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洪德耦合相互作用是导致多轨道体系发生轨道选择Mott相变的重要因素之一. 通过调控洪德耦合相互作用来研究其不同组成部分对轨道选择Mott相变的作用. 利用基于Lanczos 求解器的动力学平均场理论, 对比了双轨道的J模型和Jz模型的金属-绝缘体相变, 并重点讨论洪德耦合中的自旋翻转项和电子对跃迁项以及轨道宽度比值W2/W1如何影响轨道选择Mott 相变. 在J模型的相图中, Mott选择相占有较大的区域, 而Jz模型的轨道选择Mott 相只存在于一个很狭窄的区域内, 这说明自旋翻转项及电子对跳跃项是有利于轨道选择Mott相变发生的关键因素. 此外当轨道宽度之比大于W2/W1=0.7时, Jz 模型的轨道选择Mott 相会完全消失, 而J模型中只要轨道宽度不同都存在轨道选择Mott相. 因而, 简化后的Jz 模型只是在特定条件下才适合于研究轨道选择Mott相变.
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关键词:
- 轨道选择Mott相变 /
- 动力学平均场理论 /
- 双轨道Hubbard模型 /
- 洪德耦合
Using the dynamical mean field theory with Lanczos method as its impurity solver, we study the orbital-selective Mott transition (OSMT) in the two-orbital J model and Jz model. In the multi-orbital systems, the Mott metal-insulator transition occurs successively when the widths of the bands are different. As the narrow orbital becomes Mott insulator while the wide orbital is still in metallic phase, we find an orbital-selective Mott phase (OSMP). There are two different Hubbard models that are frequently used to describe the OSMT, which are named J model and Jz model, respectively. The J Model is composed of the whole Hund's rule coupling terms, including the spin-flip term, the pair-hopping term and the Ising type Hund's rule coupling term. However, there is only Ising type Hund's rule coupling term in the Jz model.#br#We study the ratio of bandwidth W2/W1 on the OSMT by analyzing the results of the density of states and quasi-particle weight. Comparing the phase diagrams obtained from the J and Jz models with the Hund's rule coupling J(Jz)=U/4, we find that the OSMP region of the J model is much larger than that of the Jz model when W2/W1=0.5 or W2/W1=0.2. When the ratio of bandwidth increases to W2/W1=0.8, the OSMP disappears completely in the Jz model. However in the J model, we can still find the OSMT but the area of the OSMP shrinks significantly. Therefore, the OSMT happens more easily in the J model than in the Jz model.#br#In order to discuss the cooperative effect of the bandwidth and Hund's rule coupling on the OSMT, we compare the phase diagrams for different Hund's rule couplings J(Jz)=U/4 and J(Jz)=U/2. We find that when the bandwidth W2/W1≥q 0.7, the OSMT disappears in Jz model in the case of either Jz=U/4 or Jz=U/2. However, the OSMP always exists in the J model if the bandwidths of the two orbitals are different, suggesting that the rotation invariances of the Hund's rule couplings can protect the OSMP. Therefore, one should be more careful when using the Jz model instead of the J model to study the OSMP.-
Keywords:
- orbital-selective Mott transition /
- dynamical mean-field theory /
- two-orbital Hubbard model /
- Hund'
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[28] Zhuang J N, Liu Q M, Fang Z, Dai X 2010 Chin. Phys. B 19 087104
[29] Zhao J Zh, Zhuang J N, Deng X Y, Bi Y, Cai L C, Fang Z, Dai X 2012 Chin. Phys. B 21 057106
[30] Caffarel M, Krauth W 1994 Phys. Rev. Lett. 72 1545
[31] Georges A, Kotliar G, Krauth W, Rozenberg M J 1996 Rev. Mod. Phys. 68 13
[32] Dagotto E 1994 Rev. Mod. Phys. 66 763
-
[1] Salamon M B, Jaime M 2001 Rev. Mod. Phys. 73 583
[2] Hirschfeld P J, Korshunov M M, Mazin I I 2011 Rep. Prog. Phys. 74 124508
[3] Stewart G R 2011 Rev. Mod. Phys. 83 1589
[4] Tokura Y, Nagaosa N 2000 Science 288 462
[5] Zou L J 2014 Physics 43 299 (in Chinese) [邹良剑 2014 物理 43 299]
[6] Anisimov V I, Nekrasov I A, Kondakov D E, Rice T M, Sigrist M 2002 Eur. Phys. J. B 25 191
[7] Mott N F 1968 Rev. Mod. Phys. 40 677
[8] Imada M, Fujimori A, Tokura Y 1998 Rev. Mod. Phys. 70 1039
[9] Inaba K, Koga A 2006 Phys. Rev. B 73 155106
[10] Song Y, Zou L J 2005 Phys. Rev. B 72 085114
[11] Bouadim K, Batrouni G G, Scalettar R T 2009 Phys. Rev. Lett. 102 226402
[12] Zhang Y Z 2014 Physics 43 309 (in Chinese) [张宇钟 2014 物理 43 309]
[13] Quan Y M, Liu D Y, Zou L J 2012 Acta Phys. Sin. 61 017106 (in Chinese) [全亚民, 刘大勇, 邹良剑 2012 物理学报 61 017106]
[14] Koga A, Kawakami N, Rice T M, Sigrist M 2005 Phys. Rev. B 72 045128
[15] Liebsch A 2005 Phys. Rev. Lett. 95 116402
[16] Jakobi E, Blmer N, van Dongen P 2013 Phys. Rev. B 87 205135
[17] Song Z Y, Lee H, Zhang Y Z 2015 New J. Phys. 17 033034
[18] Blmer N, Knecht C, Pozgajcić K, van Dongen P 2007 J. Magn. Mater 310 922
[19] Koga A, Kawakami N, Rice T M, Sigrist M 2005 Physica B 359 1366
[20] Koga A, Kawakami N, Rice T M, Sigrist M 2004 Phys. Rev. Lett. 92 216402
[21] Werner P, Millis A J 2007 Phys. Rev. Lett. 99 126405
[22] Song Y, Zou L J 2009 Eur. Phys. J. B 72 59
[23] Pruschke Th, Bulla R 2005 Eur. Phys. J. B 44 217
[24] de'Medici L, Georges A, Biermann S 2005 Phys. Rev. B 72 205124
[25] Ferrero M, Becca F, Fabrizio M, Capone M 2005 Phys. Rev. B 72 205126
[26] de'Medici L 2011 Phys. Rev. B 83 205112
[27] de'Medici L, Hassan S R, Capone M, Dai X 2011 Phys. Rev. Lett. 102 126401
[28] Zhuang J N, Liu Q M, Fang Z, Dai X 2010 Chin. Phys. B 19 087104
[29] Zhao J Zh, Zhuang J N, Deng X Y, Bi Y, Cai L C, Fang Z, Dai X 2012 Chin. Phys. B 21 057106
[30] Caffarel M, Krauth W 1994 Phys. Rev. Lett. 72 1545
[31] Georges A, Kotliar G, Krauth W, Rozenberg M J 1996 Rev. Mod. Phys. 68 13
[32] Dagotto E 1994 Rev. Mod. Phys. 66 763
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