Charge order driven by nonlocal coulomb interactions in La3Ni2O7

DU Zhengzhong; LI Jie; LU Yi

doi:10.7498/aps.74.20250604

Abstract

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-e_g 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.

Keywords:

Authors and contacts

1.
National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
2.
Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China

Corresponding author: LU Yi, yilu@nju.edu.cn

Funds: Project supported by the National Key R&D Program of China (Grant No. 2022YFA1403000) and the National Natural Science Foundation of China (Grant No. 12274207).

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References

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Cited By

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

Figure 1. (a) Comparison between the DFT band structure and the low-energy Wannier-projected bands (black solid lines); (b) orbital-resolved density of states.

DownLoad: Full-Size Img PowerPoint

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

Figure 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 $.

DownLoad: Full-Size Img PowerPoint

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

Figure 3. Sublattice density polarization $ n_{{\rm{diff}}} $ as a function of nearest-neighbor interaction V.

DownLoad: Full-Size Img PowerPoint

图 4 $ V=0 $与$ V=0.46 $的谱函数对比

Figure 4. Comparison of spectral functions for $ V=0 $ and $ V=0.46 $.

DownLoad: Full-Size Img PowerPoint

图 5 谱函数在参数区间$ 0.48 \leqslant V \leqslant 0.56 $内的演化

Figure 5. Spectral functions in the parameter range $ 0.48 \leqslant V \leqslant 0.56 $.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

图 7 重整化因子Z随V增大的演化

Figure 7. Evolution of renormalization factor with increasing V

DownLoad: Full-Size Img PowerPoint

[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 Google Scholar
[2]	Wang M, Wen H H, Wu T, Yao D X, Xiang T 2024 Chin. Phys. Lett. 41 077402 Google Scholar
[3]	Lee P A, Nagaosa N, Wen X G 2006 Rev. Mod. Phys. 78 17 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 Google Scholar
[8]	Christiansson V, Petocchi F, Werner P 2023 Phys. Rev. Lett. 131 206501 Google Scholar
[9]	Oh H, Zhang Y H 2023 Phys. Rev. B 108 174511 Google Scholar
[10]	LaBollita H, Pardo V, Norman M R, Botana A S 2024 arXiv: 2309.17279 [cond-mat.str-el]
[11]	Lechermann F, Gondolf J, Bötzel S, Eremin I M 2023 Phys. Rev. B 108 L201121 Google Scholar
[12]	Qu X Z, Qu D W, Chen J L, Wu C J, Yang F, Li W, Su G 2024 Phys. Rev. Lett. 132 036502 Google Scholar
[13]	Shilenko D A, Leonov I V 2023 Phys. Rev. B 108 125105 Google Scholar
[14]	Wu W, Luo Z H, Yao D X, Wang M 2024 Sci. China Phys. Mech. Astron 67 117402 Google Scholar
[15]	Yang Y F, Zhang G M, Zhang F C 2023 Phys. Rev. B 108 L201108 Google Scholar
[16]	Cao Y Y, Yang Y F 2024 Phys. Rev. B 109 L081105 Google Scholar
[17]	Gu Y H, Le C C, Yang Z S, Wu X X, Hu J P 2023 arXiv: 2306.07275 [cond-mat.supr-con]
[18]	Liu Y B, Mei J W, Ye F, Chen W Q, Yang F 2023 Phys. Rev. Lett. 131 236002 Google Scholar
[19]	Shen Y, Qin M P, Zhang G M 2023 Chin. Phys. Lett. 40 127401 Google Scholar
[20]	Yang Q G, Wang D, Wang Q H 2023 Phys. Rev. B 108 L140505 Google Scholar
[21]	Zhang Y, Lin L F, Moreo A, Maier T A, Dagotto E 2024 Nat. Commun. 15 2470 Google Scholar
[22]	Lu C, Pan Z M, Yang F, Wu C J 2024 Phys. Rev. Lett. 132 146002 Google Scholar
[23]	Fan Z, Zhang J F, Zhan B, Lv D S, Jiang X Y, Normand B, Xiang T 2024 Phys. Rev. B 110 024514 Google Scholar
[24]	Jiang K, Wang Z Q, Zhang F C 2024 Chin. Phys. Lett. 41 017402 Google Scholar
[25]	Xia C L, Liu H Q, Zhou S J, Chen H H 2025 Nat. Commun. 16 1054 Google Scholar
[26]	Wang Y X, Zhang Y, Jiang K 2025 Chin. Phys. B 34 047105 Google Scholar
[27]	Yang Y F 2025 Chin. Phys. Lett. 42 017301 Google Scholar
[28]	Xue J R, Wang F 2024 Chin. Phys. Lett. 41 057403 Google Scholar
[29]	Ghiringhelli G, Le Tacon M, Minola M, BlancoCanosa S, Mazzoli C, Brookes N, De Luca G, Frano A, Hawthorn D, He F Z, Loew T, Moretti Sala M, Peets D, Salluzzo M, Schierle E, Sutarto R, Sawatzky G, Weschke E, Keimer B, Braicovich L 2012 Science 337 821 Google Scholar
[30]	Krieger G, Martinelli L, Zeng S, Chow L E, Kummer K, Arpaia R, Moretti Sala M, Brookes N B, Ariando A, Viart N, Salluzzo M, Ghiringhelli G, Preziosi D 2022 Phys. Rev. Lett. 129 027002 Google Scholar
[31]	Tam C C, Choi J, Ding X, Agrestini S, Nag A, Wu M, Huang B, Luo H Q, Gao P, GarcíaFernández M, Qiao L, Zhou K J 2022 Nat. Mater. 21 1116 Google Scholar
[32]	Rossi M, Osada M, Choi J, Agrestini S, Jost D, Lee Y, Lu H, Wang B Y, Lee K, Nag A, Chuang Y D, Kuo C T, Lee S J, Moritz B, Devereaux T P, Shen Z X, Lee J S, Zhou K J, Hwang H Y, Lee W S 2022 Nat. Phys. 18 869 Google Scholar
[33]	Taniguchi S, Nishikawa T, Yasui Y, Kobayashi Y, Takeda J, Shamoto S i, Sato M 1995 J. Phys. Soc. Jpn. 64 1644 Google Scholar
[34]	Seo D K, Liang W, Whangbo M H, Zhang Z, Greenblatt M 1996 Inorg. Chem. 35 6396 Google Scholar
[35]	Wu G, Neumeier J J, Hundley M F 2001 Phys. Rev. B 63 245120 Google Scholar
[36]	Liu Z J, Sun H L, Huo M W, Ma X Y, Ji Y, Yi E K, Li L S, Liu H, Yu J, Zhang Z Y, Chen Z Q, Liang F X, Dong H L, Guo H J, Zhong D Y, Shen B, Li S L, Wang M 2023 Sci. China Phys. Mech. Astron. 66 217411 Google Scholar
[37]	Liu Z, Huo M W, Li J, Li Q, Liu Y C, Dai Y M, Zhou X X, Hao J H, Lu Y, Wang M, Wen H H 2024 Nat. Commun. 15 7570 Google Scholar
[38]	沈瑶 2024 物理学报 73 197104 Google Scholar Shen Y 2024 Acta Phys.Sin. 73 197104 Google Scholar
[39]	Zhao D, Zhou Y B, Huo M W, Wang Y, Nie L P, Yang Y, Ying J J, Wang M, Wu T, Chen X H 2025 Sci. Bull. 70 1239 Google Scholar
[40]	Kakoi M, Oi T, Ohshita Y, Yashima M, Kuroki K, Kato T, Takahashi H, Ishiwata S, Adachi Y, Hatada N, Uda T, Mukuda H 2024 J. Phys. Soc. Jpn. 93 053702 Google Scholar
[41]	Chen K W, Liu X Q, Jiao J C, Zou M Y, Jiang C Y, Li X, Luo Y X, Wu Q, Zhang N Y, Guo Y F, Shu L 2024 Phys. Rev. Lett. 132 256503 Google Scholar
[42]	Chen X Y, Choi J, Jiang Z C, Mei J, Jiang K, Li J, Agrestini S, García-Fernández M, Sun H L, Huang X, Shen D W, Wang M, Hu J P, Lu Y, Zhou K J, Feng D L 2024 Nat. Commun. 15 9597 Google Scholar
[43]	Wang G, Wang N N, Shen X L, Hou J, Ma L, Shi L F, Ren Z A, Gu Y D, Ma H M, Yang P T, Liu Z Y, Guo H Z, Sun J P, Zhang G M, Calder S, Yan J Q, Wang B S, Uwatoko Y, Cheng J G 2024 Phys. Rev. X 14 011040 Google Scholar
[44]	Zhang Y N, Su D J, Huang Y N, Shan Z Y, Sun H L, Huo M W, Ye K X, Zhang J W, Yang Z H, Xu Y K, Su Y, Li R, Smidman M, Wang M, Jiao L, Yuan H Q 2024 Nat. Phys. 20 1269 Google Scholar
[45]	Wang Y X, Jiang K, Wang Z Q, Zhang F C, Hu J P 2024 Phys. Rev. B 110 205122 Google Scholar
[46]	Yi X W, Meng Y, Li J W, Liao Z W, Li W, You J Y, Gu B, Su G 2024 Phys. Rev. B 110 L140508 Google Scholar
[47]	Chen X J, Jiang P H, Li J, Zhong Z C, Lu Y 2025 Phys. Rev. B 111 014515 Google Scholar
[48]	Schollwöck U 2005 Rev. Mod. Phys. 77 259 Google Scholar
[49]	Haegeman J, Cirac J I, Osborne T J, Pižorn I, Verschelde H, Verstraete F 2011 Phys. Rev. Lett. 107 070601 Google Scholar
[50]	Haegeman J, Mariën M, Osborne T J, Verstraete F 2014 J. Math. Phys. 55 021902 Google Scholar
[51]	Lu Y, Höppner M, Gunnarsson O, Haverkort M W 2014 Phys. Rev. B 90 085102 Google Scholar
[52]	Lu Y, Cao X D, Hansmann P, Haverkort M W 2019 Phys. Rev. B 100 115134 Google Scholar
[53]	Cao X D, Lu Y, Hansmann P, Haverkort M W 2021 Phys. Rev. B 104 115119 Google Scholar
[54]	Cao X D, Lu Y, Stoudenmire E M, Parcollet O 2024 Phys. Rev. B 109 235110 Google Scholar
[55]	Kresse G, Furthmüller J 1996 Comput. Mater. Sci. 6 15 Google Scholar
[56]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 Google Scholar
[57]	Mostofi A A, Yates J R, Lee Y S, Souza I, Vanderbilt D, Marzari N 2008 Comput. Phys. Commun. 178 685 Google Scholar
[58]	Marzari N, Vanderbilt D 1997 Phys. Rev. B 56 12847 Google Scholar
[59]	Souza I, Marzari N, Vanderbilt D 2001 Phys. Rev. B 65 035109 Google Scholar
[60]	Aryasetiawan F, Imada M, Georges A, Kotliar G, Biermann S, Lichtenstein A I 2004 Phys. Rev. B 70 195104 Google Scholar
[61]	Mravlje J, Aichhorn M, Miyake T, Haule K, Kotliar G, Georges A 2011 Phys. Rev. Lett. 106 096401 Google Scholar
[62]	Kugler F B, Zingl M, Strand H U R, Lee S S B, von Delft J, Georges A 2020 Phys. Rev. Lett. 124 016401 Google Scholar
[63]	Georges A, Medici L d, Mravlje J 2013 Annu. Rev. Condens. Matter Phys. 4 137 Google Scholar

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Vol. 74, Issue 17 - 2025-09-05

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Charge order driven by nonlocal coulomb interactions in La₃Ni₂O₇