Critical phenomena in bilayer excitonic condensates

Abstract

The revolution of physics from the classical to quantum mechanical view angle, ignited by a number of discoveries from the past century such as the photoelectric effect by Heinrich Hertz as well as the quantumhypothesis by Max Planck, has continued to flourish in the second half of the 20th century. One of the most intensively studied topics is the phenomenon of spontaneous symmetry breaking, which is present in both particle physics and condensed matter physics. In particle physics, the most prominent example is the mechanism leading to the prediction of a gauge boson called Higgs boson, which should give the exchange bosons for the weak inter-action, the W and Z bosons, their mass. In condensed matter physics, a similar spontaneous symmetry breaking is observed in ferromagnetism and superconductivity. When a ferromagnet is cooled down to below its Curie temperature, the magnetic moments are aligned giving rise to a finite magnetization and the rotational symmetry to any axis perpendicular to the direction of magnetization is spontaneously broken. In superconductivity, similar effect occurs when a col-lective field breaks the electromagnetic gauge symmetry and gives rise to the superconducting energy gap. There is also another type of symmetry breaking which leads to formation of energy gaps. In two-dimensional charge systems, the most prominent effect is the quantized Hall effect which arises due to the breaking of time-reversal symmetry: the Lorentz-force acting on traveling charge carriers turns the cyclotron orbit in two different directions under time-reversal. Fur-ther examples include topological insulators, the quantum Spin Hall effect and the anticipated quantum anomalous Hall effect. Strikingly, spontaneous symmetry breaking can also lead to an effect which combines some of the effects above: in closely spaced double quantum well systems, interlayer coherence can be induced when adjusting the Coulomb interaction within each layer to be similar to that between the two layers. This can be done by controlling the magnetic field, the charge carrier density in both layers as well as by the distance between the layers. At the state, in which both quantum wells exhibit a filling factor of 1/2, a quantum Hall state of the combined filling factor vT = 1 is formed. In terms of the pseudospin, a which layer degree of freedom assigned to each electron in the bilayers, the pseudospin vectors are aligned in the system’s ground state, forming a pseudospin quantum Hall ferromagnet. Since the quantum wells are half-filled, occupied and vacant states can also be thought as indirect conduction band excitons which are condensed into a BCS-like condensate giving rise to a Josephson-like interlayer tunneling up to a critical current, strongly resembling the Josephson junctions of conventional superconductors. In this work, phenomena concerning the critical currents, both out of plane and in the plane, are studied in double-well structures. After this introductive chapter, the rest of this thesis is structured as follows: - Chap. 2 introduces the physics of two-dimensional electron systems (2DES) and the in-teger quantum Hall effect. Starting with the classical Drude model, the edge state picture will be discussed in detail under the light of Landau quantization. It will be extended by distinguishing between the compressible and the incompressible strips of a 2DEG, which results in different Hall potential distribution of a single quantum Hall plateau. This chap-ter is terminated with the fractional quantum Hall effect. - Chap. 3 gives an introduction to the underlying theory of the ground state as well as low energy excited states of the vT = 1 bilayer state. Three types of ground state wave functions, which are mathematically equivalent, will be presented. In the low energy ex-citations, the concept of merons will be introduced. Finally, different types of transport including the interlayer tunneling, in-plane transport and excitonic counterflow will be discussed. - Chap. 4 opens the experimental part of this thesis and deals with the interplay between the quantum Hall breakdown and the Josephson-like interlayer tunneling. Three Hall bar samples which only differ in their interlayer spacing will be presented in terms of their critical Josephson currents. Two of them will be further investigated in order to clarify the role of in-plane transport in the interlayer tunneling. - Chap. 5 uses Corbino ring devices to study the transport in different configurations. In particular, interlayer tunneling at different edges of one Corbino sample will be compa-red in order to study the effect of edge and area. Furthermore, two Josephson interlayer currents will be applied simultaneously to investigate the interplay between these two circuits which are separated. - Chap. 6 presents two measurement setups to study the excitonic counterflow at vT = 1: series and drag counterflow. For series counterflow, one Corbino sample is used while two Corbino samples are used for the drag counterflow, from which one sample will be tilted in order to introduce a parallel magnetic field component on the 2DES. These chapters are followed by a summarizing chapter which also points at existing questi-ons and further possibilities to complete the understanding of this topic. Three appendices are provided for interested readers to know about the materials and fabrication procedures used in this work in more details.

Die tiefgreifenden Fortschritte der Halbleitertechnologien liegen der Entdeckung zweier Quantenphänomenen--dem integralen und dem fraktionellen Quanten-Hall-Effekt--zugrunde, bei denen der Längswiderstand der Probe quasi auf Null geht, während dessen Querwiderstand einen quantisierten Wert aufweist. Die vorliegende Dissertation behandelt einen besonderen Quanten-Hall-Zustand, der aufgrund von Kopplungseffekten zwischen zwei dünnen mit Elektronen gefüllten Schichten zustande kommt, wobei die verfügbaren Zustände der beiden Schichten jeweils bis zur Hälfte durch Elektronen besetzt sind. Dieser Zustand wird als der Quanten-Hall-Zustand bei totalem Füllfaktor von eins bezeichnet. Theoretisch verhält sich das durch die beide Schichten gebildete Doppellagensystem jedoch wie ein Superleiter, denn bei dem totalen Füllfaktor von eins wurden bis zu Beginn dieser Arbeit eine Reihe von supraleiterartigen Phänomenen, bspw. DC-Josephson-Effekt und verschwindend kleiner elektrischer Widerstand, etc, beobachtet. Im Rahmen dieser Doktorarbeit wurden Messungen durchgeführt, die über die Abhängigkeit des kritischen Josephson-Stroms von der Dicke der zwischen den beiden Schichten befindlichen Barriere sowie über den Zusammenhang zwischen dem kritischen Längsstrom und dem kritischen Josephson-Strom Aussagen liefern sollen. Dabei wurde gezeigt, dass der Längsstrom sich gleichmäßig mit der Barrierendicke verhält, während sich der kritische Josephson-Strom bei Änderung der Barrierendicke drastisch verändert. Eine zweite Art von Messungen trägt den Fokus auf den Suprafluss, der theoretisch für gebundene Elektron-Loch-Paare vorhergesagt wurde. Es konnte mit Hilfe von ringförmigen Proben gezeigt werden, dass der kritische Josephson-Strom eine eindeutige Flächenabhängigkeit aufweist, und dass zwischen den Rändern des Ringes kein elektrischer Strom, wohl aber ein Suprafluss getragen wird. Abschließend zeigt diese Arbeit, dass durch anlegen eines zur Probenebene parallel Magnetfeldes der Josephson-Strom verschwinden kann. Der tunnelnde Josephson-Strom scheint dabei, sofern dieser in der Probenebene fließt, eine Hall-Spannung hervorzurufen.