Topological Interface States and Nonlinear Thermoelectric Performance in Armchair Graphene Nanoribbon Heterostructures

Abstract: We investigate the emergence and topological nature of interface states (IFs) in N-AGNR/$(N-2)$-AGNR/N-AGNR heterostructure (AGNRH) segments lacking translational symmetry, focusing on their relation to the end states (ESs) of the constituent armchair graphene nanoribbon (AGNR) segments. For AGNRs with $R_1$-type unit cells, the ES numbers under a longitudinal electric field follow the relations $N = N_{A(B)} \times 6 + 1$ and $N = N_{A(B)} \times 6 + 3$, whereas $R_2$-type unit cells exhibit $(N_{A(B)} + 1)$ ESs. The subscripts $A$ and $B$ denote the chirality types of the ESs. The Stark effect lifts ES degeneracy and enables clear spectral separation between ESs and IFs. Using a real-space bulk boundary perturbation approach, we show that opposite-chirality states hybridize through junction-site perturbations and may shift out of the bulk gap. The number and chirality of IFs in symmetric AGNRHs are determined by the difference between the ESs of the outer and central segments, $N_O$ and $N_C$, according to $N_{IF,β} = |N_{O,B(A)} - N_{C,A(B)}|$, where $β$ labels the chirality. Depending on whether $N_O > N_C$ or $N_C > N_O$, the resulting IFs acquire B- or A-chirality, respectively. Calculated transmission spectra ${\cal T}_{GNR}(\varepsilon)$ reveal that AGNRHs host a topological double quantum dot (TDQD) when IFs originate from the ESs of the central AGNR segment. Using an Anderson model with effective intra-dot and inter-dot Coulomb interactions, we derive an analytical expression for the tunneling current through the TDQD via a closed-form transmission coefficient. Thermoelectric analysis shows that TDQDs yield enhanced nonlinear power output in the electron-dilute and hole-dilute charge states, with Coulomb blockade suppressing thermal current but not thermal voltage.