Interplay of superconductivity, quantum orders, and topological orders in correlated materials and the role of spin-orbit coupling

Most states or phases of condensed matter can be described by local order parameters and the associated broken symmetries. However, it is recently realized that symmetry invariance can also lead to new topological orders such as quantum Hall states and topological insulators. Therefore, an interplay of broken and invariant symmetries in a given materials can be further intriguing in realizing more exotic phenomena, in which spin-orbit coupling is known to play an important role. Here I will show that ‘spin-orbit density wave’ is one such example which involves translational symmetry breaking, while time-reversal symmetry remains intact. This order parameter will be argued to be present in the ‘hidden order’ state in URu2Si2,[1] and in Rashba-type spin-orbit coupled systems.[2] Next, I will show evidences of the presence of such ordering in other systems including iridium oxide (iridates), and LAO/STO interfaces, and will discuss our ideas for theoretical modelling. 
In the second part, I will explore the possible role of spin-orbit coupling in the superconducting state. I will start with the theory of unconventional superconductivity from repulsive interaction in iron-pnictide, and actinides superconductors.[3,4] Then I will discuss how an intercalated layer of spin-orbit coupled Rashba-state within the iron-pnictide structure can induce or enhance superconductivity in such superlattices. The possibility of intermediate coupling theory in these materials and others possible systems will also be discussed.
 
[1] Das, Sci. Rep. 2, 596 (2012).
[2] Das, PRL 109, 246406 (2012).
[3] Das, Balatsky, PRL 106, 157004 (2011).
[4] Das, Vorontsov, Vekhter, Graf, PRL 109, 187006 (2012).