各向异性ruby晶格中费米子体系的Mott相变

保安

doi:10.7498/aps.70.20210963

摘要

本文用哈伯德模型研究各向异性ruby晶格中费米子行为, 在团簇动力学平均场理论框架内将格点模型映射为有效自洽场中的杂质模型后用连续-时间量子蒙特卡罗算法求解杂质模型. 基于自洽计算的结果, 用最大熵方法得到各向异性ruby晶格中具有相互作用的费米子体系的单粒子态密度和双占据数后讨论了温度(T )、相互作用(U )和各向异性参数(λ)对体系的金属-绝缘相变的影响. 最后给出各向异性ruby晶格中费米子体系的温度-相互作用相图, 研究结果表明, 低温和弱相互作用范围体系处在金属相, 而在高温和强相互作用下体系内出现Mott绝缘体相.

关键词:

Abstract

In this work, the Hubbard model is adopted to describe fermions with on-site repulsive interaction and the nearest-neighbor hopping in anisotropic ruby lattice. The combination of cluster dynamical mean field theory and continuous-time quantum Monte Carlo algorithm is used to solve the theoretical model. It is widely accepted that the density of states and the double occupancy are two important quantities for determining the phase transition of two-dimensional strongly correlated system. Therefore, based on the self-consistent calculation, using the maximum entropy method to calculate the single particle density of states and double occupancy of fermions in anisotropic ruby lattice. Here in this work, there are 6 sites in a cluster. The influences of temperature, interaction and anisotropic parameter on metal-insulator phase transition of fermions in anisotropic ruby lattice are discussed based on the calculations of single particle density of state and double occupancy. Finally, the metal-Mott insulator phase diagram which shows the competition between temperature and on-site repulsive interaction in the phase transition of fermions in anisotropic ruby lattice is presented. The results shows that the system is in metallic state for the regime of weak interaction and low temperature, and the Mott insulator appears in the regime of strong interaction and high temperature. The metallic state and Mott insulating one are separated by the second-order transition line in the phase diagram.

Keywords:

作者及机构信息

保安

南昌工学院教育学院, 南昌　330108

通信作者: 保安, baoan204@aliyun.com

基金项目: 南昌工学院引进人才科研启动基金(批准号: NGRCZX-21-04)资助的课题.

Authors and contacts

Bao An

School of Education, Nanchang Institute of Science and Technology, Nanchang 330108, China

Corresponding author: Bao An, baoan204@aliyun.com

Funds: Project supported by the Science Foundation of Nanchang Institute of Science and Technology, China (Grant No. NGRCZX-21-04).

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参考文献

[1]	Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045 Google Scholar
[2]	Moore J E 2010 Nature 464 194 Google Scholar
[3]	Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057 Google Scholar
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[7]	He M Y, Sun H M, He Q L 2019 Fron. Phys. 14 43401 Google Scholar
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施引文献

图 1 拓扑绝缘体材料Bi₁₄Rh₃I₉的晶格结构示意图　(a)−(c) Bi₁₄Rh₃I₉的晶体结构及其构成单元, 绝缘层[Bi₂I₈]^2–的zigzag链分离由共棱RhBi₈立方体构成的六角网格状金属间的 [(Rh₄Bi)₃I]²⁺层, 六角晶格的边由共棱RhBi₈立方体覆盖; (d) 二维ruby晶格与六角晶格结构俯视图^[8]

Fig. 1. Sketch of crystal structure of topological insulator Bi₁₄Rh₃I₉: (a)−(c) Triclinic crystal structure of Bi₁₄Rh₃I₉. Insulating layers of [Bi₂I₈]^2– zigzag chains separate the intermetallic [(RhBi₄)₃I]²⁺ layers that consist of hexagonal nets of edge-sharing RhBi₈ cubes; (d) honeycomb lattice of graphene with the structure of the intermetallic layer ^[8].

下载: 全尺寸图片幻灯片

图 2 (a) Ruby晶格结构示意图; (b) ruby晶格第一布里渊区; (c) 各向异性ruby晶格($\lambda = 2.0$)中费米子体系$ T = 0.2$和$ U = 0 $时的态密度; (d) 各向异性ruby晶格($\lambda = 2.0$)中费米子体系无相互作用情况下色散关系

Fig. 2. (a) Sketch of ruby lattice; (b) first Brillouin zone of ruby lattice; (c) density of states of anisotropic ruby lattice ($\lambda = 2.0$) for $T = 0.2$, $U = 0$; (d) energy dispersion of anisotropic ruby lattice ($\lambda = 2.0$) for $T = 0.2$, $U = 0$.

下载: 全尺寸图片幻灯片

图 3 方晶格模型映射到有效自洽场杂质模型的示意图　(a) 方晶格; (b) 具有四个格点的超级晶格; (c)有效自洽场中团簇杂质模型的示意图

Fig. 3. Sketch of mapping square lattice model to impurity model in self-consistent field: (a) Square lattice; (b) sketch of supper lattice consists of 4 lattice point; (c) sketch of cluster impurity in self-consistent field.

下载: 全尺寸图片幻灯片

图 4 $\kappa = 3$时一个随机行走示意图

Fig. 4. Sketch of random walk for$\kappa = 3$.

下载: 全尺寸图片幻灯片

图 5 自洽计算的流程图

Fig. 5. Flow chart of self-consistent calculation.

下载: 全尺寸图片幻灯片

图 6 各向异性ruby晶格($\lambda =2.0 $)中费米子体系的态密度　(a) T = 0.2时不同相互作用对应的态密度; (b) U = 8时不同温度对应的态密度

Fig. 6. Density of states of anisotropic ruby lattice ($\lambda =2.0 $) with fermions: (a) Density of states for different interaction at $T = 0.2$; (b) density of states for different temperature at $U = 8.0 $.

下载: 全尺寸图片幻灯片

图 7 固定温度($T = 0.2$)和固定相互作用($U = 8.0 $)情况下, 各向异性参数对ruby晶格中费米子体系态密度的影响

Fig. 7. Comparison of the effect of anisotropic parameter λ on the density of states of fermions in ruby lattice on for $T = 2 $ and $ U = 0 $.

下载: 全尺寸图片幻灯片

图 8 各向异性ruby晶格中费米子体系的双占据数　(a) 不同相互作用下体系双占据数随温度的变化; (b) 不同温度下体系双占据数随相互作用的变化

Fig. 8. Double occupancy of anisotropic ruby lattice with fermions: (a) Comparison between double occupancy for different temperature with the change of interaction; (b) comparison between double occupancy for different interaction with the change of temperature.

下载: 全尺寸图片幻灯片

图 9 温度和相互作用固定的情况下, ruby晶格中费米子体系的双占据数随各向异性参数的变化

Fig. 9. Trend of double occupancy with the change of anisotropic parameter for fixed T and U.

下载: 全尺寸图片幻灯片

图 10 各向异性ruby晶格中费米子体系的金属-绝缘相图

Fig. 10. Metal-Insulator phase diagram of fermions in anisotropic ruby lattice.

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map

[1]	Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045 Google Scholar
[2]	Moore J E 2010 Nature 464 194 Google Scholar
[3]	Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057 Google Scholar
[4]	Qi X L, Zhang S C 2010 Phys.Today 63 33
[5]	Leggett J A 2001 Rev. Mod. Phys. 73 307 Google Scholar
[6]	Ho T L, Zhang S Z 2011 Phys. Rev. Lett. 107 150403 Google Scholar
[7]	He M Y, Sun H M, He Q L 2019 Fron. Phys. 14 43401 Google Scholar
[8]	Rasche B, Isaeva A, Ruck M, et al. 2013 Nat. Mat. 12 422 Google Scholar
[9]	Lin K Y, Ma W J 1983 J. Phys. A: Math. Gen. 16 2515 Google Scholar
[10]	Lin K Y, Ma W J 1983 J. Phys. A: Math. Gen. 16 3895 Google Scholar
[11]	Hou J M, Wang G X 2013 Commun. Theor. Phys. 60 129 Google Scholar
[12]	Hu X, Kargarian M, Fiete GA 2011 Phys. Rev. B 84 155116 Google Scholar
[13]	Jahromi S S, Orús R 2020 Phys. Rev. B 101 115114 Google Scholar
[14]	Cortexs LC, Ortix C, Brink Jvan den 2013 Phys. Rev. Lett. 111 146801 Google Scholar
[15]	Jahromi SS, Kargarian M, Masoudi S F, Langari A 2016 Phys. Rev. B 94 125145 Google Scholar
[16]	Whitsitt S, Chua V, Fiete G A 2012 New J. Phys. 14 115029 Google Scholar
[17]	Gutzwiller M C 1963 Phys. Rev. Lett. 10 159 Google Scholar
[18]	Wohlfarth E P 1953 Rev. Mod.Phys. 25 211 Google Scholar
[19]	Hubbard J 1963 P. Roy. Soc. A-Math. Phy. 276 238
[20]	Hubbard J 1964 P. Roy. Soc. A-Math. Phy. 281 401
[21]	Kanamori J 1963 Prog.Theo. Phys. 30 275 Google Scholar
[22]	Figueirido F, Karlhede A, Kivelson S, et al. 1990 Phys. Rev.B 41 4619 Google Scholar
[23]	Lüscher A, Läuchli A M 2009 Phys. Rev. B 79 195102 Google Scholar
[24]	Gull E, Millis A J, Lichtenstein A I, et al. 2011 Rev.Mod. Phys. 83 349 Google Scholar
[25]	Jarrell M 1992 Phys. Rev.Lett. 69 168 Google Scholar
[26]	Gagliano E R, Dagotto E, Moreo A, et al. 1986 Phys. Rev. B 34 1677
[27]	Nihat Berker A, Grest G S, Soukoulis C M, et al. 1984 J. App. Phys. 55 2416 Google Scholar
[28]	Vafek O, Yang K 2010 Phys. Rev. B 81 041401
[29]	Chitra R, Kotliar G 1999 Phys. Rev. Lett. 83 2386 Google Scholar
[30]	Lichtenstein A, Katsnelson M. 2000 Phys. Rev. B 62 R9283 Google Scholar
[31]	Kotliar G, Savrasov S Y, Pálsson G, et al. 2001 Phys. Rev.Lett. 87 186401 Google Scholar
[32]	Capone M, Civelli M, Kancharla S S, et al. 2004 Phys. Rev.B 69 195105 Google Scholar
[33]	Wu W, Chen Y H, TaoH S, et al. 2010 Phys. Rev. B 82 245102 Google Scholar
[34]	Bao A, Tao HS, Liu HD, et al. 2014 Sci. Rep. 4 6918
[35]	Bao A, 2019 Chin. Phys. B 28 057101 Google Scholar
[36]	Georges A, Kotliar G, Krauth W, et al. 1996 Rev. Mod. Phys. 68 13 Google Scholar
[37]	Kornilovitch P 1998 Phys. Rev.Lett. 81 5382 Google Scholar
[38]	Rubtsov A N, Savkin V V, Lichtenstein A I 2005 Phys. Rev.B 72 035122 Google Scholar
[39]	Werner P, Comanac A, de’ Medici L, et al. 2006 Phys. Rev.Lett. 97 076405 Google Scholar
[40]	Jarrell M, Gubernatis J E 1996 Phys. Rep. 269 133 Google Scholar

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各向异性ruby晶格中费米子体系的Mott相变