Control of transport through Fano resonances in molecular wires T. A. Papadopoulos, I. M. Grace and C. J. Lambert Department of Physics, Lancaster University, Lancaster, United Kingdom. Condensed Matter Theory Group (PRB 2006)

Outline The aim of this talk is to investigate the importance of resonances in order to control electron transport through single molecules. Breit – Wigner VS Fano. Which of those is most important for controlling transport through single molecules. At least for molecules that have a side-group, it seems that Fano resonances could be the most important.

The system studied Why do we study them in the first place? They form the building blocks of longer  -conjugated rigid-rod-like oligomers, recently synthesised by chemists in Durham University. They own side-groups and therefore we expect these to possess both BW resonances associated with the backbone and Fano resonances associated with the side-groups. Our purpose is to look at the relative importance of those two kinds of resonances and how they interplay with each other. Side-groups Fluorene Unit C benzene C SS Side-group Backbone

The ab initio method we use for transport Bulk Gold Bulk Gold … … … … … … Left leadRight lead The isolated molecule is relaxed to find the optimum geometry. The molecule is then extended to include surface layers of the gold leads self-consistently. Create a tight-binding hamiltonian of the extended molecule using the DFT code SIESTA. Double-  basis plus polarisation orbitals Double-  basis plus polarisation orbitals Troullier–Martins pseudopotentials Troullier–Martins pseudopotentials The Ceperley–Alder LDA method The Ceperley–Alder LDA method Scattering matrix and transmission coefficient T(E) is computed Zero-bias conductance is then extracted using the Landauer formalism. molecule

Where do Fano resonances come from? A Fano resonance consists of a resonant followed by an anti-resonant peak or the opposite. Here at E=0.1eV For E=1.2eV we have a typical BW peak since the molecule and contacts are symmetric. Artificial removal of the chemical bonds to the oxygen atom destroys the Fano resonance. The remainder of the transmission spectrum remains largely unaltered. Breit-WignerFano Fano resonances arise when a bound state is coupled to a continuum. The Fano resonance is associated with the energy levels on the Oxygen atom.

Attaching bigger side groups Replace Oxygen with a bipyridine unit What will happen if we rotate the side-group? How sensitive to this rotation are Fano and BW resonances? How will that affect transport? Side-group parallel to backbone Side-group perpendicular to backbone 0o0o 90 o Recent STM experiments on related wires have shown that it is possible to change the rotational conformation of attached side groups (W. Haiss et al.)

Fano resonances persist The BW peak is almost unaffected. The Fano resonance is sensitive to the conformation of the side group.

Energy spectrum and LDOS of the isolated molecule Rotating the side-group we see one energy level sensitive to changes in angle . This level belongs to the central unit as observed on the LDOS plots. The energy level of E=2.0eV corresponds to a BW peak. Most of the other levels remain unaffected. 30 o 75 o FanoBreit-Wigner delocalised along the backbonelocalised on central unit

Model comparison The backbone A is coupled to a side- chain B by matrix elements H 1 The leads are coupled to the backbone via weak hopping elements V, W. where N 0 (E), N N+1 (E) are the LDOS for the left and right leads Comparison between a)the analytical and b)the previous ab initio results

Conclusions We have shown that transport through this new class of molecular wires with side-groups as subunits are dominated by Fano resonances rather than Breit-Wigner resonances. With an appropriate choice of parameters, our analytical formula captures the essential features of Fano resonances in aryleneethynylene molecular wires. Electron transport can be controlled either chemically modifying the side-group or by changing the conformation of the side-group. This sensitivity, which is not present in BW resonances, opens up the possibility of novel single-molecule sensors.