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Ruddlesden-Popper型双层镍酸盐材料La3Ni2O7在高压(>14 GPa)下表现出约80 K的超导转变温度($T_{\mathrm{c}}$), 引起了广泛关注. 该材料独特的双层结构赋予其不同于铜基超导体的电子结构特性, 其超导机理具有重要的研究价值. 实验发现该体系中存在电荷密度波与自旋密度波序, 可能与超导态存在竞争关系, 深入探究其形成机制对于理解该体系的超导本质具有重要意义. 本工作结合密度泛函理论与动力学平均场理论(DFT+DMFT), 在包含两个子格点Ni-eg轨道的低能有效模型基础上, 引入Hartree平均场处理近邻格点间库仑相互作用, 系统研究了非局域库仑相互作用对电荷有序行为与电子关联效应的影响. 计算结果表明, 当$V \leqslant $$ V_{{\mathrm{c}}1} \approx 0.46$eV时, 体系保持子格点对称性, 谱函数无显著变化; 当$V > V_{{\mathrm{c}}1}$时, 子格点对称性破缺, 体系进入电荷有序相, 且谱函数发生明显的重构. 进一步增大$V$至$V_{{\mathrm{c}}2} \approx 0.63$ eV后, 体系进入完全极化态, 其中一个子格点近乎空, 占据主要集中于另一子格点, 后者接近3/4填充. 本研究揭示了近邻库仑相互作用在驱动电荷不均匀分布及调控电子关联中的关键作用, 为全面理解La3Ni2O7中的低能有序态提供了新的视角.The bilayer nickelate La3Ni2O7, a member of the Ruddlesden–Popper series, has recently received significant attention due to its superconductivity under high pressure (above 14 GPa) with a transition temperature of approximately 80 K. Its unique bilayer structure results in an electronic configuration significantly different from those observed in cuprates and infinite-layer nickelates. Consequently, understanding its correlated electronic structure and superconducting mechanism has become a topic of major scientific importance. Recent experimental observations have further identified the coexistence of charge and spin density wave orders in La3Ni2O7, suggesting a complex interplay between various competing electronic phases and superconductivity.In this work, the charge order in La3Ni2O7 is investigated using a low-energy effective model that explicitly includes the Ni-eg orbitals. By employing a combined density functional theory and dynamical mean-field theory (DFT+DMFT) framework, the influences of the nearest-neighbor Coulomb interaction V on charge ordering and electronic correlation effects are investigated, with nonlocal interactions treated at the Hartree approximation level. Our computational method features a newly developed tensor-network impurity solver, in which a natural-orbital basis and complex-time evolution are utilized, facilitating efficient and accurate evaluation of the Green's function on the real-frequency axis. Our analysis indicates that for interaction strengths below a critical value ($ V \leqslant V_{{\mathrm{c}}1} \approx 0.46 $ eV), the system retains sublattice symmetry, resulting in minimal changes of the spectral function. Several high-energy fine structures identified within the Hubbard bands correspond to the residual atomic multiplet excitations, enabling the extraction of effective Hubbard parameters. When $ V>V_{{\mathrm{c}}1} $, the sublattice symmetry is disrupted and the system transitions to a charge-ordered state. Spectral features systematically evolve with the increase of charge order, providing a clear benchmark for quantitatively evaluating the degree of charge disproportionation based on experimental data. The quasiparticle weight Z exhibits a nonmonotonic behavior with the increase of V, reaching a minimum value of nearly $ V \approx 0.60 $ eV in the more populated sublattice as it approaches half-filling. When the interaction further increases beyond $ V_{{\mathrm{c}}2} \approx 0.63 $ eV, the system becomes fully charged polarized, characterized by one sublattice becoming almost empty and the other substance being nearly three-quarters filled.These findings underscore the critical role of nonlocal Coulomb interactions in driving charge disproportionation and regulating electron correlation, thereby providing new insights into the low-energy ordering phenomena of bilayer nickelates.
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图 1 (a) DFT能带结构与Wannier投影低能能带(黑色实线)对比; (b) 轨道分辨的态密度
Fig. 1. (a) Comparison between the DFT band structure and the low-energy Wannier-projected bands (black solid lines); (b) orbital-resolved density of states.
图 2 $ V=0 $时 (a) 谱函数, 插图展示了谱函数中多重激发态特征结构的细节; (b)自能实部; (c) 自能虚部; (b), (c)虚线展示了两个轨道$ {\rm{Re}}\varSigma(\omega) \sim {\rm{Re}}\varSigma(0) + (1 - 1/Z)\omega $的线性拟合
Fig. 2. For $ V=0 $: (a) Spectral function, inset shows the details of the multiplet excitations features; (b) real part of self energy; (c) imaginary part of self energy; dashed lines in (b), (c) show the linear fits of $ {\rm{Re}}\varSigma(\omega) \sim {\rm{Re}}\varSigma(0) + (1 - 1/Z)\omega $.
图 3 子格点密度极化$ n_{{\rm{diff}}} $随近邻相互作用强度V的变化
Fig. 3. Sublattice density polarization $ n_{{\rm{diff}}} $ as a function of nearest-neighbor interaction V.
图 4 $ V=0 $与$ V=0.46 $的谱函数对比
Fig. 4. Comparison of spectral functions for $ V=0 $ and $ V=0.46 $.
图 5 谱函数在参数区间$ 0.48 \leqslant V \leqslant 0.56 $内的演化
Fig. 5. Spectral functions in the parameter range $ 0.48 \leqslant V \leqslant 0.56 $.
图 6 代表性V值的谱函数(上)与自能(下), 其中A(B)为多数(少数)占据格点, 内嵌图展示了下Hubbard带多峰结构的细节
Fig. 6. Spectral functions (top) and self energies (bottom) for representative values of V, where A(B) denotes the majority (minority) occupied sublattice. Insets show the details of the lower Hubbard band features.
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[1] Sun H L, Huo M W, Hu X W, Li J Y, Liu Z J, Han Y F, Tang L Y, Mao Z Q, Yang P T, Wang B S, Cheng J G, Yao D X, Zhang G M, Wang M 2023 Nature 621 493
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Google Scholar
[4] Keimer B, Kivelson S A, Norman M R, Uchida S, Zaanen J 2015 Nature 518 179
Google Scholar
[5] Botana A S, Norman M R 2020 Phys. Rev. X 10 011024
[6] Luo Z H, Hu X W, Wang M, Wu W, Yao D X 2023 Phys. Rev. Lett. 131 126001
Google Scholar
[7] Zhang Y, Lin L F, Moreo A, Dagotto E 2023 Phys. Rev. B 108 L180510
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[8] Christiansson V, Petocchi F, Werner P 2023 Phys. Rev. Lett. 131 206501
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[9] Oh H, Zhang Y H 2023 Phys. Rev. B 108 174511
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[10] LaBollita H, Pardo V, Norman M R, Botana A S 2024 arXiv: 2309.17279 [cond-mat.str-el]
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[63] Georges A, Medici L d, Mravlje J 2013 Annu. Rev. Condens. Matter Phys. 4 137
Google Scholar
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