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

TL;DR

This paper explores topological interface states in armchair graphene nanoribbon heterostructures, revealing their relation to edge states, topological properties, and implications for enhanced thermoelectric performance via a double quantum dot system.

Contribution

It introduces a real-space approach to analyze topological interface states in AGNR heterostructures and links these states to thermoelectric enhancement through a topological double quantum dot model.

Findings

Interface states depend on edge state numbers and chirality.

Topological double quantum dots enhance nonlinear thermoelectric power.

Coulomb blockade suppresses thermal current but not thermal voltage.

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 $N_{IF,\beta} = |N_{O,B(A)} - N_{C,A(B)}|$, where $\beta$ 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.