Correlated Topological Insulators with Mixed Valence

Abstract

We propose the local density approximation (LDA)+Gutzwiller method incorporating Green's function scheme to study the topological physics of correlated materials from the first-principles. Applying this method to typical mixed valence materials SmB6, we found its non-trivial Z2 topology, indicating that SmB6 is a strongly correlated topological insulator (TI). The unique feature of this compound is that its surface states contain three Dirac cones in contrast to most known TIs. PACS numbers:Most of Z 2 topological insulators (TI)[1-5] discovered up to now are semiconductors which are free of strong correlation effects and their topological nature can thus be predicted quite reliably by first principle calculations based on density functional theory (DFT) [6]. The Z 2 classification of band insulators has been generalized to interacting systems by looking at its response to external electric magnetic field, namely the topological magnetoelectric effect (TME) [7]. A correlated insulator is a TI if the θ-angle defines in TME is π. Given the TME theory and several simplifications [8], however, its application to realistic materials is still absent due to: (1) the lack of suitable compounds; (2) the difficulty to compute reliably correlated electronic structures from the firstprinciples. In this letter, we study a special class of materials, the mixed valence (MV) compounds, which contain rare-earth elements with non-integer chemical valence. By combining the Gutzwiller variational approach from the first-principles and the Green's function method for the TME, we found SmB 6 is a 3D correlated TI. Interestingly, it has three Dirac cones on the surface, in contrast to most of the known TIs.

Crossover of Magnetoresistance from Fourfold to Twofold Symmetry in SmB6 Single Crystal, a Topological Kondo Insulator

“…The most puzzling issue is the lack of divergence in the resistivity at low temperatures, which has always been attributed to in-gap states [13][14][15][16]. Recently, there have been theoretical and experimental demonstrations that such in-gap states might be topological surface states [17][18][19][20][21][22][23][24].…”

In-gap collective mode spectrum of the topological Kondo insulatorSmB6

“…Let us now redefine (44) and (45) so that the factors X n (k) are moved from the self-energy to the modulated propagator:…”

“…It can have only a limited quantitative accuracy, but sufficient for the reliable determination of the band topology. As an experiment-based method, it can complement abinitio calculations [43][44][45][46] whose accuracy in the low-energy sector is significantly limited by the presence of strong interactions.…”

Nonuniversal weak antilocalization effect in cubic topological Kondo insulators

“…Samarium hexaboride (SmB 6 ) along with PuB 6 and YbB 6 have recently emerged as prominent candidates [1][2][3][4][5][6] for hosting topologically protected metallic surface states. 7 In particular, SmB 6 -a material in which strong hybridization between samarium conduction d-electrons and strongly correlated f -electrons drives an onset of an insulating state at low temperatures [8][9][10][11][12] -has recently came into focus of theoretical and experimental studies as a most prominent candidate for the first correlated topological insulator.…”