Studies of magneto-tunneling into donor states and of the breakdown of the quantum Hall effect
This thesis describes an experimental investigation and analysis of two topical problems in condensed matter physics: 1.) the effect of a magnetic field on quantum states of an electron bound to a shallow donor impurity in a quantum well heterostructure and 2.) the breakdown of the quasi-dissipationless state of the integer quantum Hall effect. Two introductory chapters describe important material parameters and the experimental equipment and techniques used. Magneto-tunneling spectroscopy (MTS) is used to probe the spatial form of the eigenfunction of electrons bound in the ground state of a shallow Si-donor impurities in a GaAs/(A1Ga)As quantum well. An in-plane magnetic field, B[subscript] |, acts to tune the k-vector of the tunnelling electron through the effect of the Lorentz force. The variation with B [subscript] | of the tunnel current through the donor ground state provides a map of the Fourier transform, |ψ(k)| [superscript]2, of the probability density of the ground state donor wavefunction in real space. By applying a strong magnetic field component, B [subscript] ||, parallel to the direction of tunnel current, it is possible to magneto-compress the donor function in real space. The magneto-compression is investigated using MTS and the data are analysed in terms of a simple model, which is critically discussed. The breakdown of the integer quantum Hall effect is investigated by measuring the variation of the voltage drop Vxx along the direction of current flow for a range of currents and magnetic fields and for a number of sample geometries including Hall bars with narrow channels. The data are discussed in terms of two complementary models of breakdown: the bootstrap electron heating model and magneto-exciton formation at a charged impurity. Evidence is found for both types of breakdown depending on the type of sample used and on experimental parameters. For samples with constrictions, it is found that in the breakdown region the value of Vxx measured across a pair of contacts on one side of the Hall bar can differ substantially from that measured on the other side. A model based on magneto-exciton formation at impurities is proposed to explain this unexpected effect. The thesis concludes with a brief summary and suggestions for future work.