Interference and interactions in open quantum dots

Abstract

In this report, we review the results of our joint experimental and theoretical studies of electroninterference, and interaction, phenomena in open electron cavities known as quantum dots. The transport through these structures is shown to be heavily influenced by the remnants of their discrete density of states, elements of which remain resolved in spite of the strong coupling that exists between the cavity and its reservoirs. The experimental signatures of this density of states are discussed at length in this report, and are shown to be related to characteristic wavefunction scarring, involving a small number of classical orbits. A semiclassical analysis of this behaviour shows it to be related to the effect of dynamical tunnelling, in which electrons injected into the dot tunnel through classically forbidden regions of phase space, to access isolated regular orbits. The dynamical tunnelling gives rise to the formation of long-lived quasi-bound states in the open dots, and the many-body implications associated with electron charging at these resonances are also explored in this report.

Localization and field-periodic conductance fluctuations in trilayer graphene

“…5T 1 1 − − at nearly all gate voltages, and in most traces a second, much weaker peak at f~1 0 1 5T 2 1 − − . This periodic behaviour with a small number of dominant frequency components, as opposed to the aperiodic behaviour normally associated with universal CFs, has been observed previously in bilayer graphene systems [36] and is well-known in the case of open semiconductor-based quantum dots [37]. Assuming this to be a suitable model we can analyse these oscillations in terms of the interference of one or two discrete orbits and estimate the area enclosed by a given orbit from the Aharonov-Bohm ∼0.017-0.035 μm 2 and ∼0.041-0.062 μm 2 for the long and short periods, respectively.…”

Wave transport and statistical properties of an open non-Hermitian quantum dot with parity-time symmetry

“…much the same geometric form [11]. In our case we must, however, supplement the above equation with a complex term as…”

“…The shaded rectangle is the region used to sample data for the statistical analysis. The cavity is shaped after a particular quantum dot [11]; at the bottoms of the two "quasileads" there are regions in which V I is positive or negative (dark and white regions, respectively). The steps along the boundaries indicate the rectangular computational grid.…”

“…[7,8] has been applied to a "twolead" planar [two-dimensional (2D)] quantum dot in a gated Al x Ga (1−x) As/GaAs heterostructure [11]. Particle densities and probability current flows for a selected set of low-energy states were compared with analog measurements for an equally shaped microwave resonator [12].…”

Decoherence due to contacts in ballistic nanostructures

“…Equation (14) shows explicitly how the subdynamics looks for P ; by generalizing the proof in Appendix A, one can write the subdynamics for any other projection operator instead of P . The reason we are using P instead of the projection operator P induced by the initial environmental statistical operator is that, as stated previously, P is the only projection operator that has an orthonormal eigenbasis in which it is represented by a diagonal form (4). While any other projection operator P still projects onto its own d 2 S -dimensional image space (see Appendix A), P and 1 − P never assume simple diagonal forms, so after projecting one still needs to explicitly take the partial trace, which leaves the equations less transparent.…”