Etude des propriétés des hamiltoniens unidimensionnels aléatoires : Application au cas dimère

Abstract

By scaling the mesoscopic conductance with the system length, the theory of Anderson localisation has predicted insulator transmission regimes in one–dimensional electronic systems for any disorder. Viewed as the origin of destructive interferences, randomness contributes actively to localised states in finite region of space. However by pairing the defect cells, delocalised Bloch-like states and diffusive transport appear in disordered system when transparency conditions of the dimer unit cells occurs. This is the conventional random dimer model. The re-examination of the pioneer ideas of S. He and J.D. Maynard in the acoustic analogy of mesoscopic systems permitted us to describe the transmission properties of mechanical waves in the classical system of homogenous string charged by masses. By suitably introducing springs, the transmission at the dimer resonance can be enhanced from diffusive to ballistic response. For such ballistic transmission mechanical filters is examined and optimised for disordered host alloys within the random dimer model. In the same way, the propagation of electromagnetic waves in one-dimensional stratified systems has been examined. By dealing with particular structural parameters, principal standing resonances are added into the transmission spectrum of defect and host unit cells. Ballistic transmission canals can be obtained in binary disordered photonic films at the dimer resonances. Various interesting transmission regimes near the dimer resonances are described. The electronic transport in disordered carbon nanotubes with chemical defects is also examined. By doping simultaneously with Boron (B) and Nitrogen (N), BN dimer defect cell can be considered when B and N atoms are first closest neighbours. The BN dimer suppresses the localisation signatures induced by the isolated B and N defect states while the transmission for the BN nanodomains depends strongly on both the orientation of the BN nanodefect inside the host structure and the number of B (N) atoms in the nanodomain. By increasing the number of the BN dimers, the transmission in a BN nanodomain is governed by the tunnelling effect. Interesting resonant tunnelling transmissions can be obtained when two BN nanodefects spreading on the whole contour of the nanotube are separated inside the host nanotube according to the concept of the dimer unit cell. In our study, the propagation of waves in analogue one-dimensional random systems has been studied within the random dimer model. In addition to the universal diffusive behaviour of the conductance at the conventional dimer resonance, interesting situations improving the transmission properties at the dimer resonance have been found: With a suitable choice of the defect and host unit cells, ballistic transmission canals can be opened providing an additional way to considerably enhance the transmission properties in such particular disordered systems.

Date of Award	21 Apr 2010
Original language	French
Awarding Institution	University of Namur
Supervisor	Luc Henrard (Supervisor), Olivier Deparis (President), Muriel Lepere (Jury), Mamaar Bouamoud (Co-Supervisor) & Jean-Christophe Charlier (Jury)