Wave-Function Symmetry Mechanism of Quantum-Well States in Graphene Nanoribbon Heterojunctions

Among the various graphene-based structures, the graphene quantum well (QW) is a particularly intriguing example, as it exhibits unique electronic behavior and broad application prospects. An attractive way to achieve graphene QWs is the construction of a type-I band alignment based on an armchair graphene nanoribbon (AGNR) heterojunction, in which the electronic properties can be flexibly tuned by varying the detailed atomic structure. Intriguing characteristics of QW states have been observed in AGNR QWs, which are difficult to interpret merely by considering the band offset between the barrier and well regions. Therefore, a comprehensive understanding of the formation of QW states is required for the optimal design of AGNR QWs. An interesting phenomenon is demonstrated in that a state with a higher energy index exhibits stronger quantum confinement in the case of specific AGNR QW systems. This counterintuitive confinement originates from the wave-function symmetries of the electronic states in the constituent AGNR segments. Wave-function symmetry matching (even-even or odd-odd) leads to hybridization of corresponding states and consequently reduces the confinement, while wave-function symmetry mismatching (even-odd) suppresses the penetration of electronic states and consequently enhances the confinement. Moreover, a design method for AGNR QWs based on this wave-function symmetry mechanism through the modulation of geometric parameters and the displacement between the constituent AGNR segments is demonstrated. Finally, a demonstration of the application of this mechanism in an actual device is presented. Our perspective not only provides deep insight into the formation mechanism of QW states in AGNR QWs but also opens up a dimension for the design of AGNR QWs.