Valley physics and disorder phenomena in 2D materials

The successful isolation in 2004 of the first 2D material graphene, a single layer of carbon atoms, has opened up new pathways for both fundamental research into condensed matter at the nanoscale and the development of entirely new technologies. Among these new possibilities is the option of transferring information using a degree of freedom other than the electron charge, and in this manner redefining conventional electronics. In graphene such a degree of freedom exists in the form of distinct momentum states of electrons in two unique "valleys" of the electronic band structure. Electrons in graphene can thus be distinguished by their so-called valley index. Storing and transferring information can be accomplished by selective manipulation of electrons based on their valley index, setting up currents, not of charge, but of valley polarization. Such currents are expected to be protected from the effects of most common sources of disorder in the nanoscale system, a major advantage over conventional charge-based electronics.
In this thesis we consider how the valley degree of freedom can be manipulated in graphene through engineering of the nanoscale system. We suggest an approach to inducing currents of valley polarization in the graphene sheet which can be controlled by an external potential, and demonstrate how such tunability of the resulting tunable filtering of electrons based on their valley index predicts a clear signature in experiment. We go on to discuss the effects of disorder in realistic nanostructured systems, outlining both the robustness of our results to moderate levels of imperfections and the possibility of new regimes of valley filtering in the strongly disordered system.
Furthermore, we extend our studies of disorder to include impurities on the surface of the high-temperature superconductor FeSe, wherein recent experimental evidence indicates that local magnetism can be nucleated around defect sites. We model such impurity-induced magnetism in a microscopic model of FeSe and predict the formation and underlying symmetries of the local magnetism. Finally, we derive the expected signature of these symmetries in experiment and compare our findings with recent scanning tunneling microscopy measurements.