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A quasi-one dimensional kagomé ribbon geometry is studied in respect of its band spectrum, electronic transport as well as the thermopower within the tight-binding formalism. Analytic proposition of Bloch bands along with the dispersionless flat band states is seen to be consistent with the numerical evaluation of density of states, transmission and band dispersion. A uniform magnetic flux can act as an external agency to tune the spectral landscape and the transport at will. Flux sensitive band engineering leads to an interesting proposal of tunable thermoelectric performance of an identical model device. The tunable behavior can be explored by the calculation of Seebeck co-efficient. The external magnetic perturbation plays the key role in this demonstration and it is an easily adjustable parameter. We have critically investigated all the characteristic features using the Sommerfeld expansion within a tight-binding framework based on Green's function formalism. The present analysis may provide useful directive for constructing efficient thermoelectric devices at the nanoscale level. • Exact analytical construction of eigenstates with flat and dispersive bands is reported. • Subtle tunability of perturbation leads to a selective band engineering. • The effect of magnetic field on the location of flat band states is demonstrated. • Controlled thermoelectric behavior is studied by calculating the Seebeck co-efficient. [ABSTRACT FROM AUTHOR]

Exact construction of one electron eigenstates with flat, non-dispersive bands, and localized over clusters of various sizes is reported for a class of quasi-one-dimensional looped networks. Quasiperiodic Fibonacci and Berker fractal geometries are embedded in the arms of the loop threaded by a uniform magnetic flux. We work out an analytical scheme to unravel the localized single particle states pinned at various atomic sites or over clusters of them. 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. [ABSTRACT FROM AUTHOR]