Coherent transport of 2D electron waves: transverse magnetic focusing and cavity resonator

Abstract

from theory, the Coulomb interaction between the emitted electron and the QD implied that the hot electrons lost energy by exciting the QD. The second result discusses mode formation in open cavity resonators defined in the 2DEG. A gate-defined cavity with highly open sides showed resonant electron transmission. By adapting the framework of optical cavities to the mesoscopic system, the characteristics of the cavity resonances were identified by its longitudinal or transverse quantization. The difference in spatial distribution were confirmed for different transverse modes through magnetoconductance measurements, and their classical interpretation was supported by eigenchannel analysis using tight-binding simulations.

The rest of the text is largely a development for aforementioned topics or a pedagogical exposition. Two technical results are discussed. The first concerns QD conductance thermometry and its limitation under classical voltage noise. The second concerns the QPC operation using a trench-gate. Experiment-wise, the hardware setup has been discussed for low-frequency conductance measurements and mid-frequency noise measurements. Also, a general discussion has been provided regarding the methods to minimize electron temperature. Theory-wise, a general discussion on 2DEG, QPC, and QD formation has been given after introducing the Landauer-Büttiker framework. In particular, the QD section provides a full derivation of the n-QD constant-interaction model and its relation to the generic tunneling Hamiltonian.

Coherent transport of an 2D electron wave is symbolic to mesoscopic physics. The traditional development of 2D electron gas (2DEG) devices in GaAs/AlGaAs heterostructures signified the possibility of in situ quasiparticle control, where wavefunctions could be directly manipulated to determine the electron paths, and further dimensional reductions to quantum point contacts and quantum dots created a platform on which multidimensional components could be integrated for a general study of quantum effects. Further developments allowed the genesis of exotic many-body ground states, such as the fractional quantum Hall or multi-dot Kondo effects, while the experimental platform had the intrinsic ability to create steady-state non-equilibria through simple circuitry methods. Returning to the origin, the 2DEG system was born out of the efforts to create thinner and cleaner HEMT devices, where the conduction profile could be controlled through field-effect gating. Eventually, the HEMT devices achieved the ultimate limit where electronic motion become quantized in one direction, while the mean-free-path in the other two directions exceeded gating dimensions. Hence, the coherent 2D electrons symbolize the cross-over from bulk semiconductor control to the direct manipulation of electronic wavefunctions in solid-state physics.

In a sense, this dissertation is closely related to said crossover. The two main results are closely related to 2D electron waves. The first result discusses energy relaxations of hot electrons when emitted by QDs. The energy distribution of the relaxed hot electrons are obtained via transverse magnetic focusing (TMF) spectroscopy, where the cyclotron radius is used as the principal idea of spectral measurement. From experiment, the QD hot electrons were observed to lose a significant portion of its excitation within an ultrashort timescale following immediately its QD emission