Interplay of Symmetry Geometry and Topology in Crystalline Phases of Matter
The word “topological” has permeated condensed matter physics over the last decade. The discovery of new quantum electronic phases of matter such as topological insulators, and the promise of a fault-tolerant topological quantum computation architecture, which utilizes topological phases of matter as robust quantum bits and logic processors has transformed the ﬁeld. Twenty-ﬁve years after the discovery of the quantum Hall insulator, the ﬁrst example of a topological phase, a second topological revolution began with the prediction, and experimental discovery, of a new class of phases that require additional symmetries for their stability. An exciting outcome of these developments was the prediction that some phases could be stabilized by ordinary crystal symmetries like reﬂection or rotation symmetry. However, one might be pessimistic that these phases could be stabilized since real material samples are typically disordered and do not exactly preserve the symmetries required for topological protection. Surprisingly, this issue was immediately obviated when the ﬁrst experimental results on PbxSn1xTe alloys showed remarkably clear and robust topologically protected features, despite the fact that it is a disordered alloy. These results have opened up a frontier of exciting possibilities for new topological phases of matter and phenomena protected by crystal symmetries. There is currently not a complete theoretical framework that enables the understanding of this unexpected robustness. For now, the community has resorted to using the mantra “the symmetry is protected on average” as an explanation. Unfortunately, there is not an explicit qualitative or quantitative understanding of that statement, and thus understanding the effects of disorder in these systems is of paramount importance, especially if their properties become useful for technological applications.
During his Center appointment, Professor Hughes will use numerical and analytical techniques in order to develop such a framework so that he can determine the phase diagrams and useful properties of topological crystalline phases of matter. In addition to the effects of disorder, he will consider the impact of strong electron interactions in these materials, where a recent breakthrough from his research group has indicated that some topological phases require interactions to exist. He is now in the process of trying to understand the physical properties of these systems, as well as searching for candidate materials that could realize these interesting phases.