Correlation effects in topological insulators

Naoto Nagaosa, The University of Tokyo

Topological insulators are the new state of matter recently discovered theoretically and later confirmed experimentally. They are characterized by the nontrivial topological properties of Bloch wavefunctions in the bulk, and consequently the edge or surface states. Up to now, most of the works have been focused on the single particle physics, i.e., the band theory. In this talk, I will discuss the effects of the electron correlation on the topological insulators. First question is how the correlation leads to a new physics in the edge channels of the 2D quantum spin Hall systems, e.g. HgTe quantum well. We found that a new type of correlated liquid is realized when the two helical edge channels are coupled through the Coulomb interaction. In this semiconductor system, the electron correlation is rather weak and the effective theory can be constructed only for the edge channels, i.e., the low energy sector. This becomes questionable for the transition metal oxides, where the correlation effect is much stronger. As an example, we take Na₂IrO₃ where 5d electrons of Ir atoms are subject to both the strong Coulomb interaction and spin-orbit interaction. We propose that the band structure of this material is that of the weak topological insulator. We also discuss the role of the correlation, which leads to the novel phase diagram including the topological Mott insulator. Experimental method to distinguish between the band insulator and Mott insulator is discussed.