This comprehensive study utilizes the full tight-binding model and Green's function approach, employing the linear response theory, to investigate the electronic and thermal conductance of penta-graphene (PG) under various external parameters such as bias voltage, magnetic field, and doping. The results reveal that these parameters significantly enhance the thermoelectric properties of PG through modifications in its band structure and increased charge carrier density. By applying electric and magnetic fields, the wide band gap of PG, can be substantially reduced, with the magnetic field inducing subband splitting and modifying the band edges. The thermal properties of PG are initially negligible below 1500 K in the absence of external fields, but their magnitude increases remarkably by external fields, with the magnetic field exhibiting a more pronounced effect than the electric field. Interestingly, the chemical potential exhibits a surprising influence on the temperature dependence of PG's thermal properties, surpassing even the impact of the magnetic field at higher temperatures. The Lorenz number of PG complies with the Wiedemann-Franz law, remaining constant at low temperatures and reaching a peak value at higher temperatures and external fields alters this behavior by reducing the constant region and shifting the peak to lower temperatures. Moreover, the presence of electron-hole impurities in PG leads to peaks in the power factor (PF) and figure of merit (ZT), with the electric and magnetic fields causing these peaks to shift towards lower impurity concentrations. These findings highlight the potential of PG for various device applications and open up new avenues for further research and development in this promising field.
