Quantum dots: Eieth'ons in a new dimension

Abstract

Quantum dots represent a new class of electronic structures where the electronic configuration and degree of confinement or coupling can be tuned at will. These artificial mesoscopic structures mimic many atomic effects with a tremendous degree of flexibility. We have studied the transition from isolated to coupled quantum dots in quantum-dot and lateral-surface-superlattice structures. Our maguetocajacitance measurements probe three distinct regimes: A superlattice regime; a tight-bindin.g regime; and an isolated-quantum-dots regime. In the presence of an external magnetic field we find that the coupling of the magnetic flux with the periodic potential depends on the strength of the potential modulation. In strongly-coupled quantum wires and quantum dots, the commensurability between the superlattice period and the cyclotron orbit is reflected in a modification of the envelope of the magnetocapacitance oscillations. In weakly-coupled quantum dots, a new structure is observed. Aperiodic oscillations in the density of states are related to fractal-like behavior in the energy dispersion relation first predicted by Ilofstadter. In completely isolated quantum wires or quantum dots, the canonical magnetocapacitance oscillations are recovered with a Zeeman bifurcation of the states produced by the interplay of magnetic and spatial quantization. We will present our experimental work in light of theoretical models and discuss the fundamental physical phenomena that dominate the the.rmodynamic properties of electrons in quantum dots.