Quantum coherent transport: From mesoscopic circuits to molecular wires

The purpose of these lectures is to present some basic signatures of phase coherent transport in various electronic systems going from mesoscopic to nanoscopic scales, from micron size Aharonov Bohm rings to molecular wires such as DNA and carbon Nanotubes. The Aharonov Bohm geometry is well suitable for the investigation of phase coherence in mesoscopic rings which exhibit orbital magnetism and electrical polarisability reminding the magnetic and electric responses of molecules. This is particularly the case for semiconducting rings where energy spectrum can be resolved. On the other hand proximity induced superconductivity is a powerful tool to reveal phase coherence in molecular wires. This is specially interesting in the case of DNA where very little is known on the nature of electronic transport. In the case of carbon nanotubes the observation of high values of supercurrent strongly suggest the existence of intrinsic superconducting fluctuations as corroborated by experiments on long ropes of carbon nanotubes on normal contacts.