Molecular Quantum Rings Formed from a $\pi$-Conjugated Macrocycle

The electronic structure of a molecular quantum ring (stacks of 40-unit cyclic porphyrin polymers) is characterized via scanning tunneling microscopy and scanning tunneling spectroscopy. Our measurements access the energetic and spatial distribution of the electronic states and, utilizing a combination of density functional theory and tight-binding calculations, we interpret the experimentally obtained electronic structure in terms of coherent quantum states confined around the circumference of the $\pi$-conjugated macrocycle. These findings demonstrate that large (53 nm circumference) cyclic porphyrin polymers have the potential to act as molecular quantum rings.

Figure 1

(a) Chemical structure of $c$-P40. (b) STM image of $c$-P40 nanoring stacks on Ag(111). Individual porphyrin units are resolved ($I_{\mathrm{set}}=10\mathrm{pA}$, $V=-1.8\mathrm{V}$). (c) Energy minimized structure of $c$-P40 model and (d) structure of $c$-P40 constrained to average experimental dimensions, calculated using an extended tight-binding approach.

Figure 2

(a) Calculated energies of occupied and unoccupied orbitals for linear porphyrin chains ($l\text{−}\mathrm{P}N$, $N=1–7$) and $c$-P40 calculated with XTB and DFT methods (see legend) (eigenvalue and $\mathrm{\Delta }\mathrm{SCF}$ techniques used to calculate HOMO-LUMO and $-\mathrm{IP}$ and $-\mathrm{EA}$ values, respectively). Exponential curves fitted using $l\text{−}\mathrm{P}N$, $N=1–7$ and extrapolated values for $c$-P40 based upon DFT are shown. Break in $x$ axis after $l\text{−}\mathrm{P}7$ included for clarity, see Supplemental Material [21] for full graphs. (b) Molecular orbital structures calculated for $l\text{−}\mathrm{P}7$.

Figure 3

(a) Example forward (blue) and reverse (black) STS spectrum showing differential conductance as a function of applied sample bias. (b) STM image showing spectroscopy location (blue dot). Discontinuities in image occur due to thermal drift between spectra ($I_{\mathrm{set}}=40\mathrm{pA}$, $V=1.5\mathrm{V}$). (c) Energy levels as a function of polymer length (DFT calculations, see legend). Experimentally determined values for electronic resonances $R_0$, $R_1$, and $R_2$ are shown. STM image and spectrum acquired at $\sim 78\mathrm{K}$.

Figure 4

Differential conductance maps for a $c$-P40 nanoring stack acquired at sample bias $+1.3$ to $-1.3\mathrm{V}$ (intensity normalized to maximum measured $dI/dV$ across all images). Color scale shows normalized differential tunneling conductance ($I_{\mathrm{set}}=40\mathrm{pA}$, image dimensions $28.4\times 23.5\mathrm{nm}$). Bright contrast features occur at bias values matching observed resonances in $dI/dV$ spectra. Bright stripe features visible for several biases.

Figure 5

Comparisons of stripe features observed in computational models and experiment. (a) Conductance map acquired at $-1.1\mathrm{V}$ showing stripe features; positions and separations indicated ($I_{\mathrm{set}}=40\mathrm{pA}$). (b) Model of $c$-P40 HOMO-8 energy level (XTB), showing areas of high electron density separated by 6.7 nm.