  In this study, we investigate the charge transport properties of
semiconducting armchair graphene nanoribbons (AGNRs) and heterostructures
through their topological states (TSs), with a specific focus on the Coulomb
blockade region. Our approach employs a two-site Hubbard model that takes into
account both intra- and inter-site Coulomb interactions. Using this model, we
calculate the electron thermoelectric coefficients and tunneling currents of
serially coupled TSs (SCTSs). In the linear response regime, we analyze the
electrical conductance ($G_e$), Seebeck coefficient ($S$), and electron thermal
conductance ($\kappa_e$) of finite AGNRs. Our results reveal that at low
temperatures, the Seebeck coefficient is more sensitive to many-body spectra
than the electrical conductance. Furthermore, we observe that the optimized $S$
at high temperature is less sensitive to electron Coulomb interactions than
$G_e$ and $\kappa_e$. In the nonlinear response regime, we observe a tunneling
current with negative differential conductance through the SCTSs of finite
AGNRs. This current is generated by electron inter-site Coulomb interactions
rather than intra-site Coulomb interactions. Additionally, we observe current
rectification behavior in asymmetrical junction systems of SCTSs of AGNRs.
Notably, we also uncover the remarkable current rectification behavior of SCTSs
of 9-7-9 AGNR heterostructure in the Pauli spin blockade configuration.
Overall, our study provides valuable insights into the charge transport
properties of TSs in finite AGNRs and heterostructures. We emphasize the
importance of considering electron-electron interactions in understanding the
behavior of these materials.
