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

We report the existence of flat band state in a periodic diamond dot lattice within the tight-binding 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.