Tunable quantum transport and thermodynamic response in bilayer β-graphyne: interplay of stacking symmetry and external fields

A comprehensive theoretical investigation of the electronic, thermodynamic, and thermoelectric properties of bilayer β-graphyne is presented within a tight-binding framework combined with Green’s function formalism and Kubo transport theory. The effects of interlayer stacking geometry, external bias voltage, and perpendicular magnetic field are systematically examined for four representative bilayer configurations, namely AA, AB1, AB2, and AB3. The results reveal that the low-energy electronic spectrum is highly sensitive to the stacking arrangement, leading to pronounced differences in the electronic and thermoelectric responses. The calculated DOS reveals a strong stacking dependence, where AA configuration remains metallic, while the AB stackings exhibit a small gap near the Fermi level. The application of bias voltage redistributes the low-energy DOS around the Fermi level, whereas the perpendicular magnetic field modulates the VHSs through Zeeman splitting. These field-induced electronic modifications directly influence thermodynamic and transport behavior. In particular, the electronic specific heat and electrical conductivity display strong field‑dependent responses with increasing temperature. Furthermore, the Seebeck coefficient and Lorenz number exhibit pronounced enhancements under strong bias voltage, accompanied by noticeable deviations from the Wiedemann-Franz law. These results demonstrate that stacking‑dependent interlayer coupling provides an efficient mechanism for tuning the electronic and thermoelectric properties of bilayer β‑graphyne.