- The paper employs GW approximation and a four-band tight-binding model to analyze layer-dependent band gaps in black phosphorus.
- It finds that monolayer BP exhibits a 1.5 eV gap while multilayer forms show reduced semiconductor gaps.
- The study identifies key in-plane and out-of-plane hopping parameters, with t₂ playing a crucial role in tuning electronic properties.
Quasiparticle Band Structure and Tight-Binding Model for Black Phosphorus
The paper examines the electronic properties of black phosphorus (BP) through a detailed analysis using the quasiparticle GW approximation. This work primarily focuses on elucidating the band structure characteristics of black phosphorus in both single-layer and bilayer configurations, with discussions extended to multilayer and bulk forms.
Ab Initio and Tight-Binding Model Analysis
Performed ab initio calculations within the GW approximation reveal a significant discrepancy in the band gaps of black phosphorus as the number of layers changes, with a value around 1.5 eV for monolayers. This computational analysis aligns with empirical data that shows the variation in electrical properties based on the number of layers. The paper introduces a four-band tight-binding model, designed to accurately represent the monolayer and bilayer BP band structures near the band gap. The results underscore the importance of interlayer hopping in governing the observed band gap differences.
Key Findings on Electronic Structure
The electronic properties derived from the GW approximation indicate that monolayer BP is distinctively an insulator with a larger band gap compared to its bulk form, which is a semiconductor with a smaller band gap. This electronic transition between different configurations of BP ties back to the alteration in electronic band structure, particularly around the valence and conduction bands. The paper highlights two predominant hopping parameters in the tight-binding model: one for in-plane interactions (t₁) and one for out-of-plane interactions (t₂), with the latter having a notable positive value indicating a repulsive nature.
In-depth analysis confirms that these hopping parameters significantly affect the band gap, with t₂ being primarily responsible for causing the band gap in a monolayer. The band structures produced by the tight-binding model reveal uniform shifts in both valence and conduction bands in response to changes in t₂, thus offering a method for tuning the band gap in BP by adjusting interlayer interactions.
Implications and Future Directions
The findings reveal a unique behavior of BP compared to other two-dimensional materials like graphene, where typically one hopping parameter suffices. The puckered structure of BP and consequential electronic properties suggest potential for novel applications, particularly in electronic and optoelectronic devices where tunable band gaps are advantageous.
Further research should focus on exploring the self-consistent treatment within the GW methodology to refine the accuracy of band gap predictions in bulk BP and enhance the model's applicability to a wider class of materials. Moreover, investigating the implication of the observed anisotropic transport properties could open avenues for the development of highly directional electronic components.
In conclusion, this work provides a comprehensive model for understanding the band structure of BP, leveraging both GW calculations and tight-binding models. Its insights into layer-dependent electronic properties set the stage for further exploration and technological advancement in the field of two-dimensional materials.
