Flat-band in s1/s2 pyrochlore oxides and the effect of spin-orbit interaction

The energy of electrons in a crystal generally has dispersion. However, in a model such as a nearest-neighbor isotropic tight-binding model on pyrochlore lattice, flat bands without dispersion appear due to the quantum interference effect. In this flat band model, attractive physical properties such as perfect ferromagnetism, high-temperature superconductivity, and fractional quantum Hall effect are predicted [1,2]. Furthermore, it is known that when the spin-orbit coupling ${\lambda}$ is introduced into this model, a gap is created when ${\lambda}$a is negative, resulting in a strong topological insulator [3].
However, in the actual pyrochlore compound, there has been no example so far in which an approximate flat band was observed near the Fermi level due to the influence of the anisotropy of the transfer integral. Based on first-principles calculations, we have found that such a system (s1 system, s2 system) in which the uppermost part of the valence band is mainly the s orbital of the A site, such as Sn$_2$Nb$_2$O$_7$ and Tl$_2$Nb$_2$O$_7$, is such an example [4-6]. This time, we performed first-principles calculations incorporating spin-orbit interaction in these s1/s2 systems and compared them with the results of the flat band model (see the figure below) [7]. Details will be reported in the presentation.