Date of Award

Spring 1-1-2017

Document Type


Degree Name

Doctor of Philosophy (PhD)

First Advisor

Michael Hermele

Second Advisor

Victor Gurarie

Third Advisor

Ana Maria Rey

Fourth Advisor

Dmitry Reznik

Fifth Advisor

Joel Eaves


Spin-orbit coupling exists in materials in general. However, it entangles the spin and orbital degrees of freedom and complicates the model. Thus, theorists usually neglect the effects induced by spin-orbit coupling first and consider spin-orbit coupling as perturbation next. The non-perturbative effects brought up by spin-orbit coupling are thus often less studied or overlooked.

On the other hand, the majority in the study of interacting topological order focusing on the general structure of theories and made significant advances by leaving material details behind. It is thus important to find possible microscopic models that could realize the new phases in laboratories and benefits from the progress of theories to make experimental predictions.

In this thesis, we study the physical effects due to strong spin-orbit coupling from the perspective of searching new quantum orders and the non-trivial responses.

(i) The first project, we propose the nontrivial dipolar-octupolar (DO) doublets on the pyrochlore lattice. By studying the most general symmetry allowed model at the localized and the itinerant limit for DO doublets, we found two 3D symmetry enriched topological orders and topological insulator correspondingly. (ii) In the second project, we analyze the 2D model descending from the localized limit of DO doublets on pyrochlore. The discrete onsite symmetry and space group symmetry could lead to a symmetry-enriched topological order with symmetry fractionalization pattern that cannot emerge from a spin model with continuous spin rotational symmetry. The non-trivial symmetry fractionalization pattern contributes to the striking numerical signal that can help identifying the topological order. (iii) In the third project, we develop a theory to understand the high-energy Raman signal in Sr2IrO4.