6. Quantum effects in nanomechanical devices

(R. Shekhter, L. Gorelik, M. Jonson, G. Rozenblioum)

Electronic and mechanical degrees of freedom of hybrid systems containing both flexible and rigid parts are coupled on the nanometre length scale. This coupling is the basis for the emerging research area dealing with nanoelectromechanical systems (NEMS). Hybrid systems based on carbon nanotubes operating close to the quantum limit are good examples of NEMS systems of considerable current interest – bringing as they do the remarkable mechanical and electronic properties of this unique carbon material into focus. Recently we have suggested that a mechanical instability leading to measurable flexural self oscillations of a doubly clamped single-wall carbon nanotube can be induced by injecting a current into the tube from an STM tip [1]. In addition we have found that a unique coupling between coherent electron motion through the tube and quantum coherent nanotube vibrations may give rise to a novel topological transport phenomenon in the presence of a transverse magnetic field – an electronic Aharonov-Bohm effect induced by quantum vibrations [2]. Our theoretical prediction is valid in the limit of weak tunnelling injection of the electrical current into the carbon nanotube. Other transport regimes that remain to be investigated are those of resonant tunneling, ballistic and diffusive transport regimes as well as the regime of strong joule heating corresponding to large values of the injected current. This is the framework for proposed PhD project, which requires the student to work with the following methods of mathematics and theoretical physics: - Quantum scattering theory - Quantum dynamics of electrons in inhomogeneous magnetic fields - Non-equilibrium Green’s function techniques (Keldysh formalism) - Kinetic theory based on the Boltzmann equation A preliminary study shows that the combined quantum dynamics of the electrons and the nanotube can be reduced reduced to the dynamics of an “effective particle” in a particular localized magnetic field. The project will be carried out in the Department of Physics but in close collaboration with Professor G. Rozenblioum at Matematiska vetenskaper. He has recently developed an efficient method for the spectral analysis of operators in inhomogeneous magnetic fields, and is expected to contribute significantly to the project.