Topographical fingerprints of many-body interference in STM junctions on thin insulating films

Negative differential conductance is a nonlinear transport phenomenon ubiquitous in molecular nanojunctions. Its physical origin can be the most diverse. In rotationally symmetric molecules with orbitally degenerate many-body states it can be ascribed to interference effects. We establish in this paper a criterion to identify the interference blocking scenario by correlating the spectral and the topographical information achievable in a scanning tunneling microscopy (STM) single-molecule measurement. Simulations of current-voltage characteristics as well as constant-height and constant-current STM images for a Cu-phthalocyanine on a thin insulating film are presented as experimentally relevant examples.

Figure 1

Artistic view of an STM single-molecule junction. We show in yellow (light gray) the metallic leads (tip and substrate), in red (dark gray) the thin insulating film, and in green (medium gray) the schematic representation of a CuPc.

Figure 2

Left: Current through a CuPc single-molecule junction as a function of the substrate (and tip) work function ${\phi }_0$ and of the sample bias $V_b$. The tip apex position is set at $(x,y,z-d)=(+5,-5,7)$ Å, with the origin taken on the metal-insulator interface and in correspondence with the center of the molecule and with $d$ being the thickness of the insulating layer (see Fig. 1). The tip and substrate resonant lines (with positive and negative slopes, respectively) divide the parameter space into four regions. T (S) indicates a region in which the current is proportional to the tip (substrate) tunneling rate. Right: Current obtained from a cut of the left-hand plot corresponding to ${\phi }_0=4.1$ eV. The numbers in the current-voltage plot refer to the current maps in Fig. 3. The current scale is the same for the left and right panels.

Figure 3

Constant-height current maps calculated for different bias voltages. The color bar on the left (right)-hand side corresponds to maps 1 and 3 (maps 2 and 4). The 5-Å-long white line sets the scale of the images. The numbers in the maps refer to the biases indicated in the right panel in Fig. 2. The current map in the interference blockade regime (map 4) appears to be flat in the molecule region. The characteristic nodal plane pattern appears instead to be much more pronounced at the positive and negative bias resonances (maps 1 and 3) and even in the Coulomb blockade region (map 2). The tip apex is placed at 7 Å above the molecular plane, while the substrate biases are, respectively $V_{b1}=0.1153$ V, $V_{b2}=-0.5303$ V, $V_{b3}=-0.7201$ V, and $V_{b4}=-0.9118$ V.

Figure 4

Schematic representation of the many-body states participating in the transport. On the vertical axis we report the grand canonical energies $E_0^{\prime }:=E_0-\mathrm{N}{\mu }_0$ and $E_1^{\prime }:=E_1-(\mathrm{N}+1){\mu }_0$, where ${\mu }_0$ is the equilibrium chemical potential for the leads. (a) We adopt the angular momentum representation; (b) the decoupling basis is introduced for the anionic states (see text for details).

Figure 5

Current vs tip-molecule distance calculated for different biases. Numbers in the legend correspond to the different cases illustrated in Fig. 3: $V_{b1}=0.1153$ V, $V_{b2}=-0.5303$ V, $V_{b3}=-0.7201$ V, and $V_{b4}=-0.9118$ V. Note, in particular, the wide plateau associated with the interference blockade regime (line 4) and its crossing with the Coulomb blockade line for $Z_{\mathrm{tip}}-d=7$ Å.

Figure 6

Isosurfaces of constant current calculated in the proximity of the Coulomb blockade (upper panel; $V_b=-0.5303$ V) and interference blockade (lower panel; $V_b=-0.9118$ V) regimes. The surfaces correspond, in both cases, to the currents: $I=3.15$, $3.075$, $3.0$, $2.925$, and $2.85$ pA.