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

Abstract

We report the existence of flat band state in a periodic diamond dot lattice within the tightbinding framework. An analytical scheme to detect such non-dispersive state has been discussed elaborately. The dispersionless signature is clarified from the study of dispersion relation that is obtained by using real space renormalization group technique. The robustness of the flat band state with respect to the application of a uniform magnetic flux is analyzed along with the extensive numerical calculation of general spectral profile and two-channel transmission property. The amplitudes corresponding to this self-localized bound state are confined either within a finite size atomic cluster or pinned at a particular vertex making the particle immobile owing to the divergent effective mass. The challenging probability to engineer the band curvature (or equivalently the effective mass) using an external perturbation may inspire the experimentalists. The group velocity of the wave train can be manipulated (both in magnitude and sign) by virtue of the applied flux and hence the effective mass exhibits a re-entrant crossover as a function of the same external parameter.

Flatband Line States in Photonic Super‐Honeycomb Lattices

“…[ 18,19 ] The physical boundary formed by the sites with zero amplitude is related to the “local symmetry partition” that makes the associated electronic wave functions remain localized in space inside the characteristic trapping “prison.” The frozen amplitude distribution inside the “prison” does not allow any dynamics of the “prisoner” beyond the trapping cell, making the kinetic information solely quenched. [ 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.…”

Localized States Emerging from Singular and Nonsingular Flat Bands in a Frustrated Fractal‐Like Photonic Lattice

“…The frozen amplitude distribution inside the prison does not allow any dynamics of the prisoner beyond the trapping cell making the kinetic information solely quenched. [ 4 ] This immobility of the CLSs can be seen as a consequence of the divergent effective mass tensor and the singularity in the density of states profile of the flat band. This gives rise to anomalous behavior in the transport and the response of the system.…”

Application of the real space decimation method in determining intricate electronic phases of matter: a review

“…19,20 Some decorated lattices, described by a tight binding Hamiltonian, possess a typical character due to which one or more bands for a lattice geometry (Fig. 1) may become dispersionless and the corresponding single-particle energy spectrum E(k) becomes independent of momentum k. The so called flat bands [21][22][23][24][26][27][28][29][30][31][32][33][34][35][36] are produced. Such bands arise as a consequence of consecutive destructive interference caused by the geometrical arrangement of the lattice points.…”

“…1) may become dispersionless and the corresponding single-particle energy spectrum E ( k ) becomes independent of momentum k . The so called flat bands 21–24,26–36 are produced. Such bands arise as a consequence of consecutive destructive interference caused by the geometrical arrangement of the lattice points.…”