Flat-band engineering of mobility edges

Abstract

Properly modulated flatband lattices have a divergent density of states at the flatband energy. Quasiperiodic modulations are known to host a metal insulator transition already in one space dimension. Their embedding into flatband geometries consequently allows for a precise engineering and fine tuning of mobility edges. We obtain analytic expressions for singular mobility edges for two flatband lattice examples. In particular, we engineer cases with arbitrarily small energy separations of mobility edge, zeroes, and divergencies.

Engineering flat electronic bands in quasiperiodic and fractal loop geometries

“…Such states thus belong to the U = 1 class of FBS as per the nomenclature introduced by Danieli et al [8]. However, the rule of constructing the distribution of amplitudes, as shown as an ex- Berker-diamond array in its 3rd generation.…”

“…The density of packing may even lead, for a large enough generation of the hierarchical structure, to a re-entrant dispersive to non-dispersive crossover in the behavior of the electrons. A recent inspiring work by Danieli et al [8] has shown that a quasiperiodically modulated flat band geometry may even allow for a precise engineering of the mobility edges.…”

“…The magnetic field is varied to control, in a subtle way, the extent of localization and the location of the flat band states in energy space. In addition to this we show that an appropriate tuning of the field can lead to a re-entrant behavior of the effective mass of the electron in a band, with a periodic flip in its sign.Geometrically frustrated lattices (GFLs) supporting flat, dispersionless bands in their energy spectrum with macroscopically degenerate eigenstates have drawn great interest in recent times [1][2][3][4][5][6][7][8]. Initial interest in antiferromagnetic Heisenberg model on frustrated lattices [9][10][11][12][13][14] has evolved into extensive studies of the gapped flat band states to gapless chiral modes in graphenes [15], in optical lattices of ultracold atoms [16], waveguide arrays [17], or in microcavities having exciton-polaritons [18].…”

Nonlinear localized flat-band modes with spin-orbit coupling

“…(13). Values of the phase, marked in the figure near the respective lattice sites, are φ1 = − arctan λ 2 − λ 2 − 1 / λ 2 + 1 and φ2 = − arctan λ 2 + 1 / λ 2 − 1 .…”

“…The CLS existence has been experimentally probed in the same settings where FB lattices may be realized, as mentioned above: waveguiding arrays [7][8][9], exciton-polariton condensates [10], and atomic BECs [4]. The impact of various perturbations, such as disorder [5,11], correlated potentials [12,13], and external magnetic and electric fields [14], on FB lattices and the corresponding CLSs was studied too.…”