Magnetically-controlled Fano resonance in wavefunction-coupled QPCs
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In this thesis, we describe the observation of a resonant interaction between coupled quantum point contacts (QPCs) that we attribute to a Fano resonance, caused by the self-consistent formation of a bound-state (BS) in one of the QPCs. The presence of this BS (in the "swept QPC") is detected by making measurements of the conductance of the other QPC, which therefore serves as a detector. A key feature of our work is the demonstration of a strong modulation of the detector resonance by applying a perpendicular magnetic field ( B ⊥ ). This induces a distinct asymmetry (with respect to magnetic-field reversal) in the magneto-conductance of the detector, which is shown to be due to the influence magnetic electron focusing. In this effect, the electron trajectories correspond to classical skipping orbits, which undergo complete motion due to the high mobility of the two-dimensional electron gas. At even higher B ⊥ , the detector resonance, which at zero magnetic field is only weakly asymmetric, evolves into the classic, highly asymmetric, Fano form. Such asymmetry indicates that the nonresonant contribution to detector resonance becomes comparable to the resonant one at high fields. We explain these results in terms of two key properties of quantum-dot eigenstates in a magnetic field, namely: the tendency for their wavefunctions to be compressed towards the center of the quantum-dot potential, and; that for their eigenenergies to increase due to the associated enhancement in the effective degree of confinement. In this thesis, we confirm these ideas by performing a Fock-Darwin analysis to account for the evolution of the detector Fano resonance in the magnetic field. The strong modulations of the Fano resonance that we observe as a function of B ⊥ are shown to represent a new manifestation of this ubiquitous resonance.