INTRODUCTION
Condensed matter physics is the study of a tremendously large number of particles crowded (condensed) together so that the effects they have on one another cannot be ignored. It is an exciting field of physics because even though all the particles obey known physical laws, solving the physical equations for such a large number of particles is not always feasible. So it is not always known what will happen in a condensed matter system and there are still some surprises to be found.
The condensed matter system studied in this thesis is a system of electrons that have been confined so that they can only move in two dimensions – a two-dimensional electron system (2DES). Roughly 10^10 electrons are crowded into one square centimeter, all repelling each other electrically. Although an equation can be written describing all the electrons’ interactions with one another, with 10^10 electrons, it is too difficult to solve. So it was a surprise when it was found that under certain conditions, involving the application of a perpendicular magnetic field, the electrons will specially arrange themselves in accord with the magnetic flux quanta passing through the layer in such a way as to lower the energy of the entire system. This surprise was called the fractional quantum Hall effect (FQHE) and was discovered in 1982 by Horst Stormer [1].
In this thesis, we study a system in which two layers of these two-dimensional electrons are brought very close together in parallel (a bilayer 2DES). We show that when the layers are sufficiently close together and subjected to a specific value of perpendicular magnetic field, a new, uniquely bilayer, state is formed that is mathematically similar to the FQHE state. In this state, the system achieves a lower energy when the electrons in one layer become highly correlated with the electrons in the other layer.
This correlated state can be portrayed as one where the electrons lose track of which layer they are in (this view is discussed in Section 4.6), or as one where the electrons in one of the layers line up with the vacancies between the electrons in the other layer. These vacancies are called “holes” and behave much like positively charged electrons. The holes in one layer are electrically attracted to the electrons in the other layer, and the two bind together to form composite particles called excitons. Excitons are a type of boson and can undergo a process called Bose-Einstein condensation (BEC); thus the excitons all condense into the same quantum state. This view of the state as a BEC of excitons is covered in Section 4.7.
The main goal of this thesis is to detect this excitonic BEC. We aim to detect it by probing the bilayer 2DES using electrical transport measurements. Wires are electrically contacted to the electron layers, and currents are sent through one or both of the layers. The voltages measured in response to these currents yield a great deal of information on the state of the bilayer electron system.
The excitonic BEC can be detected through electrical transport if a flow of the BEC is set up through the layers. Electrical transport due to such a flow will be vastly different from the usual currents carried by electrons. BECs exhibit superfluid properties that we can detect as a vanishing of the current’s dissipation when the system enters the excitonic BEC state. Additionally, transport due to the flow of excitons will be unaffected by the magnetic field since excitons are charge-neutral. This will show itself as a vanishing of the Hall resistance when the system is in this state. Both of these indicators were detected and are discussed in Chapter 7.
This state was first detected more indirectly, using an electrical transport measurement called “Coulomb drag.” In this measurement, interlayer electron scattering processes are directly detected when current is sent through one of the layers, and voltages are probed in the non-current-carrying layer. The first-ever observation of “quantized Hall drag,” the remarkable spectacle in which a quantized Hall voltage appears in a layer that has no net current flow, is an indirect display of the likely excitonic superfluid, and is shown in Chapter_5.
Coulomb drag, although only an indirect method for detecting the excitonic superfluidity, is an excellent probe of the phase transition out of the BEC state as the (effective) layer separation is increased. Studies of this phase transition are covered in Chapter 6, including the interesting result that the BEC state becomes more robust when the electron densities in the two layers are not equal.
The theoretical framework for understanding this special state is covered in Chapter 4. Readers interested only in the theory and experiments on the correlated bilayer excitonic state should proceed directly to this chapter.
Chapter 3 shows early Coulomb drag work done in zero magnetic field. It precedes the other chapters mainly because the work was done chronologically earlier, although it also lays the foundation for understanding the Coulomb drag measurements performed in the exciton BEC state shown in later chapters. Coulomb drag experiments in zero magnetic field are used to study electron-electron scattering processes – Coulomb drag is the first measurement technique to detect these processes directly. Our experiments have led to a better understanding of the nature of these interactions.
The Coulomb drag measurement itself is discussed extensively in Chapter 2, including the theory and history of electron-electron scattering and Coulomb drag in zero magnetic field. A detailed equation for zero field electron-electron Coulomb drag scattering derived by Jauho and Smith [2] is extended theoretically, and a Fortran program that numerically solves this equation for a variety of experimental conditions can be found in Appendix K.
In Chapter 1, the double quantum wells that are used to confine the electrons to two dimensions are discussed, with special focus on the parameters that affect the ability to achieve and perform electrical measurements on the exciton BEC state. Also included is a basic description of the crystal processing, which allows for experimental access to the electron layers.
For those who wish to perform these types of experiments, there are eleven Appendices that contain detailed information on the experimental procedures.
References:
1 D.C. Tsui, H.L. Störmer and A.C. Gossard, Phys. Rev. Lett. 48, 1559 (1982).
2 A.P. Jauho and H. Smith, Phys. Rev. B 47, 4420 (1993).
Copyright © 2005 by Melinda Jane Kellogg
Download thesis at these locations:
Evidence for Excitonic Superfluidity in a Bilayer Two-Dimensional Electron System (2005)
http://thesis.library.caltech.edu/3080/1/MindyKelloggThesis.pdf
