Metal-Insulator Transition in Two Dimensions

The discovery of a metal-insulator phase transition in two-dimensional electronic systems in 1994/95 and its confirmation by other groups on different device designs and materials have generated much excitement because the general belief has been that all states are localized at low temperatures. In 1979 the seminal paper of Abrahams, Anderson, Licciardello and Ramakrishnan demonstrated that no true metallic behavior is possible for non- interacting 2D electrons at T = 0 beeause even weak disorder is sufficient to localize the electrons. Before the new experimental findings, a large amount of experimental results confirmed the localization of electrons in 2D as T à 0. Therefore, the belief that all states are localized in two dimensions has remained largely unquestioned. For the interacting systems, no satisfying theoretical picture has emerged yet, despite the application of scaling principles and field-theoretical methods. The metal-insulator phase transition in 2D-systems represents just now one of the most topical and fundamental problems in solid state physics. It is the purpose of this work, to perform investigations on the unexpected metal-insulator transition in two-dimensional electron systems in order to distinguish between the various proposed models about its origin. The largest amount of investigations will be carried out on high mobility Si-MOS samples, but in addition measurements on 2D Si/SiGe and PbEuTe heterostructures will be performed. The conductivity measurement on the various samples will be performed down to 300 mK in He 3 and down to about 5 mK in He 3 /He 4 systems. The influence of a magnetic field perpendicular or parallel to the layer of the electron system is also an important aspect. We will investigate the logarithmic temperature dependence at very low temperatures as its sign gives important information about the symmetry of the system and the interactions involved. The investigation of the metallic phase over a wide carrier concentration and temperature range will distinguish between one-parameter or multi- parameter scaling behavior. The response of the conductivity for magnetic field applied parallel to the layer of the 2D electron system will give information about the spin contributions. The frequency dependence of the conductivity should be important in the case that the metallic state of the electron system is a spin liquid or Wigner glass. And further, the comparison of Si-MOS sample with Si/SiGe and PbEuTe quantum well samples gives information on the influence of effective masses, asymmetry of the confining potential and the Landé g-factor.

A few years ago, an unexpected metallic state was discovered in Silicon field effect transistors (Si-FET`s) at very low temperatures below 1 Kelvin. This was in contradiction to the widely accepted theories according to which every two-dimensional electron system should become electrically insulating if it approaches the zero point of temperature. The insulating state should be formed due to the localization of electrons by quantum interference effects. It was not clear, whether the new metallic state is formed by a new electronic ground state or it may be described by an extension of the existing models. In the conducted project of the Austrian science foundation (FWF), the metallic state and the related metal-to- insulator transition in two-dimensional electron systems were investigated in detail. The research activities are clearly related to basic research activities as the motivation is to understand and clarify the origin of the new effect. But the attained knowledge can later be used for applied research activities. In order to decide whether the metallic state has a quantum mechanical origin or if it is caused rather by "conventional" effects, a well known quantum interference effect, the "weak localization" was investigated in detail. The analysis showed that the quantum interference effects are not present everywhere and that there exist metallic regions which can be completely described by the "conventional" effects like impurity scattering and electrostatic screening. It has thus been found that a metallic state can be explained by an extension of the existing models. Nevertheless, there is still experimental and theoretical evidence that at very low electron densities indeed the electron-electron interaction and quantum interference effects create a new electronic ground state. In the frame of the project, the understanding of the metal-to-insulator transition could be strongly enhanced and one knows a lot more about the interplay of "conventional" and quantum mechanical effects at low temperatures. The conducted work lead also to three articles in the well recognized journal "Physical Review Letters". The attained understanding can be transferred to other low dimensional electron systems and with the ongoing miniaturization of electronic devices, the investigated quantum effects will become more and more relevant there.