Microscopic response theory is used to study the linear electromagnetics of a Möbius jellium quantum wire. In the energy range of interest ($\hbar \omega \sim 1 {-} 200 \;{\rm meV}$), the wire can be considered as a Möbius band with complete transverse electron confinement (${\sim}$ one-level quantum well with width $w \sim k_F^{- 1} \ll \lambda = c/\omega$). The electronic energy eigenvalues and eigenstates are calculated numerically via a diagonalization of a scalar determinant in which the relevant matrix elements of the geometrical potential (given in terms of string curvature and torsion) occur. The exact lowest lying states for a 50 nm long heavily doped GaAs wire are compared to those obtained in lowest-order perturbation theory. The sequence (from the bottom) EOEEOEOO… of the even (E) and odd (O) parity states is not the even–odd sequence EOEOEOEO… of a harmonic potential. The interchanges originate in the peak structure of the geometrical potential. Significant energy splitting of the lowest lying eigenvalues of the Möbius wire is observed when compared to the degenerate energy eigenvalues of a corresponding circular wire. The frequency dependence of the conductivity tensor components are calculated, and the peak structure is identified from the $E \to E$, and $O \to O$ and $E \leftrightarrow O$ transitions. It is shown that elastic light scattering might be a versatile probe for determining the Möbius wire’s electronic-state structure.

中文翻译：

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介观莫比乌斯量子线的电动力学

微观响应理论用于研究莫比乌斯量子线的线性电磁学。在感兴趣的能量范围内（$ \ hbar \ omega \ sim 1 {-} 200 \; {\ rm meV} $），可以将导线视为具有完全横向电子约束的Möbius带（$ {\ sim} $宽度为$ w \ sim k_F ^ {-1}的一级量子阱\ ll \ lambda = c / \ omega $）。电子能量本征值和本征态通过标量行列式的对角线化计算得出，其中发生了几何势的相关矩阵元素（根据弦曲率和扭转）。将50 nm长的重掺杂GaAs导线的精确最低横卧状态与最低阶扰动理论中获得的横卧状态进行比较。偶数（E）和奇数（O）奇偶状态的序列EOEEOEOO…不是谐波电位的偶数序列EOEOEOEO…。互换源于几何势的峰结构。与相应圆线的简并能量本征值相比，观察到莫比乌斯线的最低本征值有明显的能量分裂。$ E \ to E $，以及$ O \ to O $和$ E \ leftrightarrow O $转换。结果表明，弹性光散射可能是确定莫比乌斯线的电子态结构的通用探针。