Computational Design of Flat-Band Material

Abstract

Quantum mechanics states that hopping integral between local orbitals makes the energy band dispersive. However, in some special cases, there are bands with no dispersion due to quantum interference. These bands are called as flat band. Many models having flat band have been proposed, and many interesting physical properties are predicted. However, no real compound having flat band has been found yet despite the 25 years of vigorous researches. We have found that some pyrochlore oxides have quasi-flat band just below the Fermi level by first principles calculation. Moreover, their valence bands are well described by a tight-binding model of pyrochlore lattice with isotropic nearest neighbor hopping integral. This model belongs to a class of Mielke model, whose ground state is known to be ferromagnetic with appropriate carrier doping and on-site repulsive Coulomb interaction. We have also performed a spin-polarized band calculation for the hole-doped system from first principles and found that the ground state is ferromagnetic for some doping region. Interestingly, these compounds do not include magnetic element, such as transition metal and rare-earth elements.

Possible Three-Dimensional Topological Insulator in Pyrochlore Oxides

“…First, we show the band structure of Pb2Ta2O7 in Figure 2a. Similar to other quasi-FB oxides [14][15][16][17][18], this compound also shows a characteristic quasi-FB just below EF. The origin of this quasi-FB is explained as follows.…”

Flat-Band in Pyrochlore Oxides: A First-Principles Study

“…In our previous study [28], we proposed a guiding principle to obtain FB near the Fermi level ( E F ). The point was to use “s2” ions, in other words, the ions that had two electrons on the outermost s-orbitals.…”

“…The recipe is very simple: (1) Put the s2 ions on the pyrochlore A-site; (2) Fill other sites by closed-shell ions by keeping charge neutrality (e.g., Sn 2+ 2 Nb 5+ 2 O 2− 7 ); and (3) Calculate the band structure and check whether FB is found or not. There are many candidates with FB chosen by steps (1) and (2), but we have shown that only the (+2, +5) type, i.e., A 2+ 2 B 5+ 2 O 2− 7 may exhibit clear (i.e., without being masked by other bands) FB [28]. Due to the large DOS at the top of the valence band, these compounds may show a ferromagnetic ground state when some holes are doped [28,29].…”

“…There are many candidates with FB chosen by steps (1) and (2), but we have shown that only the (+2, +5) type, i.e., A 2+ 2 B 5+ 2 O 2− 7 may exhibit clear (i.e., without being masked by other bands) FB [28]. Due to the large DOS at the top of the valence band, these compounds may show a ferromagnetic ground state when some holes are doped [28,29].…”

Analytical Study of Quasi-One-Dimensional Flat Band Networks and Slow Light Analogue

“…Localization transition in one-dimensional quasiperiodic lattices has also been investigated experimentally in recent times [42]. Also quite recently, the computational design of flat band models [43,44] has enriched this section of study. The present proposal, to our mind, can thus be tested with an appropriately designed wave guide network.…”