Abstract
An essential attribute of many fractal structures is self-similarity. A Sierpinski gasket (SPG) triangle is a promising example of a fractal lattice that exhibits localized energy eigenstates. In the present work, for the first time we establish that a mixture of both extended and localized energy eigenstates can be generated yeilding mobility edges at multiple energies in presence of a time-periodic driving field. We obtain several compelling features by studying the transmission and energy eigenvalue spectra. As a possible application of our new findings, different thermoelectric properties are discussed, such as electrical conductance, thermopower, thermal conductance due to electrons and phonons. We show that our proposed method indeed exhibits highly favorable thermoelectric performance. The time-periodic driving field is assumed through an arbitrarily polarized light, and its effect is incorporated via Floquet-Bloch ansatz. All transport phenomena are worked out using Green’s function formalism following the Landauer–Büttiker prescription.
Highlights
The nearest-neighbor hopping (NNH) hopping integrals are considered in the wide-band limit, where it is set for the electrodes as t0 = 2eV, and in the Sierpinski gasket (SPG) as t = 1 eV
We have given a new prescription to get mobility edge separating the localized and extended states by irradiating an SPG network, and we exploit the existence of mobility edge in TE applications
A higher generation SPG has been studied to observe the existence of mobility edge by studying the electronic transmission spectrum and energy eigenvalues in the presence of light irradiation
Summary
A(τ ) · dl , where the symbols e, c, and ħ carry their usual meaning. Without losing any generality, we can write the vector potential in the form A(τ ) = (Ax sin( τ ), Ay sin( τ + φ), 0) , which represents an arbitrarily polarized field in the X-Y plane. We employ the Green’s function formalism to calculate the transmission probability of an electron from source to drain through the SPG network. When the temperature difference between the two contact electrodes is infinitesimally small, the phonon thermal conductance is evaluated from the expression[34,35,36] ħ kph = 2π ωc 0. Tph is the phonon transmission coefficient across the SPG, and it is computed using the well known Green’s function prescription through the relation. Guo et al.[41] have discussed the anharmonic phonon-phonon scattering in heat transport at an ideal Si/Ge interface via NEGF formalism They have assumed that the anharmonicity is present only in the interface device region, whereas the contacts are harmonic. In view of the possibility to compute the thermal conductance in the presence of anharmonicity, we wish to study the effect of anharmonic phonon-phonon scattering in our future work, which may lead to some interesting features
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