Electronic transport and thermoelectric performance in quasiperiodic Fibonacci bilayer graphene superlattices

We investigate the electronic transport and thermoelectric performance of Fibonacci bilayer graphene superlattices (FBGSLs) and compare them systematically with their periodic counterparts. The study, conducted for high-order Fibonacci generations, utilizes a four-band effective Dirac Hamiltonian, the Sturm–Liouville formalism, and the numerically stable hybrid matrix method within the Landauer–Büttiker formalism. Our results demonstrate that while periodic arrangements provide robust transport through broad minibands, the aperiodic order of the Fibonacci sequence induces a fragmentation of the transmittance and the emergence of critical states with multifractal characteristics. This fragmentation effectively activates additional energy regions with high thermoelectric response. However, we find that periodic bilayer graphene superlattices (PBGSLs), characterized by a well-defined boxcar-shaped transmission band in the hole region, achieve a superior simultaneous optimization of both conversion efficiency and maximum power output. We find that the Seebeck coefficient reaches values up to ±0.6 mV/K, the power factor and the figure of merit exhibits sharp peaks about 4 pW/K2 and 15, respectively. While the FBGSLs induced fragmentation enables high-precision energy filtering in specific regions, the PBGSLs remains the optimal configuration for maximizing the efficiency-power trade-off, allowing for conversion efficiencies that saturate near the theoretical limit (≈0.5ηC) for finite-power output quantum heat engines operating within the linear-response regime. These findings suggest a dual strategy for device design: utilizing aperiodicity for multi-band spectral selectivity and periodicity for peak power-efficiency optimization.