Perfect flat band with chirality and charge ordering out of strong spin-orbit interaction

Abstract

Spin-orbit interaction has established itself as a key player in the emergent phenomena in modern condensed matter, including topological insulator, spin liquid and spin-dependent transports. However, its function is rather limited to adding topological nature to band kinetics, leaving behind the growing interest in the direct interplay with electron correlation. Here, we prove by our spinor line graph theory that a very strong spin-orbit interaction realized in 5d pyrochlore electronic systems generates multiply degenerate perfect flat bands. Unlike any of the previous flat bands, the electrons in this band localize in real space by destructively interfering with each other in a spin selective manner governed by the SU(2) gauge field. These electrons avoid the Coulomb interaction by self-organizing their localized wave functions, which may lead to a flat-band state with a stiff spin chirality. It also causes perfectly trimerized charge ordering, which may explain the recently discovered exotic low-temperature insulating phase of CsW2O6.

Deep learning approach to genome of two-dimensional materials with flat electronic bands

“…Therefore, for most of the observed flat bands, the constituent electrons originate from a single element in the compound, assuming that the probability of accidental band degeneracy is low. Our conjecture is supported by several studies showing that it is the elemental sublattices which obey specific lattice and orbital symmetries that lead to flat bands 22,[30][31][32] . For example, in intermetallic CoSn, the flat band is attributed to the kagome sublattice of the transition metal element 30 , and in HgF 2 , it is the diamond-octagon sublattice of mercury 21 .…”

Machine learning approach to genome of two-dimensional materials with flat electronic bands

“…Therefore, for most of the observed flat bands the constituent electrons originate from one element of a compound assuming that probability of accidental band degeneracy is low. Our conjecture is supported by research shown that elemental sublattices which obey specific lattice and orbital symmetries lead to flat bands [37][38][39] . For example, in intermetallic CoSn the flat band is attributed to the kagome sublattice of the transition metal element 37 , and in HgF 2 it is the diamond-octagon sublattice of mercury 24 .…”

Coherent magnetic and electronic structure symmetry broken in frustrated bilayer Kagome ferromagnet Fe3Sn2

“…Among these topological materials, magnetic Kagome materials are fascinating platforms to study the exotic physical properties due to their geometric frustration of crystal and magnetic structure [17], which is considered to be the root of many topological properties, like quantum spin liquid phase [18], flat band structure [19], Dirac or Weyl fermions [20][21][22], magnetic skyrmions [23], charge density wave [24][25][26] and so on. In Kagome materials, the SOC is also a key interaction to the topological properties [27,28], so they are ideal materials to study the influence of external magnetic field on electronic states, which has also been confirmed in some materials, like Fe 3 Sn 2 [29][30][31] and YMn 6 Sn 6 [32].…”