发表机构
Centro Universitario de los Valles; Tecnologico de Monterrey; Norwegian University of Science and Technology（瓦列斯大学; 蒙特雷科技大学; 挪威科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究各向异性和倾斜狄拉克与外尔系统中马约拉纳束缚态，通过建立分析框架，推导二维狄拉克系统相关表达式，研究倾斜影响，还考虑三维外尔系统，揭示配对对称性等特性，为理解其微观性质提供了新视角和描述。
AI 中文摘要
拓扑超导体拥有马约拉纳边界模式，其稳健性受体博戈留波夫准粒子谱的非平凡拓扑保护。虽与狄拉克和外尔准粒子相关的马约拉纳束缚态已被广泛研究，但各向异性准粒子速度和倾斜能带结构如何改变其微观性质却知之甚少。本文为描述拓扑超导体表面准粒子的有效二维博戈留波夫 - 德热纳狄拉克理论中的马约拉纳束缚态建立了一个分析框架，并通过超导配对与相同的低能描述建立微观联系，将分析扩展到三维倾斜外尔系统。对于各向异性二维狄拉克系统，我们推导了连续拓扑不变量、马约拉纳波函数、局域长度、传播速度和任意界面取向的有限尺寸小能隙的封闭解析表达式。我们表明，马约拉纳通道的手征性由速度矩阵行列式的符号决定，而其局域化和色散由速度张量和界面几何共同控制。对于倾斜的二维狄拉克锥，我们证明倾斜使旋量本征态、贝里相位和投影配对对称性不变，但随着接近 I 型和 II 型区域之间的里夫希茨转变，强烈抑制马约拉纳传播速度和有限尺寸小能隙。最后，我们考虑超导倾斜三维外尔系统，并表明传统自旋单重态 s 波配对相互作用在低能外尔带上的投影自然地产生有效的手征 px ± ipy 配对对称性，提供了一个支持局域化马约拉纳表面态的微观博戈留波夫 - 德热纳描述。
英文摘要
Anisotropy and cone tilt change how Majorana states propagate along an interface and decay away from it. We derive a two-dimensional Majorana surface Hamiltonian from a fully gapped three-dimensional superconductor, with the surface mass generated by the relative phase between triplet and singlet pairing. For a mass domain wall on this surface, we obtain the wave function, propagation velocity, and localization length of the resulting one-dimensional channel for a general invertible velocity tensor and an arbitrary wall orientation. The product of propagation speed and localization length is independent of wall orientation in the anisotropic model. For a smooth closed channel without a vortex, the propagation time around the wall determines the lowest excitation energy. For a tilted surface cone, the normal and parallel components of tilt affect confinement and propagation differently. We also solve a separate three-dimensional Weyl model with uniform singlet pairing and a reversing exchange field. In the regime supporting interface states, its bulk remains gapless. At zero chemical potential, two states confined perpendicular to the wall and propagating within its plane have the same dispersion over a finite momentum interval. Numerical diagonalization confirms the analytical energies and wave functions.
