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First-principles study on Jahn-Teller effect in Cr monolayer film

## First-principles study on Jahn-Teller effect in Cr monolayer film

Zhang Wei, Chen Kai-Bin, Chen Zhen-Dong
• #### Abstract

Computational physics has been used in many scientific research fields, in which first-principles calculation based on density functional theory has made brilliant achievements. Unlike three-dimensional materials, low-dimensional materials present fantastic physical effect, due to the reduction of material dimensions. With the rapid development of two-dimensional materials, people have a more in-depth understanding of them. Requirements for high performance of two-dimensional materials are raised for potential applications, so the exploration of some effects affecting the stability of two-dimensional materials becomes more and more important. Based on the pioneers' work, Jahn-Teller effect is found to have a certain influence on the stabilities of two-dimensional structure of some elements. In the present paper, we explain the stable structure of Cr monolayer film through theoretical calculation, providing a guidance for experimental synthesis. Using first-principles calculation, we study a series of two-dimensional structures (rectangular, square, hexagonal, oblique and centered rectangular) of Cr monolayer film, focusing on the structural stability and electronic properties. Firstly, the equilibrium lattice constant and cohesive energy of each structure are calculated. Then, the bond angle and lattice constant dependence of the total energy are analyzed in detail. Finally, we investigate the energy band structures, total electronic densities of states, charge densities and electron occupation numbers of orbitals. The results show that low-symmetry oblique and centered rectangular lattice are stable in the two-dimensional system of Cr, while high-symmetry square and hexagonal lattices are not stable and the adhesive energy of the rectangular lattices is very small. Two stable structures of Cr monolayer sheet are formed due to hexagonal structure distortion. The hexagonal structure can shape into a centered rectangular structure with the increase of bond angle, while it changes into an oblique structure with the decrease of bond angle. Because of Jahn-Teller effect, the degenerate energy level spontaneously splits. Then the structure deforms into two reduced-symmetry structures, resulting in a stable system. Therefore, we can infer that the Jahn-Teller effect plays a crucial role in the structural stability of monolayer sheet.

#### Authors and contacts

• Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11504051) and the Science Fund for Distinguished Young Scholars of Fujian Province, China (Grant No. 2018J06001).

#### References

 [1] Chhowalla M, Shin H S, Eda G, Li L, Loh K P, Zhang H 2013 Nat. Chem. 5 263 [2] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666 [3] Li S S, Wang S F, Tang D M, Zhao W J, Xu H L, Chu L Q, Bando Y, Golberg D, Eda G 2015 Appl. Mater. Today 1 60 [4] Zhou J D, Lin J H, Huang X W, Zhou Y, Chen Y, Xia J, Wang H, Xie Y, Yu H M, Lei J C, Wu D, Liu F C, Fu Q D, Zeng Q S, Hsu C H, Yang C L, Lu L, Yu T, Shen Z X, Lin H, Yakobson B I, Liu Q, Suenaga K, Liu G T, Liu Z 2018 Nature 556 355 [5] Liu C C, Feng W X, Yao Y G 2011 Phys. Rev. Lett. 107 76802 [6] Xu Y, Yan B H, Zhang H J, Wang J, Xu G, Tang P Z, Duan W H, Zhang S C 2013 Phys. Rev. Lett. 111 136804 [7] Ezawa M 2012 Phys. Rev. Lett. 109 55502 [8] Liu N, Jin S F, Guo L W, Wang G, Shao H Z, Chen L, Chen X L 2017 Phys. Rev. B 95 155311 [9] Kresse G, Hafner J 1993 Phys. Rev. B 47 558 [10] Kresse G, Furthmuller J 1996 Phys. Rev. B 54 11169 [11] Blöchl P E 1994 Phys. Rev. B 50 17953 [12] Kresse G, Joubert D 1999 Phys. Rev. B 59 1758 [13] Perdew J P, Chevary J A, Vosko S H, Jackson K A, Pederson M R, Singh D J, Fiolhais C 1992 Phys. Rev. B 46 6671 [14] Monkhors H J, Pack J D 1976 Phys. Rev. B 13 5188 [15] Blöchl P E, Jepsen O, Andersen O K 1994 Phys. Rev. B 49 16223 [16] TonKov E T, Ponyatovsky E G 2005 Phase Transformations of Elements Under High Pressure (Boca Raton: CRC Press) pp242-244 [17] Olle M, Ceballos G, Serrate D, Gambardella P 2012 Nano Lett. 12 4431 [18] Robertson A W, Warner J H 2011 Nano Lett. 11 1182

#### Cited By

•  [1] Chhowalla M, Shin H S, Eda G, Li L, Loh K P, Zhang H 2013 Nat. Chem. 5 263 [2] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666 [3] Li S S, Wang S F, Tang D M, Zhao W J, Xu H L, Chu L Q, Bando Y, Golberg D, Eda G 2015 Appl. Mater. Today 1 60 [4] Zhou J D, Lin J H, Huang X W, Zhou Y, Chen Y, Xia J, Wang H, Xie Y, Yu H M, Lei J C, Wu D, Liu F C, Fu Q D, Zeng Q S, Hsu C H, Yang C L, Lu L, Yu T, Shen Z X, Lin H, Yakobson B I, Liu Q, Suenaga K, Liu G T, Liu Z 2018 Nature 556 355 [5] Liu C C, Feng W X, Yao Y G 2011 Phys. Rev. Lett. 107 76802 [6] Xu Y, Yan B H, Zhang H J, Wang J, Xu G, Tang P Z, Duan W H, Zhang S C 2013 Phys. Rev. Lett. 111 136804 [7] Ezawa M 2012 Phys. Rev. Lett. 109 55502 [8] Liu N, Jin S F, Guo L W, Wang G, Shao H Z, Chen L, Chen X L 2017 Phys. Rev. B 95 155311 [9] Kresse G, Hafner J 1993 Phys. Rev. B 47 558 [10] Kresse G, Furthmuller J 1996 Phys. Rev. B 54 11169 [11] Blöchl P E 1994 Phys. Rev. B 50 17953 [12] Kresse G, Joubert D 1999 Phys. Rev. B 59 1758 [13] Perdew J P, Chevary J A, Vosko S H, Jackson K A, Pederson M R, Singh D J, Fiolhais C 1992 Phys. Rev. B 46 6671 [14] Monkhors H J, Pack J D 1976 Phys. Rev. B 13 5188 [15] Blöchl P E, Jepsen O, Andersen O K 1994 Phys. Rev. B 49 16223 [16] TonKov E T, Ponyatovsky E G 2005 Phase Transformations of Elements Under High Pressure (Boca Raton: CRC Press) pp242-244 [17] Olle M, Ceballos G, Serrate D, Gambardella P 2012 Nano Lett. 12 4431 [18] Robertson A W, Warner J H 2011 Nano Lett. 11 1182
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•  Citation:
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• Abstract views:  81
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##### Publishing process
• Received Date:  07 September 2018
• Accepted Date:  01 October 2018

## First-principles study on Jahn-Teller effect in Cr monolayer film

• 1. Fujian Provincial Key Laboratory of Quantum Manipulation and New Energy Materials, College of Physics and Energy, Fujian Normal University, Fuzhou 350117, China;
• 2. Fujian Provincial Collaborative Innovation Center for Optoelectronic Semiconductors and Efficient Devices, Xiamen 361005, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 11504051) and the Science Fund for Distinguished Young Scholars of Fujian Province, China (Grant No. 2018J06001).

Abstract: Computational physics has been used in many scientific research fields, in which first-principles calculation based on density functional theory has made brilliant achievements. Unlike three-dimensional materials, low-dimensional materials present fantastic physical effect, due to the reduction of material dimensions. With the rapid development of two-dimensional materials, people have a more in-depth understanding of them. Requirements for high performance of two-dimensional materials are raised for potential applications, so the exploration of some effects affecting the stability of two-dimensional materials becomes more and more important. Based on the pioneers' work, Jahn-Teller effect is found to have a certain influence on the stabilities of two-dimensional structure of some elements. In the present paper, we explain the stable structure of Cr monolayer film through theoretical calculation, providing a guidance for experimental synthesis. Using first-principles calculation, we study a series of two-dimensional structures (rectangular, square, hexagonal, oblique and centered rectangular) of Cr monolayer film, focusing on the structural stability and electronic properties. Firstly, the equilibrium lattice constant and cohesive energy of each structure are calculated. Then, the bond angle and lattice constant dependence of the total energy are analyzed in detail. Finally, we investigate the energy band structures, total electronic densities of states, charge densities and electron occupation numbers of orbitals. The results show that low-symmetry oblique and centered rectangular lattice are stable in the two-dimensional system of Cr, while high-symmetry square and hexagonal lattices are not stable and the adhesive energy of the rectangular lattices is very small. Two stable structures of Cr monolayer sheet are formed due to hexagonal structure distortion. The hexagonal structure can shape into a centered rectangular structure with the increase of bond angle, while it changes into an oblique structure with the decrease of bond angle. Because of Jahn-Teller effect, the degenerate energy level spontaneously splits. Then the structure deforms into two reduced-symmetry structures, resulting in a stable system. Therefore, we can infer that the Jahn-Teller effect plays a crucial role in the structural stability of monolayer sheet.

Reference (18)

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