AI 中文总结
该研究建立各向异性多谷狄拉克系统界面态的低能理论，推导锐/平滑界面下束缚态的色散等特性，结合连续与晶格模型展示谷界面模式杂化规律，为狄拉克界面态控制提供设计原则。
AI 中文摘要
我们针对各向异性多谷狄拉克系统的界面态建立了低能理论，这类系统的质量和动力学参数可跨界面变化。对于锐界面，电流守恒的匹配条件给出了束缚态存在性、局域化和色散的解析表达式。我们证明，界面速度由界面两侧的加权切向动力学项决定；这些项的抵消可抑制线性速度，并在投影狄拉克点附近生成零阶近似下平坦的界面带。对于狄拉克质量和切向动力学系数均反向（大小不变）的特殊反对称构型，在狄拉克线性理论的所有守恒动量范围内，透明锐界面解完全无色散，而周围的体带仍有色散。我们将该理论扩展到平滑界面，其中修正后的束缚态包络通过切向动力学系数的空间平均改变线性界面速度。我们还研究了动力学σₓ和σᵧ通道中的二次修正；在其系数的一阶及界面动量的线性阶下，这些项会移动界面态能量，但不会对线性速度产生额外修正。最后，我们结合连续介质模型和晶格模型，展示了不同谷的界面模式如何杂化，以及所得色散如何依赖于微观界面性质。我们的结果为控制狄拉克界面态的色散、局域化和杂化建立了设计原则；我们还研究了两种基于石墨烯的质量畴壁模型，作为色散同向传播和反向传播界面态的实验启发示例。
英文摘要
We develop a low-energy theory of interface states in anisotropic multivalley Dirac systems whose masses and kinetic parameters are allowed to vary across an interface. For sharp interfaces, current-conserving matching conditions yield analytic expressions for the existence, localization and dispersion of the bound states. We show that the interface velocity is determined by the weighted tangential kinetic terms on the two sides of the seam. Their cancellation can suppress the linear velocity and generate an interface band that is flat to leading order near the projected Dirac point. For the special antisymmetric configuration in which both the Dirac mass and the tangential kinetic coefficient reverse sign with unchanged magnitude, the transparent sharp-interface solution is exactly dispersionless for all conserved momenta within the linear Dirac theory, while the surrounding bulk bands remain dispersive. We extend the theory to smooth interfaces, where the modified bound-state envelope changes the linear interface velocity through a spatial average of the tangential kinetic coefficient. We also investigate quadratic corrections in the kinetic \(σ_x\) and \(σ_y\) channels. To first order in their coefficients and through linear order in the interface momentum, these terms shift the interface-state energy but produce no additional correction to the linear velocity. Finally, we combine continuum and lattice models to show how interface modes from distinct valleys hybridize and how the resulting dispersions depend on microscopic interface properties. Our results establish design principles for controlling the dispersion, localization, and hybridization of Dirac interface states. We further examine two graphene-based mass-domain-wall models as experimentally inspired examples of dispersive copropagating and counterpropagating interface states.
