Double-gated quantum rings and nanohelices : from theory to novel applications

The double quantum well potential on the real line is a prevalent description of many physical systems. The concepts of tunnel coupling between adjacent wells and quantum superpositions of individual well states have contributed to the renown ammonia maser for example, whereas understanding the first double quantum well heterostructures has led to the explosive development of semiconductor superlattice physics. On the contrary, the lesser known double quantum well system on a ring has been less visited. However, with the advent of modern nano-fabrication techniques, this system could be realised, and in turn lend itself to a host of novel optoelectronic purposes. This thesis therefore theoretically considers the optoelectronic properties of a double quantum well system induced along the angular coordinate of a ring by two electrostatic gates. Part of this thesis is also devoted to the related problem of a gate-induced binary superlattice along a nanohelix. This thesis presents four broadly self-contained research Chapters, each attacking a particular problem. The first considers the terahertz properties of an electron confined to a double-gated semiconductor quantum ring. This system is a double quantum well with degenerate minima. In particular, the selection rules for inter-level dipole transitions, caused by linearly polarized excitations, depend on the polarization angle with respect to the gates. Transitions are then allowed between the ground and both of the first two excited states. This system could therefore be used in a three-level lasing scheme. The second research Chapter approaches a related problem, wherein the double quantum well potential has different minima. The corresponding eigenproblem is elegantly shown to be quasi-exactly solvable. A novel proposal is developed for using this system as a charge qubit which could be manipulated solely via electrostatic gates. The third problem considers the case of an interacting electron-hole pair, a neutral exciton, in the double-gated ring geometry. This system may yield some advantages compared to few electron spin qubits. The fourth and final research Chapter develops the properties of a binary superlattice (two wells per unit cell) induced along a nanohelix by two parallel gates. Notably, the band structure exhibits energy band crossings for some combinations of potential parameters. Additionally, irradiating the system with circularly polarized light induces a photogalvanic effect. Together, these phenomena make this an attractive system for polarization-sensitive detection.