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Tuning the electronic properties of low-dimensional materials is helpful in building nano electronic devices. Here, we investigate the structural and electronic structures of one-dimensional helical Se atomic chain by using first-principles calculations. Our results show that this structure has a much lower energy than the one with a straight-line structure. Our phonon calculations and ab initio molecular dynamics simulations suggest that this structure is both dynamically and thermally stable. The band structure shows that it is a semiconductor with a gap of about 2.0 eV and Rashba-type splitting near the X point. The helical structure is good for tuning the electronic properties by using strains. As a result, a 5% strain leads to a 20% change in the band gap while the Rashba energy offset is doubled. Moreover, we find that the valence band is a flat band, over which hole doping can induce ferromagnetism and the system becomes half-metallic. Further increasing the doping level can transform the system into a ferromagnetic metal. Such a strategy is then applied to one-dimensional helical Te atomic chain and similar results are obtained.
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Keywords:
- one-dimensional atomic chain /
- Rashba effect /
- electronic structure /
- strain tuning /
- flat band
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图 1 一维螺旋Se原子链的结构与稳定性 (a)结构的俯视图(上)和侧视图(下)(黑色方框代表原胞); (b) 螺旋型和直线型结构的总能随晶格常数的变化; (c) 螺旋型结构的声子谱; (d) T = 300 K, ab initio分子动力学模拟结果与模拟中的始末状态结构
Figure 1. Geometric structures and stability of one-dimensional helical Se atomic chain: (a) Top (up) and side (bottom) views of the structure (The black box represents the primitive cell); (b) total energies as a function of the lattice constant for both the helical and linear chains; (c) the simulated phonon spectrum of the helical structure; (d) results from ab initio molecular dynamics simulations and the initial and final geometric structures during the simulation at T = 300 K.
图 2 一维螺旋结构Se原子链的能带结构 (a) 不考虑SOC; (b) 考虑SOC; (c) 考虑SOC时X点附近的导带
Figure 2. Band structures of the one-dimensional helical Se atomic chain: (a) Without SOC; (b) with SOC; (c) the conduction bands near X from SOC calculations.
图 3 一维螺旋结构Se原子链的应力调控 (a) 带隙随应变的变化; (b) Rashba能量偏移(上)和动量偏移(下)
Figure 3. Strain tuning of the one-dimensional helical Se atomic chain: (a) Band gap vs. strain; (b) Rashba energy (up) and momentum (bottom) offsets.
图 4 空穴掺杂浓度 Nh对一维螺旋Se原子链结构的影响 (a) 平均每个Se原子的磁矩随 Nh的变化(FM代表铁磁序); (b) Nh = 1.0和(c) Nh = 2.0的能带结构 (虚线代表费米能级)
Figure 4. Influences of the hole doping concentration Nh on the structure of one-dimensional helical Se atomic chain: (a) The average magnetic momentum per Se atomic vs. Nh (FM denotes the ferromagnetic ordering); band structures with (b) Nh = 1.0 and (c) Nh = 2.0 (The dotted line represents the Fermi level).
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[1] Bychkov Y A, Rashba É I 1984 JETP Lett. 39 78
[2] Datta S, Das B 1990 Appl. Phys. Lett. 56 665
Google Scholar
[3] Fu L, Kane C L, Mele E J 2007 Phys. Rev. Lett. 98 106803
Google Scholar
[4] Qi X L, Zhang S C, 2011 Rev. Mod. Phys. 83 1057
Google Scholar
[5] LaShell S, McDougall B A, Jensen E 1996 Phys. Rev. Lett. 77 3419
Google Scholar
[6] Koroteev Y M, Bihlmayer G, Gayone J E, Chulkov E V, Blügel S, Echenique P M, Hofmann Ph 2004 Phys. Rev. Lett. 93 046403
Google Scholar
[7] Ast C R, Henk J, Ernst A, Moreschini L, Falub M C, Pacilé D, Bruno P, Kern K, Grioni M 2007 Phys. Rev. Lett. 98 186807
Google Scholar
[8] Bihlmayer G, Blügel S, Chulkov E V 2007 Phys. Rev. B 75 195414
Google Scholar
[9] Meier F, Petrov V, Guerrero S, Mudry C, Patthey L, Osterwalder J, Dil J H 2009 Phys. Rev. B 79 241408
Google Scholar
[10] Yaji K, Ohtsubo Y, Hatta S, Okuyama H, Miyamoto K, Okuda T, Kimura A, Namatame H, Taniguchi M, Aruga T 2010 Nat. Commun. 1 17
Google Scholar
[11] Matetskiy A V, Ichinokura S, Bondarenko L V, Tupchaya A Y, Gruznev D V, Zotov A V, Saranin A A, Hobara R, Takayama A, Hasegawa S 2015 Phys. Rev. Lett. 115 147003
Google Scholar
[12] Qin W, Li L, Zhang Z 2019 Nat. Phys. 15 796
Google Scholar
[13] 龚士静, 段纯刚 2015 64 187103
Google Scholar
Gong S J, Duan C G 2015 Acta Phys. Sin. 64 187103
Google Scholar
[14] Ming W, Wang Z F, Zhou M, Yoon M, Liu F 2016 Nano Lett. 16 404
Google Scholar
[15] Ishizaka K, Bahramy M S, Murakawa H, Sakano M, Shimojima T, Sonobe T, Koizumi K, Shin S, Miyahara H, Kimura A, Miyamoto K, Okuda T, Namatame H, Taniguchi M, Arita R, Nagaosa N, Kobayashi K, Murakami Y, Kumai R, Kaneko Y, Onose Y, Tokura Y 2011 Nat. Mater. 10 521
Google Scholar
[16] Chen M, Liu F 2021 Natl. Sci. Rev. 8 nwaa241
Google Scholar
[17] Sante D D, Barone P, Bertacco R, Picozzi S 2012 Adv. Mater. 25 509
Google Scholar
[18] Meng Y H, Bai W, Gao H, Gong S J, Wang J Q, Duan C G, Chu J H 2017 Nanoscale 9 17957
Google Scholar
[19] Hanakata P Z, Rodin A S, Park H S, Campbell D K, Castro Neto A H 2018 Phys. Rev. B 97 235312
Google Scholar
[20] Iijima S 1991 Nature 34 56
Google Scholar
[21] Kondo Y, Takayanagi K 1997 Phys. Rev. Lett. 79 3455
Google Scholar
[22] Dresselhaus M S, Lin Y M, Rabin O, Jorio A, Souza Filho A G, Pimenta M A, Saito R, Samsonidze G G, Dresselhaus G 2003 Mater. Sci. Eng. C 23 129
Google Scholar
[23] Qin J K, Liao P Y, Si M, Gao S, Qiu G, Jian J, Wang Q, Zhang S Q, Huang S, Charnas A, Wang Y, Kim M J, Wu W, Xu X, Wang H Y, Yang L, Yap Y K, Ye P D 2020 Nat. Electron. 3 141
Google Scholar
[24] Du Y, Qiu G, Wang Y, Si M, Xu X, Wu W, Ye P D 2017 Nano Lett. 17 3965
Google Scholar
[25] Ren W, Ye J T, Shi W, Tang Z K, Chan C T and Sheng P 2009 New J. Phys. 11 103014
Google Scholar
[26] Hirayama M, Okugawa R, Ishibashi S, Murakami S, Miyake T 2015 Phys. Rev. Lett. 114 206401
Google Scholar
[27] Han J, Zhang A, Chen M, Gao W, Jiang Q 2020 Nanoscale 12 10277
Google Scholar
[28] Andharia E, Kaloni T P, Salamo G J, Yu S Q, Churchill H O H, Barraza-Lopez S 2018 Phys. Rev. B 98 035420
Google Scholar
[29] Kresse G, Furthmüller J 1996 Phys. Rev. B 54 11169
Google Scholar
[30] Blochl P E 1994 Phys. Rev. B 50 17953
Google Scholar
[31] Kresse G, Joubert D 1999 Phys. Rev. B 59 1758
Google Scholar
[32] Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
Google Scholar
[33] Togo A, Tanaka I 2015 Scr. Mater. 108 1
Google Scholar
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