搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

莫特物理——量子材料的主旋律之一

封东来

引用本文:
Citation:

莫特物理——量子材料的主旋律之一

封东来

Mott physics: One of main themes in quantum materials

Feng Dong-Lai
PDF
HTML
导出引用
  • 关联量子材料中电子的巡游性与局域化两种行为的竞争与合作, 即莫特物理, 是许多量子材料体系多样物态背后的主要物理机制. 本文回顾了莫特物理在多种量子材料体系中的体现, 论述了其作为量子材料的主旋律之一的各种表现. 因此寻找和理解其千变万化的演生方式, 是实验凝聚态物理研究的中心任务之一.
    The competition and cooperation between the itinerancy behavior and localization behavior of electrons in correlated quantum materials, known as Mott physics, is the physical mechanism behind the diverse states of many quantum materials. This article reviews the manifestation of Mott physics in various quantum materials and establishes it as one of the main themes of quantum materials. Finding and understanding its ever-changing ways of manifestation is one of the central tasks of experimental research on condensed matter physics.Specifically, the filling-control route of Mott transition is illustrated by exampling the surface K-dosed Sr2IrO4, which exhibits d-wave gap, pseudogap behavior in underdoped regime, and phase separation with inhomogeneous electronic state distribution. All of these show strong resemblances to the doped cuprate superconductors, another prototypical filling-control type of Mott transition case. On the other hand, the bandwidth-control route of Mott transition could be found in NiS2–xSex, where its bandwidth continuously decreases with decreasing Se concentration, until it becomes an insulator. In addition, the essence of various ways of doping in iron-based superconductors is to change their bandwidths. The superconductivity shows up at intermediate bandwidth with moderate correlations, and it diminishes when the bandwidth is large and the electron correlations are weak. For heavily electron-doped iron-selenides, there is even a Mott insulator phase with strong correlations.For carbon based materials, the phase transition between the antiferromagnetic insulator and superconducting state of A15 Cs3C60 as the volume of fullerene anions decreases could be understood in terms of a bandwidth-control Mott transition; the insulator-superconductor transition discovered in electrically gated “magic angle” twisted-angle bilayer graphene could be understood as a filling-control Mott transition.For f electron systems, the interplay between itinerancy and localization dominates the heavy fermion behavior and their ground states. The behaviors of the f electrons are demonstrated by using the angle-resolved photoemission data of CeCoIn5, whose f electron band becomes more coherent with decreasing temperature, and the c-f hybridization is thus enhanced and the band mass of conduction band continuously increases. The c-f hybridization behaviors of CeCoIn5, CeIrIn5, and CeRhIn5 are compared with each other, and the differences in hybridization strength put their ground states into different regimes of the Doniach phase diagram. Similarly, the Skutterudites 4f2 Kondo lattice system PrOs4Sb12 and its sibling 4f1 system CeOs4Sb12 also have different ground states due to a slight difference in their c-f hybridization strengths.
      通信作者: 封东来, dlfeng@ustc.edu.cn
    • 基金项目: 国家自然科学基金 (批准号: 11888101)和腾讯新基石基金资助的课题.
      Corresponding author: Feng Dong-Lai, dlfeng@ustc.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11888101) and the New Cornerstone Science Foundation, China.
    [1]

    Kotliar G, Savrasov S Y, Haule K, Oudovenko V S, Parcollet O, Marianetti C A 2006 Rev. Mod. Phys. 78 865Google Scholar

    [2]

    Kim B J, Jin H, Moon S J, Kim J Y, Park B G, Leem C S, Yu J, Noh T W, Kim C, Oh S J, Park J H, Durairaj V, Cao G, Rotenberg E 2008 Phys. Rev. Lett. 101 076402Google Scholar

    [3]

    Wang F, Senthil T 2011 Phys. Rev. Lett. 106 136402Google Scholar

    [4]

    Yan Y J, Ren M Q, Xu H C, Xie B P, Tao R, Choi H Y, Lee N, Choi Y J, Zhang T 2015 Phys. Rev. X 5 041018

    [5]

    Kim Y K, Krupin O, Denlinger J D, Bostwick A , Rotenberg E, Zhao Q, Mitchell J F, Allen J W, Kim B J 2014 Science 345 187Google Scholar

    [6]

    Yao X, Honig J M, Hogan T, Kannewurf C, Spalek J 1996 Phys. Rev. B 54 17469Google Scholar

    [7]

    Xu H C, Zhang Y, Xu M, Peng R, Shen X P, Strocov V N, Shi M, Kobayashi M, Schmitt T, Xie B P, Feng D L 2014 Phys. Rev. Lett. 112 087603Google Scholar

    [8]

    Zhang X Y, Rozenberg M J, Kotliar G 1993 Phys. Rev. Lett. 70 1666Google Scholar

    [9]

    Brinkman W F, Rice T M 1970 Phys. Rev. B 2 4302Google Scholar

    [10]

    Mazin I I, Schmalian J 2009 Physica C 469 614Google Scholar

    [11]

    Kuroki K, Onari S, Arita R, Usui H, Tanaka Y, Kontani H, Aoki H 2008 Phys. Rev. Lett. 101 087004Google Scholar

    [12]

    Scalapino D J 2012 Rev. Mod. Phys. 84 1383Google Scholar

    [13]

    Seo K J, Bernevig A, Hu J P 2008 Phys. Rev. Lett. 101 206404Google Scholar

    [14]

    Shibauchi T, Carrington A, Matsuda Y, Langer J S 2014 Annu. Rev. Condens. Matter Phys. 5 113Google Scholar

    [15]

    Ye Z R, Zhang Y, Chen F, Xu M, Jiang J, Niu X H, Wen C H P, Xing L Y, Wang X C, Jin C Q, Xie B P, Feng D L 2014 Phys. Rev. X 4 031041Google Scholar

    [16]

    Niu X H, Chen S D, Jiang J, Ye Z R, Yu T L, Xu D F, Xu M, Feng Y, Yan Y J, Xie B P, Zhao J, Gu D C, Sun L L, Mao Q, Wang H, Fang M, Zhang C J, Hu J P, Sun Z, Feng D L 2016 Phys. Rev. B 93 054516Google Scholar

    [17]

    Takabayashi Y, Ganin A Y, Jeglic P, Arcon D, Takano T, Iwasa Y, Ohishi Y, Takata M, Takeshita N, Prassides K, Rosseinsky M J 2009 Science 323 1585Google Scholar

    [18]

    Cao Y, Fatemi V, Demir A, Fang S, Tomarken S L, Luo J Y, Sanchez-Yamagishi J D, Watanabe K, Taniguchi T, Kaxiras E, Ashoori R C, Jarillo-Herrero P 2018 Nature 556 80Google Scholar

    [19]

    Cao Y, Fatemi V, Fang S, Watanabe K, Taniguchi T, Kaxiras E, Jarillo-Herrero P 2018 Nature 556 43Google Scholar

    [20]

    Shim J H, Haule K, Kotliar G 2007 Science 318 1615Google Scholar

    [21]

    Chen Q Y, Xu D F, Niu X H, Jiang J, Peng R, Xu H C, Wen C H P, Ding Z F, Huang K, Shu L, Zhang Y J, Lee H, Strocov V N, Shi M, Bisti F, Schmitt T, Huang Y B, Dudin P, Lai X C, Kirchner S, Yuan H Q, Feng D L 2017 Phys. Rev. B 96 045107Google Scholar

    [22]

    Doniach S 1977 Physica B+C 91 231Google Scholar

    [23]

    Chen Q Y, Xu D F, Niu X H, Peng R, Xu H C, Wen C H P, Liu X, Shu L, Tan S Y, Lai X C, Zhang Y J, Lee H , Strocov V N, Bisti F, Dudin P, Zhu J X, Yuan H Q, Kirchner S, Feng D L 2018 Phys. Rev. Lett. 120 066403Google Scholar

    [24]

    Lou X, Yu T L, Song Y H, Wen C H P, Wei W Z, Leithe-Jasper A, Ding Z F, Shu L, Kirchner S, Xu H C, Peng R, Feng D L 2021 Phys. Rev. Lett. 126 136402Google Scholar

  • 图 1  (a) 薛定谔的猫和方程; (b) 一维势阱模型

    Fig. 1.  (a) Schrödinger’s cat and equation; (b) the model of one-dimensional potential well.

    图 2  (a) 一维氢原子链模型; (b) 哈伯德能带示意图, 下哈伯德带(lower Hubbard band, LHB)是填满的, 上哈伯德带(upper Hubbard band, UHB)是空带; (c)二维哈伯德模型

    Fig. 2.  (a) One dimensional hydrogen atom chain model; (b) the schematic illustration of Hubbard bands, where the lower Hubbard band (LHB) is filled, and the upper Hubbard band (UHB) is empty; (c) two-dimensional Hubbard model.

    图 3  (a) 莫特相变的两种途径. 考虑杂质局域势场影响以及有限体系尺寸, 相图中的绝缘态随着掺杂的相转变边界是位于有限的掺杂浓度下的. (b) 动力学平均场计算模拟出的Hubbard模型, 在T = 0时, 不同强度U下的局域谱函数展示了带宽调控莫特相变的过程 (D = W/2, W是能带宽度)[1]

    Fig. 3.  (a) Two routes of Mott phase transition. Considering the influence of impurity local potential and the finite system size, the phase boundary is located at a finite doping concentration. (b) The spectral functions of the Hubbard model calculated by dynamic mean field theory at different U (T = 0), demonstrating the process of bandwidth-control Mott phase transition (D =W/2, W being the bandwidth) [1].

    图 4  (a) 考虑自旋轨道耦合和Hubbard U情况下, 5d5态的能级示意图, 展示了总角动量Jeff = 1/2的莫特绝缘体基态; (b) 0.5 ML (monolayer) 钾原子覆盖下的Sr2IrO4的费米面结构 (T = 70 K) [5]; (c) 不同掺杂量的钾原子覆盖下的Sr2IrO4的能隙随动量(费米面角)的依赖关系[5]; (d) 0.6 ML钾原子覆盖下的Sr2IrO4表面的电子态在E = 20 meV下的分布图(T = 20 K), 展示了不均匀的能隙分布情况[4]; (e) 图(d)中不同区域的典型隧道谱[4]

    Fig. 4.  (a) Schematic diagram of the 5d5 states, considering spin orbit coupling and Hubbard U, where the ground state is a Mott insulator with a total angular momentum of Jeff = 1/2; (b) the Fermi surface of Sr2IrO4 covered by 0.5 ML (monolayer) potassium atoms (T = 70 K)[5]; (c) the energy gap as a function momentum (Fermi surface angle) for K-dosed Sr2IrO4 with different potassium coverages[5]; (d) the local electronic density-of-states map at E = 20 meV for the Sr2IrO4 surface covered by 0.6 ML potassium atoms shows an uneven distribution of energy gaps (T=20 K)[4]; (e) typical tunnelling spectra in different regions in Figure (d)[4].

    图 5  (a) ARPES测得NiS2–xSex的费米面随着Se掺杂的演化[7]; (b) ARPES能谱展示能带色散随着Se掺杂的演化[7]; (c) 图(b)中的α能带宽度随掺杂演化的对比[7]; (d) NiS2–xSex两个能带的费米速度在掺杂相图中的演化, 在接近莫特绝缘相过程中呈现带宽变窄、有效质量发散的行为[7]

    Fig. 5.  (a) ARPES data of the Fermi surface of NiS2–xSex as Se doping is varied[7]; (b) ARPES spectra show that the band dispersion changes with Se doping[7]; (c) summary of the band width evolution with doping in figure (b)[7]; (d) the evolution of the Fermi velocities of two bands of NiS2–xSex in the phase diagram as a function of doping, showing a narrowing bandwidth and effective mass divergence near the Mott insulating phase [7].

    图 6  (a) 基于FeAs面的铁基超导的相图示意图[14]; (b) 重电子掺杂的多种铁硒类超导体系符合统一的相图[16]

    Fig. 6.  (a) Schematic phase diagram of FeAs-based superconductor[14]; (b) many heavily electron-doped iron-selenide superconductors conform to a unified phase diagram [16].

    图 7  (a) A15 Cs3C60 (晶体群Pm3n)的晶体结构, 其中取向有序的${\mathrm{C}}_{60}^{3-} $阴离子按照体心立方的结构堆叠, 红色为Cs+阳离子[17]; (b) A15 Cs3C60加压后的相图, 显示了反铁磁与超导相变温度随着富勒烯阴离子体积的演化[17]

    Fig. 7.  (a) The crystal structure of A15 Cs3C60 (crystal group Pm3n), where ${\mathrm{C}}_{60}^{3-} $ anions with an ordered orientation are stacked in a body centered cubic structure, and Cs+ cations are shown in red[17]; (b) the phase diagram of A15 Cs3C60 under pressure shows the evolution of antiferromagnetic and superconducting phase transition temperature with the volume of fullerene anions [17].

    图 8  (a) 转角双层石墨烯中的莫尔超晶格[18]; (b) 在转角为“魔角”(θ = 1.08°)时双层石墨烯的能带结构, 在费米能附近看到平带(蓝色曲线)[18]; (c) “魔角” 双层石墨烯中调控电荷浓度得到的相图, 在半填充的莫特绝缘相附近存在两个超导的拱形区域[19]

    Fig. 8.  (a) Moiré superlattice in twisted-angle bilayer graphene[18]; (b) the calculated band structure of the twisted bilayer graphene at the magic twisted angle (θ = 1.08°), exhibiting a flat band (blue curve) near the Fermi energy[18]; (c) the phase diagram of “magic angle” twisted bilayer graphene as a function of charge concentration, there are two superconducting domes near the half-filled Mott insulator phase[19].

    图 9  (a) CeCoIn5高低温的能带结构对比图, 上图测量温度为170 K, 下图测量温度为17 K[21]; (b) CeCoIn5高低温的费米面对比图, 上图测量温度为170 K, 下图测量温度为17 K[21]; (c) CeCoIn5Γ点附近4f电子谱重随温度的演化[21]; (d) CeCoIn5αγ能带的有效质量与温度的依赖关系[21]

    Fig. 9.  (a) The band structures of CeCoIn5 at 170 and 17 K, respectively[21]; (b) the Fermi surface maps of CeCoIn5 at 170 and 17 K, respectively[21]; (c) the evolution of 4f electron spectral weight near the Γ point as a function of temperature in CeCoIn5[21]; (d) the effective masses of the α and γ bands of CeCoIn5 as a function of temperature [21].

    图 10  (a) Doniach相图, 图中箭头标出了CeCoIn5, CeIrIn5和CeRhIn5在该相图中的大致位置[23]; (b) CeCoIn5, CeIrIn5和CeRhIn5中费米能附近能带杂化行为的对比[23]

    Fig. 10.  (a) Doniach phase diagram, with arrows indicating the schematic positions of CeCoIn5, CeIrIn5, and CeRhIn5 in the diagram[23]; (b) comparison of the hybridization behavior of the bands near the Fermi energy in CeCoIn5, CeIrIn5, and CeRhIn5 [23].

  • [1]

    Kotliar G, Savrasov S Y, Haule K, Oudovenko V S, Parcollet O, Marianetti C A 2006 Rev. Mod. Phys. 78 865Google Scholar

    [2]

    Kim B J, Jin H, Moon S J, Kim J Y, Park B G, Leem C S, Yu J, Noh T W, Kim C, Oh S J, Park J H, Durairaj V, Cao G, Rotenberg E 2008 Phys. Rev. Lett. 101 076402Google Scholar

    [3]

    Wang F, Senthil T 2011 Phys. Rev. Lett. 106 136402Google Scholar

    [4]

    Yan Y J, Ren M Q, Xu H C, Xie B P, Tao R, Choi H Y, Lee N, Choi Y J, Zhang T 2015 Phys. Rev. X 5 041018

    [5]

    Kim Y K, Krupin O, Denlinger J D, Bostwick A , Rotenberg E, Zhao Q, Mitchell J F, Allen J W, Kim B J 2014 Science 345 187Google Scholar

    [6]

    Yao X, Honig J M, Hogan T, Kannewurf C, Spalek J 1996 Phys. Rev. B 54 17469Google Scholar

    [7]

    Xu H C, Zhang Y, Xu M, Peng R, Shen X P, Strocov V N, Shi M, Kobayashi M, Schmitt T, Xie B P, Feng D L 2014 Phys. Rev. Lett. 112 087603Google Scholar

    [8]

    Zhang X Y, Rozenberg M J, Kotliar G 1993 Phys. Rev. Lett. 70 1666Google Scholar

    [9]

    Brinkman W F, Rice T M 1970 Phys. Rev. B 2 4302Google Scholar

    [10]

    Mazin I I, Schmalian J 2009 Physica C 469 614Google Scholar

    [11]

    Kuroki K, Onari S, Arita R, Usui H, Tanaka Y, Kontani H, Aoki H 2008 Phys. Rev. Lett. 101 087004Google Scholar

    [12]

    Scalapino D J 2012 Rev. Mod. Phys. 84 1383Google Scholar

    [13]

    Seo K J, Bernevig A, Hu J P 2008 Phys. Rev. Lett. 101 206404Google Scholar

    [14]

    Shibauchi T, Carrington A, Matsuda Y, Langer J S 2014 Annu. Rev. Condens. Matter Phys. 5 113Google Scholar

    [15]

    Ye Z R, Zhang Y, Chen F, Xu M, Jiang J, Niu X H, Wen C H P, Xing L Y, Wang X C, Jin C Q, Xie B P, Feng D L 2014 Phys. Rev. X 4 031041Google Scholar

    [16]

    Niu X H, Chen S D, Jiang J, Ye Z R, Yu T L, Xu D F, Xu M, Feng Y, Yan Y J, Xie B P, Zhao J, Gu D C, Sun L L, Mao Q, Wang H, Fang M, Zhang C J, Hu J P, Sun Z, Feng D L 2016 Phys. Rev. B 93 054516Google Scholar

    [17]

    Takabayashi Y, Ganin A Y, Jeglic P, Arcon D, Takano T, Iwasa Y, Ohishi Y, Takata M, Takeshita N, Prassides K, Rosseinsky M J 2009 Science 323 1585Google Scholar

    [18]

    Cao Y, Fatemi V, Demir A, Fang S, Tomarken S L, Luo J Y, Sanchez-Yamagishi J D, Watanabe K, Taniguchi T, Kaxiras E, Ashoori R C, Jarillo-Herrero P 2018 Nature 556 80Google Scholar

    [19]

    Cao Y, Fatemi V, Fang S, Watanabe K, Taniguchi T, Kaxiras E, Jarillo-Herrero P 2018 Nature 556 43Google Scholar

    [20]

    Shim J H, Haule K, Kotliar G 2007 Science 318 1615Google Scholar

    [21]

    Chen Q Y, Xu D F, Niu X H, Jiang J, Peng R, Xu H C, Wen C H P, Ding Z F, Huang K, Shu L, Zhang Y J, Lee H, Strocov V N, Shi M, Bisti F, Schmitt T, Huang Y B, Dudin P, Lai X C, Kirchner S, Yuan H Q, Feng D L 2017 Phys. Rev. B 96 045107Google Scholar

    [22]

    Doniach S 1977 Physica B+C 91 231Google Scholar

    [23]

    Chen Q Y, Xu D F, Niu X H, Peng R, Xu H C, Wen C H P, Liu X, Shu L, Tan S Y, Lai X C, Zhang Y J, Lee H , Strocov V N, Bisti F, Dudin P, Zhu J X, Yuan H Q, Kirchner S, Feng D L 2018 Phys. Rev. Lett. 120 066403Google Scholar

    [24]

    Lou X, Yu T L, Song Y H, Wen C H P, Wei W Z, Leithe-Jasper A, Ding Z F, Shu L, Kirchner S, Xu H C, Peng R, Feng D L 2021 Phys. Rev. Lett. 126 136402Google Scholar

  • [1] 罗旭, 王丽红, 吕良, 曹书峰, 董学成, 赵建国. 基于面磁荷密度的金属磁记忆检测正演模型. 物理学报, 2022, 71(15): 154101. doi: 10.7498/aps.71.20220176
    [2] 卿煜林, 彭小莉, 文林, 胡爱元. 自旋为1/2的双层平方晶格阻挫模型的基态相变. 物理学报, 2022, 71(3): 037501. doi: 10.7498/aps.71.20211584
    [3] 卿煜林, 彭小莉, 胡爱元. 自旋为1的双层平方晶格阻挫模型的相变. 物理学报, 2022, 71(4): 047501. doi: 10.7498/aps.71.20211685
    [4] 卿煜林, 彭小莉, 文林, 胡爱元. 自旋为1/2的双层平方晶格阻挫模型的基态相变研究. 物理学报, 2021, (): . doi: 10.7498/aps.70.20211584
    [5] 尤冰凌, 刘雪莹, 成书杰, 王晨, 高先龙. Jaynes-Cummings晶格模型和Rabi晶格模型的量子相变. 物理学报, 2021, 70(10): 100201. doi: 10.7498/aps.70.20202066
    [6] 周晓凡, 樊景涛, 陈刚, 贾锁堂. 光学腔中一维玻色-哈伯德模型的奇异超固相. 物理学报, 2021, 70(19): 193701. doi: 10.7498/aps.70.20210778
    [7] 保安. 各向异性ruby晶格中费米子体系的Mott相变. 物理学报, 2021, 70(23): 230305. doi: 10.7498/aps.70.20210963
    [8] 孔令元, 丁洪. 铁基超导涡旋演生马约拉纳零能模. 物理学报, 2020, 69(11): 110301. doi: 10.7498/aps.69.20200717
    [9] 尹训昌, 刘万芳, 马业万, 孔祥木, 闻军, 章礼华. 一簇金刚石晶格上S 4模型的相变. 物理学报, 2019, 68(2): 026401. doi: 10.7498/aps.68.20181315
    [10] 何菊生, 张萌, 潘华清, 邹继军, 齐维靖, 李平. 基于变温霍尔效应方法的一类n-GaN位错密度的测量. 物理学报, 2017, 66(6): 067201. doi: 10.7498/aps.66.067201
    [11] 陈锟, 邓友金. 用量子蒙特卡罗方法研究二维超流-莫特绝缘体相变点附近的希格斯粒子. 物理学报, 2015, 64(18): 180201. doi: 10.7498/aps.64.180201
    [12] 侯清玉, 乌云, 赵春旺. Magnli相亚氧化钛的莫特相变和磁电性能的模拟计算. 物理学报, 2013, 62(23): 237102. doi: 10.7498/aps.62.237102
    [13] 吴绍全, 陈佳峰, 赵国平. 串型耦合双量子点之间库仑作用对其近藤共振的影响. 物理学报, 2012, 61(8): 087203. doi: 10.7498/aps.61.087203
    [14] 郑晓军, 张俊, 黄忠兵. 扩展哈伯德模型中原子团簇的结构和热力学性质研究. 物理学报, 2010, 59(6): 3897-3904. doi: 10.7498/aps.59.3897
    [15] 侯清玉, 张 跃, 张 涛. 高氧空位浓度对锐钛矿TiO2莫特相变和光谱红移及电子寿命影响的第一性原理研究. 物理学报, 2008, 57(3): 1862-1866. doi: 10.7498/aps.57.1862
    [16] 杨昌平, 周智辉, 王 浩, K. Iwasa, M. Kohgi. 填充式方钴矿化合物CeOs4Sb12近藤相互作用的非弹性中子散射研究. 物理学报, 2006, 55(12): 6643-6646. doi: 10.7498/aps.55.6643
    [17] 吴绍全, 何 忠, 阎从华, 谌雄文, 孙威立. 嵌入并联耦合双量子点介观环系统中的近藤效应. 物理学报, 2006, 55(3): 1413-1418. doi: 10.7498/aps.55.1413
    [18] 吴绍全, 孙威立, 余万伦, 王顺金. 嵌入单量子点Aharonov-Bohm环中的近藤效应. 物理学报, 2005, 54(6): 2910-2917. doi: 10.7498/aps.54.2910
    [19] 王燕, 云峰, 廖显伯, 孔光临. MPS结构中的光生伏特现象. 物理学报, 1996, 45(10): 1615-1621. doi: 10.7498/aps.45.1615
    [20] 李炳安. 层子模型中的(1/2)+重子的电磁性质和△(1236)的光生电生现象. 物理学报, 1975, 24(2): 124-140. doi: 10.7498/aps.24.124
计量
  • 文章访问数:  2235
  • PDF下载量:  214
  • 被引次数: 0
出版历程
  • 收稿日期:  2023-09-17
  • 修回日期:  2023-10-17
  • 上网日期:  2023-11-13
  • 刊出日期:  2023-12-05

/

返回文章
返回