Oligothiophene Nanorings as Electron Resonators for Whispering Gallery Modes

Structural and electronic properties of oligothiophene nanowires and rings synthesized on a Au(111) surface are investigated by scanning tunneling microscopy. The spectroscopic data of the linear and cyclic oligomers show remarkable differences which, to a first approximation, can be accounted by considering electronic state confinement to one-dimensional boxes having, respectively, fixed and periodic boundary conditions. A more detailed analysis shows that polythiophene must be treated as a ribbon (i.e., having an effective width) rather than a purely 1D structure. A fascinating consequence is that the molecular nanorings act as whispering gallery mode resonators for electrons, opening the way for new applications in quantum electronics.

Figure 1

(a) Sketch of the on-surface polymerization reaction of DBrTT on Au(111). (b) Large scale topographic STM image ($I=100\mathrm{pA}$ and $V_{\mathrm{sample}}=0.1\mathrm{V}$) and close-up views (c)–(e) of various oligothiophene structures resulting from the polymerization reaction. The white scale bars correspond 5 nm (b) and 1 nm (c)–(e).

Figure 2

(a) Topographic STM image ($I=100\mathrm{pA}$ and $V_{\mathrm{sample}}=0.1\mathrm{V}$, $6.6\times 2.4{\mathrm{nm}}^2$) and (b) constant height differential conductance spectra (set point: $I=5\mathrm{pA}$ and $V_{\mathrm{sample}}=1\mathrm{V}$) of a linear-[12]-thiophene. The gray and black spectra correspond to two positions of the tip on top of the wire [see gray and black arrows in (a)]. Light gray (green) lines are Gaussian function fits. (c)–(f) Constant height conductance maps acquired at voltages corresponding to maxima in (b). The same data were acquired for a cyclo-[12]-thiophene: (g) topographic STM image ($2.8\times 2.8{\mathrm{nm}}^2$), (h) constant height differential conductance spectra acquired on top of the wire, and (i)–(k) constant height conductance maps acquired at voltages corresponding to maxima in (h). No resonances were resolved at negative sample voltages. (l) Molecular state energies as a function of oligomer lengths for linear- (dashed red lines) and cyclo- (full blue lines) [$N$]-thiophene ([12]-thiophene wires are shaded [highlighted in yellow]).

Figure 3

Experimental (a) and calculated (b) dispersion data for linear and cyclic oligomers. The connecting lines correspond to fits with a 1D tight-binding expression. In (b) the parabolic dispersion of an infinite wire is represented (dashed lines). Details about the fits and the error bars are provided in Ref. 25.

Figure 4

(a) Finite square potential $V(r)$ (black dashed lines), effective potential $V_{\mathrm{eff}}(r)$ [light gray (blue) lines], and WGM probability density [dark gray (red) lines] for $l=0$, $l=1$, and $l=2$ modes. (b) 3D representations of the calculated WMG probability density for the $l=0$, $l=1$, $l=2$ modes and for $(a,b)=(0.25,0.75)$. (c) Constant height differential conductance maps of the cyclic-[12]-thiophene ($2.8\times 2.8{\mathrm{nm}}^2$) at energies of the LUMO, $\mathrm{LUMO}+1$, and $\mathrm{LUMO}+2$. Experimental and calculated representations are at the same scale. $r_{\rho }$ is the radius defined as the distance from the center to the maxima of the circular resonances.