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We present a theoretical investigation of electron heat current inasymmetrical length armchair graphene nanoribbon (AGNR) heterostructures withvacancies, focusing on the topological states (TSs). In particular, we examinethe 9-7-9 AGNR heterostructures where the TSs are well-isolated from theconduction and valence subbands. This isolation effectively mitigates thermalnoise of subbands arising from temperature fluctuations during chargetransport. Moreover, when the TSs exhibit an orbital off-set, intriguingelectron heat rectification phenomena are observed, primarily attributed tointer-TS electron Coulomb interactions. To enhance the heat rectification ratio($\eta_Q$), we manipulate the coupling strengths between the heat sources andthe TSs by introducing asymmetrical lengths in the 9-AGNRs. This approachoffers control over the rectification properties, enabling significantenhancements. Additionally, we introduce vacancies strategically positionedbetween the heat sources and the TSs to suppress phonon heat current. Thisarrangement effectively reduces the overall phonon heat current, while leavingthe TSs unaffected. Our findings provide valuable insights into the behavior ofelectron heat current in AGNR heterostructures, highlighting the role oftopological states, inter-TS electron Coulomb interactions, and the impact ofstructural modifications such as asymmetrical lengths and vacancy positioning.These results pave the way for the design and optimization of graphene-baseddevices with improved thermal management and efficient control of electron heattransport.

Thermal rectification through the topological states of asymmetrical length armchair graphene nanoribbons heterostructures with vacancies