Design of band structure simulation experiments for a two-dimensional electronic device course

Driven by topological properties, two-dimensional valleytronics is pivotal for the design of low-power electronic devices. Consequently, incorporating simulation experiments of valleytronic devices into solid-state physics curricula significantly enhances the practicality and innovativeness of a course.

Leveraging band theory and the tight-binding model, this experiment presents a simulation design for two-dimensional graphene-based valleytronic devices. First, taking graphene as a prototype, the physical foundations of valleytronics within a hexagonal honeycomb structure are reviewed, and the fundamental characteristics of the valley degree of freedom are introduced. Second, a two-dimensional electronic device model is constructed based on monolayer graphene to simulate the band structure and spatial electron distribution of topologically confined electronic states in a single-channel configuration. Third, the electronic properties of two-dimensional topological valley devices with three and four channels are investigated. The channel number parity significantly alters the band structure at the Fermi level, indicating that interchannel coupling of electronic states is decisive for the electronic properties of the system. Specifically, in the three-channel configuration, each valley hosts a single linear topological conducting near-zero-energy state, with these states having opposite propagation directions for the two valleys. Notably, these states are not localized in a single channel but are uniformly distributed near the first and third channels. In contrast, in the four-channel system, interchannel coupling opens a global band gap in the band structure, and consequently, the system exhibits insulating behavior at zero energy. At finite low energies, the wavefunctions of the electronic states display strong interchannel coupling. Furthermore, the mechanisms influencing these multichannel two-dimensional topological transport devices are explored by varying sublattice onsite energy ratios and external magnetic fields.

The results demonstrate that modifying the sublattice onsite energy ratio between adjacent regions effectively regulates the distribution proportion of electrons across real-space channels. Specifically, in the three-channel configuration, an increase in U₂/U₁ causes the zero-energy states that are originally uniformly distributed near the first and third channels to progressively localize in the first channel. This process culminates in the exclusive localization of zero-energy states in the first channel owing to the decoupling of electronic wavefunctions across channels. In contrast, decreasing U₂/U₁ reverses this trend, leading to a gradual accumulation of zero-energy states near the third channel. A similar modulation phenomenon is also observed in the four-channel system. Moreover, applying an external magnetic field breaks the time-reversal symmetry of the system, substantially modifying the band structure and spatially separating electrons from different valleys. Additionally, the transmission direction and distribution channels of electrons in real space can be manipulated by adjusting the magnetic field direction or the carrier type.

Given the physical equivalence between modulating sublattice onsite energy in a monolayer system and applying a perpendicular external electric field in a multilayer system, these results indicate that external electric or magnetic fields exert critical regulatory effects on topological conducting states. This influence enables the selective control of transmission channels and directions for electrons in different valleys within the device. This simulation experiment not only demonstrates an intuitive application of band theory in two-dimensional topological electronic devices but also provides an ideal platform for teaching practices and research training in solid-state physics–related courses.