The importance of Charge Fluctuations for the Topological Phase in SmB$_6$

The discovery of topologically non-trivial states in band insulators has induced an extensive search for topological phase in strongly correlated electron systems. In particular, samarium hexaboride (SmB$_6$) has drawn much attention as it might represent a new class of condensed matter called topological Kondo insulator. Kondo insulators (KI) can have non-trivial Z$_2$ topology because the energy gap opens at the Fermi energy ($E_F$) by hybridization between an odd- parity renormalized $f$ band and an even- parity conduction $d$ band. However, the characteristics of SmB$_6$ deviate from the conventional KI because its gap is insensitive to doping and pressure. Thus, it is unclear what makes the gap of SmB$_6$ different from that of KI, and how the band inversion features occur. In this manuscript, we demonstrate the importance of charge fluctuations in SmB$_6$. Our angle-resolved photoemission spectroscopy (ARPES) results reveal that with decreasing temperature the bottom of the $d$-$f$ hybridized band at the $\bar{\text{X}}$ point gradually shifts from below to above $E_F$. This shift accompanies a redistribution of spectral weight from the upper to the lower quasiparticle band, and reflects the change in both carrier density and the number of localized $f$ electron. Moreover, because this hybridized band is predicted to have odd parity and to induce a non-trivial $Z_{2}$ topology, we compare our ARPES spectra with theoretical surface band structures and find signatures of topological surface states. Therefore, our results indicate that SmB$_6$ is a charge fluctuating topological insulator having the odd-parity hybridized band above $E_F$ at the $X$ point. This demonstrates that the charge fluctuations do not only drive the insulating bulk phase but also the non-trivial topological phase.