Engineering of Electron States and Spin Relaxation in Quantum Rings and Quantum Dot-Ring Nanostructures

Abstract

Quantum nanostructures are frequently referred to as artificial atoms. Like the natural atoms they show a discrete spectrum of energy levels but at the same time they exhibit new physics which has no analogue in real atoms. Electrons in an atom are attracted to the nucleus by a potential that diminishes inversely proportional to the distance from the center of the atom. This feature, together with the Coulomb interactions between electrons, determines properties of natural atoms. On the other hand, in quantum nanostructures one can (almost) freely design the shape of the confinement potential. As a result, a variety of properties of quantum nanostructure can be modified according to the designer’s will.

The aim of this chapter is to demonstrate in a detailed way how these properties depend on the geometry of the confinement potentials. Quantum rings can be narrow, quasi-one-dimensional objects with periodic boundary conditions. But they also can be wide, like a quantum dot with a small hole in the center that leads to a nontrivial topology. The electronic properties, determined by the energy spectrum and the distribution of the wave functions, are very different in these limiting cases. They are also different from the properties of a quantum dot. In this chapter we demonstrate how selected properties are modified when the confinement changes in such a way that the nanostructure evolves from a quantum dot to a wide quantum ring and than to a narrow, quasi-one-dimensional nanoring. Besides single quantum rings we describe properties of two coupled nanorings and of systems composed of a quantum ring coupled to a quantum dot. We are mainly interested in properties that are connected to possible applications of quantum nanostructures. There is a common belief that such systems are among the most promising candidates for realization of qubits in quantum computing. However, physical implementation requires, among others, relatively long decoherence time, much longer than the gate operation times. Assuming the spin-orbit-mediated electron-phonon interaction as the dominant relaxation mechanism for spin qubits, we show how the relaxation time depends on the details of the confinement potential. We first compare the relaxation times calculated for quantum dots and quantum rings of different shapes and sizes. However, it seems that complex structures composed of a quantum dot surrounded by a quantum ring can have far more interesting properties due to the high controllability of the spatial distribution of the electronic wave function. The results indicate that the main factor that determines the relaxation time is the so-called overlap factor, i.e., the overlap of the radial parts of the wave functions of the ground and first two excited states. With this knowledge, one can try to optimize the confinement potential with respect to the relaxation time. By tuning the relative positions of the bottoms of the ring and dot confinement potentials one can control the overlap factor, what in turn allows to control the relaxation time. The same effect can be achieved by modifying the height of the potential barrier between the ring and the dot. A high controllability is also expected in a similar system where the central quantum dot is replaced by a small ring, i.e., in a system of two coupled concentric quantum rings.

The wave function engineering allows one to control not only the relaxation time. We demonstrate that the same overlap factor determines also optical properties of quantum nanostructures. Using realistic parameters we show that changing the shape of the confinement potential it is possible to modify the microwave and infrared absorption cross sections of the dot-ring nanostructure. That way, the nanostructures can be moved over from highly absorbing to almost transparent. The last property analyzed in this chapter is the conductivity of a system composed of many dot-ring nanostructures. Apart from unique properties of a single nanostructure, interesting behavior emerges when such structures are combined into a two-dimensional array. If they are located sufficiently close to each other, electrons can tunnel between them, making a system that resembles a narrow band crystal. Since the tunneling rate depends on the overlap of the electron wave functions on adjoining structures, the transport properties would be dependent on the shape of the confinement potential. As a result, a metal-insulator transition can be easily induced in the array. We demonstrate a way how to control the confinement potential globally for the whole array.