Proposal for valleytronic materials: Ferrovalley metal and valley gapless semiconductor
San-Dong Guo, Yu-Ling Tao, Guangzhao Wang, Shaobo Chen, Dong Huang, Yee Sin Ang
Proposal for valleytronic materials: Ferrovalley metal and valley gapless semiconductor
Valleytronic materials can provide new degrees of freedom to future electronic devices. In this work, the concepts of the ferrovalley metal (FVM) and valley gapless semiconductor (VGS) are proposed, which can be achieved in valleytronic bilayer systems by electric field engineering. In valleytronic bilayer systems, the interaction between out-of-plane ferroelectricity and A-type antiferromagnetism can induce layer-polarized anomalous valley Hall (LP-AVH) effect. The K and −K valleys of FVM are both metallic, and electron and hole carriers simultaneously exist. In the extreme case, the FVM can become VGS by analogizing spin gapless semiconductor (SGS). Moreover, it is proposed that the valley splitting enhancement and valley polarization reversal can be achieved by electric field engineering in valleytronic bilayer systems. Taking the bilayer as an example, our proposal is confirmed by the first-principle calculations. The FVM and VGS can be achieved in bilayer by applying electric field. With appropriate electric field range, increasing electric field can enhance valley splitting, and the valley polarization can be reversed by flipping electric field direction. To effectively tune valley properties by electric field in bilayer systems, the parent monolayer should possess out-of-plane magnetization, and have large valley splitting. Our results shed light on the possible role of electric field in tuning valleytronic bilayer systems, and provide a way to design the ferrovalley-related material by electric field.
valleytronics / electric field / bilayer
[1] |
X. Xu, W. Yao, D. Xiao, T. F. Heinz. Spin and pseudospins in layered transition metal dichalcogenides. Nat. Phys., 2014, 10(5): 343
CrossRef
ADS
Google scholar
|
[2] |
Y. Liu, C. S. Lian, Y. Li, Y. Xu, W. Duan. Pseudospins and topological effects of phonons in a Kekulé lattice. Phys. Rev. Lett., 2017, 119(25): 255901
CrossRef
ADS
Google scholar
|
[3] |
M. Zeng, Y. Xiao, J. Liu, K. Yang, L. Fu. Exploring two-dimensional materials toward the next-generation circuits: from monomer design to assembly control. Chem. Rev., 2018, 118(13): 6236
CrossRef
ADS
Google scholar
|
[4] |
K. F. Mak, K. He, J. Shan, T. F. Heinz. Control of valley polarization in monolayer MoS2 by optical helicity. Nat. Nanotechnol., 2012, 7(8): 494
CrossRef
ADS
Google scholar
|
[5] |
D. MacNeill, C. Heikes, K. F. Mak, Z. Anderson, A. Kormányos, V. Zólyomi, J. Park, D. C. Ralph. Breaking of valley degeneracy by magnetic field in monolayer MoSe2. Phys. Rev. Lett., 2015, 114(3): 037401
CrossRef
ADS
Google scholar
|
[6] |
H. Zeng, J. Dai, W. Yao, D. Xiao, X. Cui. Valley polarization in MoS2 monolayers by optical pumping. Nat. Nanotechnol., 2012, 7: 490
CrossRef
ADS
Google scholar
|
[7] |
A. Srivastava, M. Sidler, A. V. Allain, D. S. Lembke, A. Kis, A. Imamoglu. Valley Zeeman effect in elementary optical excitations of monolayer WSe2. Nat. Phys., 2015, 11(2): 141
CrossRef
ADS
Google scholar
|
[8] |
C. Zhao, T. Norden, P. Zhang, P. Zhao, Y. Cheng, F. Sun, J. P. Parry, P. Taheri, J. Wang, Y. Yang, T. Scrace, K. Kang, S. Yang, G. Miao, R. Sabirianov, G. Kioseoglou, W. Huang, A. Petrou, H. Zeng. Enhanced valley splitting in monolayer WSe2 due to magnetic exchange field. Nat. Nanotechnol., 2017, 12(8): 757
CrossRef
ADS
Google scholar
|
[9] |
H. Zeng, J. Dai, W. Yao, D. Xiao, X. Cui. Valley polarization in MoS2 monolayers by optical pumping. Nat. Nanotechnol., 2012, 7(8): 490
CrossRef
ADS
Google scholar
|
[10] |
J. R. Schaibley, H. Yu, G. Clark, P. Rivera, J. S. Ross, K. L. Seyler, W. Yao, X. Xu. Valleytronics in 2D materials. Nat. Rev. Mater., 2016, 1(11): 16055
CrossRef
ADS
Google scholar
|
[11] |
M. S. Mrudul, Á. Jiménez-Galán, M. Ivanov, G. Dixit. Light-induced valleytronics in pristine graphene. Optica, 2021, 8(3): 422
CrossRef
ADS
Google scholar
|
[12] |
M. S. Mrudul, G. Dixit. Controlling valley-polarisation in graphene via tailored light pulses. J. Phys. At. Mol. Opt. Phys., 2021, 54(22): 224001
CrossRef
ADS
Google scholar
|
[13] |
W. Y. Tong, S. J. Gong, X. Wan, C. G. Duan. Concepts of ferrovalley material and anomalous valley Hall effect. Nat. Commun., 2016, 7(1): 13612
CrossRef
ADS
Google scholar
|
[14] |
H. Hu, W. Y. Tong, Y. H. Shen, X. Wan, C. G. Duan. Concepts of the half-valley-metal and quantum anomalous valley Hall effect. npj Comput. Mater., 2020, 6: 129
CrossRef
ADS
Google scholar
|
[15] |
S. D. Guo, J. X. Zhu, W. Q. Mu, B. G. Liu. Possible way to achieve anomalous valley Hall effect by piezoelectric effect in a GdCl2 monolayer. Phys. Rev. B, 2021, 104(22): 224428
CrossRef
ADS
Google scholar
|
[16] |
X. Y. Feng, X. L. Xu, Z. L. He, R. Peng, Y. Dai, B. B. Huang, Y. D. Ma. Valley-related multiple Hall effect in monolayer VSi2P4. Phys. Rev. B, 2021, 104(7): 075421
CrossRef
ADS
Google scholar
|
[17] |
Q. R. Cui, Y. M. Zhu, J. H. Liang, P. Cui, H. X. Yang. Spin-valley coupling in a two-dimensional VSi2N4 monolayer. Phys. Rev. B, 2021, 103(8): 085421
CrossRef
ADS
Google scholar
|
[18] |
X. Zhou, R. Zhang, Z. Zhang, W. Feng, Y. Mokrousov, Y. Yao. Sign-reversible valley-dependent Berry phase effects in 2D valley-half-semiconductors. npj Comput. Mater., 2021, 7: 160
CrossRef
ADS
Google scholar
|
[19] |
I. Khan, B. Marfoua, J. Hong. Electric field induced giant valley polarization in two dimensional ferromagnetic WSe2/CrSnSe3 heterostructure. npj 2D Mater. Appl., 2021, 5: 10
CrossRef
ADS
Google scholar
|
[20] |
H. X. Cheng, J. Zhou, W. Ji, Y. N. Zhang, Y. P. Feng. Two-dimensional intrinsic ferrovalley GdI2 with large valley polarization. Phys. Rev. B, 2021, 103(12): 125121
CrossRef
ADS
Google scholar
|
[21] |
R. Li, J. W. Jiang, W. B. Mi, H. L. Bai. Room temperature spontaneous valley polarization in two-dimensional FeClBr monolayer. Nanoscale, 2021, 13(35): 14807
CrossRef
ADS
Google scholar
|
[22] |
K. Sheng, Q. Chen, H. K. Yuan, Z. Y. Wang. Monolayer CeI2: An intrinsic room-temperature ferrovalley semiconductor. Phys. Rev. B, 2022, 105(7): 075304
CrossRef
ADS
Google scholar
|
[23] |
P. Jiang, L. L. Kang, Y. L. Li, X. H. Zheng, Z. Zeng, S. Sanvito. Prediction of the two-dimensional Janus ferrovalley material LaBrI. Phys. Rev. B, 2021, 104(3): 035430
CrossRef
ADS
Google scholar
|
[24] |
R. Peng, Y. Ma, X. Xu, Z. He, B. Huang, Y. Dai. Intrinsic anomalous valley Hall effect in single-layer Nb3I8. Phys. Rev. B, 2020, 102(3): 035412
CrossRef
ADS
Google scholar
|
[25] |
K. Sheng, B. K. Zhang, H. K. Yuan, Z. Y. Wang. Strain-engineered topological phase transitions in ferrovalley 2H−RuCl2 monolayer. Phys. Rev. B, 2022, 105(19): 195312
CrossRef
ADS
Google scholar
|
[26] |
S. D. Guo, J. X. Zhu, M. Y. Yin, B. G. Liu. Substantial electronic correlation effects on the electronic properties in a Janus FeClF monolayer. Phys. Rev. B, 2022, 105(10): 104416
CrossRef
ADS
Google scholar
|
[27] |
S. D. Guo, W. Q. Mu, B. G. Liu. Valley-polarized quantum anomalous Hall insulator in monolayer RuBr2. 2D Mater., 2022, 9: 035011
CrossRef
ADS
Google scholar
|
[28] |
H. Huan, Y. Xue, B. Zhao, G. Y. Gao, H. R. Bao, Z. Q. Yang. Strain-induced half-valley metals and topological phase transitions in MBr2 monolayers (M = Ru, Os). Phys. Rev. B, 2021, 104(16): 165427
CrossRef
ADS
Google scholar
|
[29] |
S. D. Guo, Y. L. Tao, W. Q. Mu, B. G. Liu. Correlation-driven threefold topological phase transition in monolayer OsBr2. Front. Phys., 2023, 18(3): 33304
CrossRef
ADS
Google scholar
|
[30] |
S. D. Guo, Y. L. Tao, H. T. Guo, Z. Y. Zhao, B. Wang, G. Z. Wang, X. T. Wang. Possible electronic state quasi-half-valley metal in a VGe2P4 monolayer. Phys. Rev. B, 2023, 107(5): 054414
CrossRef
ADS
Google scholar
|
[31] |
X. L. Wang. Proposal for a new class of materials: Spin gapless semiconductors. Phys. Rev. Lett., 2008, 100(15): 156404
CrossRef
ADS
Google scholar
|
[32] |
T. Zhang, X. L. Xu, B. B. Huang, Y. Dai, L. Z. Kou, Y. D. Ma. Layer-polarized anomalous Hall effects in valleytronic van der Waals bilayers. Mater. Horiz., 2023, 10(2): 483
CrossRef
ADS
Google scholar
|
[33] |
X. Liu, A. P. Pyatakov, W. Ren. Magnetoelectric coupling in multiferroic bilayer VS2. Phys. Rev. Lett., 2020, 125(24): 247601
CrossRef
ADS
Google scholar
|
[34] |
A. O. Fumega, J. L. Lado. Ferroelectric valley valves with graphene/MoTe2 van der Waals heterostructures. Nanoscale, 2023, 15(5): 2181
CrossRef
ADS
Google scholar
|
[35] |
W. Y. Tong, C. G. Duan. Electrical control of the anomalous valley Hall effect in antiferrovalley bilayers. npj Quantum Mater., 2017, 2: 47
CrossRef
ADS
Google scholar
|
[36] |
P. Hohenberg, W. Kohn. Inhomogeneous electron gas. Phys. Rev., 1964, 136(3B): B864
CrossRef
ADS
Google scholar
|
[37] |
W. Kohn, L. J. Sham. Self-consistent equations including exchange and correlation effects. Phys. Rev., 1965, 140(4A): A1133
CrossRef
ADS
Google scholar
|
[38] |
G.Kresse, Ab initio molecular dynamics for liquid metals, J. Non-Cryst. Solids 193, 222 (1995)
|
[39] |
G. Kresse, J. Furthmüller. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci., 1996, 6(1): 15
CrossRef
ADS
Google scholar
|
[40] |
G. Kresse, D. Joubert. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B, 1999, 59(3): 1758
CrossRef
ADS
Google scholar
|
[41] |
J. P. Perdew, K. Burke, M. Ernzerhof. Generalized gradient approximation made simple. Phys. Rev. Lett., 1996, 77(18): 3865
CrossRef
ADS
Google scholar
|
[42] |
M. Cococcioni, S. de Gironcoli. Linear response approach to the calculation of the effective interaction parameters in the LDA + U method. Phys. Rev. B, 2005, 71(3): 035105
CrossRef
ADS
Google scholar
|
[43] |
See Supplemental Material for calculating U; crystal structures; energy difference between FM and AFM and MAE as a function of E; the related energy band structures.
|
[44] |
S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys, A. P. Sutton. Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study. Phys. Rev. B, 1998, 57(3): 1505
CrossRef
ADS
Google scholar
|
[45] |
S. Grimme, S. Ehrlich, L. Goerigk. Effect of the damping function in dispersion corrected density functional theory. J. Comput. Chem., 2011, 32(7): 1456
CrossRef
ADS
Google scholar
|
[46] |
T. Fukui, Y. Hatsugai, H. Suzuki. Chern numbers in discretized Brillouin zone: Efficient method of computing (spin) Hall conductances. J. Phys. Soc. Jpn., 2005, 74(6): 1674
CrossRef
ADS
Google scholar
|
[47] |
H.J. Kim,
|
[48] |
H.J. KimC. LiJ.FengJ.H. ChoZ.Zhang, Competing magnetic orderings and tunable topological states in two-dimensional hexagonal organometallic lattices, Phys. Rev. B 93, 041404(R) (2016)
|
[49] |
To easily meet energy convergence criterion, the parameter DIPOL=0.5 0.5 0.5 is set, and the convergent charge density under small electric field gradually feeds to the calculations with large electric field.
|
[50] |
P. Zhao, Y. Dai, H. Wang, B. B. Huang, Y. D. Ma. Intrinsic valley polarization and anomalous valley hall effect in single-layer 2H-FeCl2. Chem. Phys. Mater., 2022, 1(1): 56
CrossRef
ADS
Google scholar
|
[51] |
R. Li, J. W. Jiang, W. B. Mi, H. L. Bai. Room temperature spontaneous valley polarization in two-dimensional FeClBr monolayer. Nanoscale, 2021, 13(35): 14807
CrossRef
ADS
Google scholar
|
[52] |
D. Xiao, M. C. Chang, Q. Niu. Berry phase effects on electronic properties. Rev. Mod. Phys., 2010, 82(3): 1959
CrossRef
ADS
Google scholar
|
[53] |
B. I. Weintrub, Y. L. Hsieh, S. Kovalchuk, J. N. Kirchhof, K. Greben, K. I. Bolotin. Generating intense electric fields in 2D materials by dual ionic gating. Nat. Commun., 2022, 13(1): 6601
CrossRef
ADS
Google scholar
|
/
〈 | 〉 |