二次和三次节点线半金属中的等离激元模式
Plasmon modes in quadratic and cubic nodal line semimetals
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中文总结 AI 辅助
该研究在随机相位近似下探究三维二次和三次节点线半金属的等离激元模式，明确其等离激元频率的载流子密度标度律，揭示相关各向异性特征，为高阶色散节点线半金属的集体动力学提供研究框架。
中文摘要 AI 辅助
节点线半金属（NLSMs）具有独特的拓扑性质和非常规的集体激发。虽然线性NLSMs中的等离激元已得到充分研究，但高阶色散NLSMs的等离激元仍知之甚少。我们在随机相位近似（RPA）框架下研究三维二次和三次NLSMs中的等离激元模式，该近似适用于$r_s\ll1$，但在小掺杂的三次NLSMs区域（态密度发散）会失效。通过推导单圈极化率并从完整三维林哈德积分数值计算其系数，我们发现了不同的载流子密度标度律：二次NLSMs的等离激元频率满足$\omega_p\sim n^{1/2}$，而三次NLSMs在大掺杂时表现为$\omega_p\sim n^{2/3}$，在小掺杂时转变为$\omega_p\sim n^{3/4}$。$n^{3/4}$定律在定量上不可靠：当$n\sim10^{18}$ cm$^{-3}$时，发散的态密度已使$r_s>1$，可观测的掺杂窗口最多为$10^{18}\lesssim n\lesssim10^{19}$ cm$^{-3}$；低于该范围时，超越RPA的关联效应至关重要。这些标度律源于幂律态密度和带内（德鲁德）响应，在相空间幂次计数上分别类似于双层和三层石墨烯。长波带内极化主导等离激元频率，而带间贡献为次阶（当$\Omega\ll\mu$时小两到三个数量级）。两种体系在细环极限下均具有等离激元各向异性$\Omega_p^z/\Omega_p^\perp\to\sqrt{2}$，这是环形费米面几何的普遍结果。该$\sqrt{2}$双重态虽可通过高分辨电子能量损失谱（HREELS）观测，但无法区分二次和三次色散；密度标度指数才是真正的区分特征。我们的结果为高阶色散NLSMs的集体动力学提供了框架，并提出了可通过HREELS实验验证的特征。
英文摘要
Nodal line semimetals (NLSMs) host distinctive topological properties and unconventional collective excitations. While plasmons in linear NLSMs are well studied, those of higher-order dispersive NLSMs remain poorly understood. We investigate plasmon modes in 3D quadratic and cubic NLSMs within the random phase approximation (RPA), valid for $r_s\ll1$ but breaking down in the small-doping cubic regime where the density of states diverges. Deriving the one-loop polarizability and evaluating its coefficients numerically from the full 3D Lindhard integral, we find distinct carrier-density scaling laws: quadratic NLSMs exhibit $ω_p\sim n^{1/2}$, while cubic NLSMs show $ω_p\sim n^{2/3}$ at large doping crossing over to $ω_p\sim n^{3/4}$ at small doping. The $n^{3/4}$ law is not quantitatively reliable: the diverging density of states drives $r_s>1$ already at $n\sim10^{18}$ cm$^{-3}$, limiting the observable window to at most $10^{18}\lesssim n\lesssim10^{19}$ cm$^{-3}$; below this, beyond-RPA correlations are essential. These scalings originate from the power-law density of states and intraband (Drude) response, and are analogous in phase-space power counting to bilayer and trilayer graphene, respectively. The long-wavelength intraband polarization dominates the plasmon frequency, while interband contributions are subleading (two to three orders of magnitude smaller for $Ω\llμ$). Both systems share a plasmon anisotropy $Ω_p^z/Ω_p^\perp\to\sqrt{2}$ in the thin-ring limit, a generic consequence of the torus Fermi-surface geometry. This $\sqrt{2}$ doublet, though observable by HREELS, cannot distinguish quadratic from cubic dispersion; the density scaling exponent is the true distinguishing signature. Our results provide a framework for the collective dynamics of higher-order dispersive NLSMs and suggest experimentally testable signatures accessible by HREELS.
