Interacting two-dimensional electron and hole systems in perpendicular magnetic fields

Abstract

Electron and hole systems confined in two dimensions exhibit a plethora of exotic quantum phases under perpendicular magnetic field at sufficiently low temperature. In this thesis, we explore several of these quantum phases in state-of-the-art high-quality InAs and GaAs quantum wells and study their formation, phase diagram, and geometric resonance behavior under a one-dimensional periodic magnetic modulation.

The two-dimensional (2D) electron system in an InAs quantum well has emerged as a prime candidate for hosting exotic quasi-particles with non-abelian statistics such as Majorana fermions and parafermions. To attain its full promise, however, the electron system has to be clean enough to exhibit electron-electron interaction phenomena. In the first part of the thesis, we present the observation of the fractional quantum Hall effect in a very low disorder InAs quantum well. At sufficiently low temperature and very high perpendicular magnetic field, a deep minimum in the longitudinal resistance, accompanied by a nearly quantized Hall plateau at Landau level filling factor nu=4/3 was observed.

A sufficiently large perpendicular magnetic field quenches the kinetic (Fermi) energy of an interacting 2D system of fermions, making them susceptible to the formation of a Wigner solid (WS) phase in which the charged carriers organize themselves in a periodic array to minimize their Coulomb repulsion energy. In low-disorder 2D electron systems confined to modulation-doped GaAs heterostructures, signatures of a magnetic-field-induced WS appear at low temperatures and very small Landau level filling factors (nu~1/5). In dilute GaAs 2D hole systems, on the other hand, thanks to the larger hole effective mass and the ensuing Landau level mixing, the WS forms at relatively higher fillings (nu~1/3). In the second part of the thesis, we present our measurements of the fundamental temperature vs. filling phase diagram for the 2D holes' WS-liquid thermal melting. Moreover, via changing the 2D hole density, we also probe their Landau level mixing vs. filling WS-liquid quantum melting phase diagram. We find our data to be in good agreement with the results of very recent calculations, although intriguing subtleties remain.

A high-quality 2D electron system under a small perpendicular magnetic field exhibits ballistic cyclotron motion. When the size of the cyclotron orbit is commensurate with an external one-dimensional (1D) density modulation, a series of longitudinal resistance minima are observed as a result of this geometric resonance condition. In a GaAs 2D electron system, such 1D density modulation can be achieved through the piezoelectric effect along the [110] and [-110] crystallographic directions. In the third part of this thesis, we discuss a technique that imposes a 1D magnetic modulation to the GaAs 2D electron system in the [100] and [010] crystallographic directions where the piezoelectric effect essentially zero. This technique can be implemented to study the geometric resonance of other 2D systems such as the AlAs 2D electron system, where the major axes of the carrier pockets are along the <100> directions. By extending this technique to higher perpendicular magnetic fields, one can also add an additional tool to probe the physics of the composite fermion systems.