Universiteit Leiden

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The symmetry of crystals and the topology of electrons

Promotor: J. Zaanen, Co-Promotor: V. Juricic

Robert-Jan Slager
12 januari 2016
Thesis in Leiden Repository

The concept of topology, having played a perpetual center stage role in the field of mathematics and physics for already a few centuries, heuristically pertains to the study of properties of geometrical objects that are preserved under smooth deformations. Recently, it was uncovered that such topological structures may in particular emerge in the quantum world of electron systems that are subjected to the presence of discrete symmetries such as time reversal symmetry, particle hole symmetry and chiral symmetry. Nonetheless, the role of the most prominent and necessarily present symmetry in this regard, being that of the underlying lattice, has remained elusive. In this work we signify the profound interplay between topological order in electronic band theory and the associated crystal symmetries by exploring the physics of defects, with the emphasis on dislocations. We find that in addition to a plethora of interesting mechanisms, which are related to the defects themselves and culminate, inter alia, in helical propagating fermionic modes bound to freely deformable channels and exotic isospinless graphene-like states that can be linked to illustrious field theoretical anomalies, these results in turn expose an extension of the classification of topological electrons systems.