Mott physics and band topology in materials with strong spin–orbit interaction

Abstract

Recent theory and experiment have revealed that strong spin-orbit coupling can have dramatic qualitative effects on the band structure of weakly interacting solids. Indeed, it leads to a distinct phase of matter, the topological band insulator. In this paper, we consider the combined effects of spin-orbit coupling and strong electron correlation, and show that the former has both quantitative and qualitative effects upon the correlation-driven Mott transition. As a specific example we take Irbased pyrochlores, where the subsystem of Ir 5d electrons is known to undergo a Mott transition. At weak electron-electron interaction, we predict that Ir electrons are in a metallic phase at weak spinorbit interaction, and in a topological band insulator phase at strong spin-orbit interaction. Very generally, we show that with increasing strength of the electron-electron interaction, the effective spin-orbit coupling is enhanced, increasing the domain of the topological band insulator. Furthermore, in our model, we argue that with increasing interactions, the topological band insulator is transformed into a "topological Mott insulator" phase, which is characterized by gapless surface spin-only excitations. The full phase diagram also includes a narrow region of gapless Mott insulator with a spinon Fermi surface, and a magnetically ordered state at still larger electron-electron interaction. Introduction: The spin-orbit interaction (SOI), though apparently a "weak" relativistic correction to the Schrödinger equation (outside of high energy physics), is coming increasingly to the fore in modern condensed matter physics. The discovery of Topological Band Insulators (TBIs) in theory [1, 2,3,4] and experiment [5,6] has revealed a surprising omission in the "textbook" Bloch theory of the electronic structure of weakly correlated solids. In these remarkable materials, strong spin-orbit interactions allow a non-trivial topology of the electron bands, resulting in protected "helical" edge and surface states in two and three dimensional systems. Many other interesting phenomena, including quantum number fractionalization and magneto-electric effects have been predicted to occur in these systems, and are the subjects of a growing experimental effort. In parallel, strong SOIs have been identified in a growing variety of Mott insulators, in which the insulating behavior is driven by electron correlation rather than band structure. For instance, SOIs are likely responsible for the large Wilson ratios observed in many frustrated magnets at low temperature [7,8], and may be the driving force for the formation of a "spin-orbital liquid" in some Fe-spinels [9]. They have been experimentally shown to control the orbital state in the Ir oxide Sr 2 IrO 4 using resonant x-ray scattering [10]. A natural question is how these two classes of phenomena are connected -how does a material progress from weak to strong correlation with strong SOIs? This is the subject of the Mott transition with strong SOIs.In the search for strong SOIs, one is driven t...

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