Flux modulated flat band engineering in square-kagomé ladder network

Abstract

The origin of non-dispersive flat band modes for a quasi-one dimensional square-kagomé ladder network is explored analytically by virtue of the real space renormalization group (RSRG) technique. A section of the eigenstates is non-diffusive i.e., localized within a cluster of sub-lattice sites partly by the destructive type of quantum interference and partly by the physical boundary created by the site with zero wave function amplitude. By making the amplitude vanish at the selective sites it becomes possible to confine the incoming excitation within the trapping cell leading to the formation of compact localized states. The effective mass of the particle becomes infinitely large corresponding to those self-localized modes and hence the mobility of the wave train becomes vanishingly small. This quenched kinetic energy leads to a momentum independent contribution to a dispersion curve. The present analysis is corroborated by numerical calculation of spectral landscape and the corresponding dispersion profile. The application of uniform magnetic flux may lead to a comprehensive engineering of the position as well as the curvature of the band. Also, one-to-one mapping between electronic case and photonic case within the tight-binding framework helps us to study the photonic localization in an analogous single mode wave guide system. The concept of slow light eventually introduces the possibility of spatial compression of light energy.

Flatband Line States in Photonic Super‐Honeycomb Lattices

“…[ 20 ] Interestingly, the momentum independence of the CLSs leads to divergent effective mass tensor and singularity in the profile of density of states, resulting in anomalous behavior in the transport as well as in the response of the system. [ 21 ] The tunability of the CLSs is another important aspect associated with flatband. [ 22 ] The robustness of the CLSs to disorder crucially depends on the flatband feature, for instance, whether the flatband touches with the dispersive bands or not.…”

Robust flat band and flux induced engineering of dispersive band in a periodic lattice

“…Also we should observe the distinctly visible central spiky state (at E = 0) which is the flat band state [44][45][46][47] formed by the phase cancellation. The momentum insensitivity can be understood from the second decoupled equation.…”

“…We shall however proceed to analyze transport property of the system by virtue of the standard transfer matrix formalism. The basic concept is that we have to sandwich the given structure in between a pair of semi-infinite ordered leads (so called source and drain) with the corresponding parameters [47]. It is then customary to renormalize the finite size network to transform it into an effective dimer [49] with the energy-dependent parameters.…”

Flat bands and nontrivial topological properties in an extended Lieb lattice

“…Due to the vanishing group velocity corresponding to the FBs, wave transport in the system is completely suppressed, leading to a strong localization of the eigenstates. In fact, these localized states span only a few lattice sites, forming a compact localized state (CLS) [30][31][32][33][34]. The study of such FB systems has always kept scientists intrigued as it provides an ideal playground to investigate various interesting strongly correlated phenomena, such as unconventional Anderson localization [35,36], Hall ferromagnetism [37,38], high-temperature superconductivity [39], and superfluidity [40,41], to name a few.…”

“…On the other hand, translationally invariant lattice systems which exhibit one or more flat bands (FBs) in their Bloch spectrum have generated considerable interest over the course of time [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. The presence of these momentum-independent zero-dispersion bands in the spectrum implies the existence of a macroscopic number of entirely degenerate single-particle states at the flat-band energy.…”