Topological Phase and Strong Correlation in Rare-Earth Hexaborides XB₆ (X = La, Ce, Pr, Nd, Pm, Sm, Eu)

The rare-earth hexaboride SmB₆, known as the topological Kondo insulator, has attracted tremendous attention in recent years. It was revealed that the topological phase of SmB₆ is insensitive to the value of on-site Coulomb interactions (Hubbard U), indicating that the topological phase in SmB₆ is robust against strong correlations. On the contrary, the isostructural YbB₆ displays a sensitivity to the Hubbard U value. As U increases, YbB₆ transforms from topological Kondo insulator to trivial insulator, showing the weak robustness of the topological phase of YbB₆ against U. Consequently, the dependence of the topological phase on Hubbard U is a crucial issue in the rare-earth hexaboride family. In this work, we investigate the structural and electronic properties of rare-earth hexaboride compounds through first-principles calculations based on density functional theory. By taking the strong correlations into consideration using a wide range of on-site U values, we study the evolution of the topological phases in rare-earth hexaboride (XB₆, X = La, Ce, Pr, Nd, Pm, Sm, Eu). Unlike YbB₆, the topological trends in all the examples of XB₆ studied in this work are insensitive to the U values. We conclude that in addition to the well-known SmB₆, PmB₆, NdB₆ and EuB₆ are also topologically nontrivial compounds, whereas LaB₆, CeB₆ and PrB₆ are topologically trivial metal.