发表机构
IBM Research（IBM研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究构建横向电场下一维晶格的倒空间哈密顿量，通过悬线修正项得到马蒂厄方程，推导场依赖的能带与布拉格能隙，揭示横向电场重构低维周期系统布洛赫谱的机制。
AI 中文摘要
我们研究了一个有效一维周期性原子链，该链受到垂直于链轴的弱静电场作用。本征晶格在倒空间中由谐波加权的周期性赝势表示，而横向场产生弱的弹性和极化响应，其最低能量分布近似为周期性重复的悬链线轮廓。布洛赫约化将这两种贡献置于同一个倒空间哈密顿量中。本征晶格产生|r-s|⁻¹层级，而悬线贡献是对称托普利茨修正，其系数与(1+π²(r-2)⁻¹)成正比，因此渐近行为为|r-s|⁻²。悬线贡献的全部非零倒空间权重绝对收敛，总和为|V_c|/e。在单胞层面，最低阶本征谐波与悬线项共同构成包含余弦和双曲余弦调制的马蒂厄方程。随后的第一布里渊区约化得到与场相关的能带能量及对应的布拉格能隙层级。该模型揭示了一种简单机制，通过该机制横向电场可重构低维周期性系统的布洛赫谱。
英文摘要
We consider an infinite one dimensional array of alternating charges embedded in a two-dimensional configuration space and subjected to a weak static electric field transverse to the lattice axis. Expansion of the Coulomb interaction about a lattice site gives a transverse restoring stiffness $κ\propto ζ(3)/L^3$, defining the oscillator length $a_y$, while Bloch periodicity is retained along the lattice direction and the transverse motion is represented in a harmonic basis. The Coulomb matrix elements are governed by the dimensionless scale $η_{r-s}$, which couples the reciprocal-lattice transfer to the transverse oscillator length. A regularized one dimensional extension is also introduced through Coulomb regularization, yielding a finite diagonal offset and an exponentially decaying even-transfer coupling in reciprocal space. Small $η_{r-s}$ yields logarithmic, parity-dependent transverse-state coupling, while large $η_{r-s}$ approaches the one-dimensional Coulomb limit. In the finite-order spectrum, the latter approaches the Kronig Penney reference toward the band edge while retaining distinct Brillouin zone curvature. The formulation therefore identifies two characteristic quantities of the alternating lattice: the transverse restoring stiffness and the one-dimensional Madelung form, while retaining the two dimensional structure required to describe the response to a transverse electric field. Keywords: alternating charge lattice; Bloch states; Coulomb interaction; transverse electric field; regularization; reciprocal space coupling; Brillouin zone spectrum.
CommentsA revised replacing the previously withdrawn manuscript. Title refined, the current version is substantially expanded with Brillouin-zone analysis and regularization of the one-dimension problem. 16 pages, 2 figures and Glossary included
