axis).

Figure 10

Transmission of CuPc on Ag(111) in tip position II. The vertical lines mark the Kondo resonance at $0\mathrm{eV}$ (dash-dotted line) and the positions of the Hubbard satellites (dashed lines).