Inheritance of the exciton geometric structure from Bloch electrons in two-dimensional layered semiconductors

doi:10.1007/s11467-023-1386-z

Frontiers of Physics

2024, Vol. 19

Issue (4): 43210 https://doi.org/10.1007/s11467-023-1386-z

本期目录

Inheritance of the exciton geometric structure from Bloch electrons in two-dimensional layered semiconductors

Jianju Tang¹, Songlei Wang¹, Hongyi Yu^1,²(

)

¹. Guangdong Provincial Key Laboratory of Quantum Metrology and Sensing & School of Physics and Astronomy, Sun Yat-sen University (Zhuhai Campus), Zhuhai 519082, China
². State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University (Guangzhou Campus), Guangzhou 510275, China

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Abstract：

We theoretically studied the exciton geometric structure in layered semiconducting transition metal dichalcogenides. Based on a three-orbital tight-binding model for Bloch electrons which incorporates their geometric structures, an effective exciton Hamiltonian is constructed and solved perturbatively to reveal the relation between the exciton and its electron/hole constituent. We show that the electron−hole Coulomb interaction gives rise to a non-trivial inheritance of the exciton geometric structure from Bloch electrons, which manifests as a valley-dependent center-of-mass anomalous Hall velocity of the exciton when two external fields are applied on the electron and hole constituents, respectively. The obtained center-of-mass anomalous velocity is found to exhibit a non-trivial dependence on the fields, as well as the wave function and valley index of the exciton. These findings can serve as a general guide for the field-control of the valley-dependent exciton transport, enabling the design of novel quantum optoelectronic and valleytronic devices.

Key words： transition metal dichalcogenides exciton geometric structure Berry curvature van der Waals stacking

收稿日期: 2023-10-24 出版日期: 2024-03-08

Corresponding Author(s): Hongyi Yu

引用本文:

. [J]. Frontiers of Physics, 2024, 19(4): 43210.
Jianju Tang, Songlei Wang, Hongyi Yu. Inheritance of the exciton geometric structure from Bloch electrons in two-dimensional layered semiconductors. Front. Phys. , 2024, 19(4): 43210.

链接本文:

https://academic.hep.com.cn/fop/CN/10.1007/s11467-023-1386-z
https://academic.hep.com.cn/fop/CN/Y2024/V19/I4/43210

Fig.1

$Ω r$	$Ω c$	$Ω v$	$Ω T (τ ′ = + 1)$	$Ω T (τ ′ = − 1)$	$δ Ω (τ ′ = + 1)$	$δ Ω (τ ′ = − 1)$

0.023	−0.125	0.148	−0.072	0.030	0.036	−0.138

Tab.1

Fig.2

Fig.3

Fig.4

1	Ciarrocchi A., Tagarelli F., Avsar A., Kis A.. Excitonic devices with van der Waals heterostructures: Valleytronics meets twistronics. Nat. Rev. Mater., 2022, 7(6): 449 https://doi.org/10.1038/s41578-021-00408-7
2	F. Mak K., Xiao D., Shan J.. Light-valley interactions in 2D semiconductors. Nat. Photonics, 2018, 12(8): 451 https://doi.org/10.1038/s41566-018-0204-6
3	D. Xu X., Yao W., Xiao D., F. Heinz T.. Spin and pseudospins in layered transition metal dichalcogenides. Nat. Phys., 2014, 10(5): 343 https://doi.org/10.1038/nphys2942
4	F. Mak K., Shan J.. Photonics and optoelectronics of 2D semiconductor transition metal dichalcogenides. Nat. Photonics, 2016, 10(4): 216 https://doi.org/10.1038/nphoton.2015.282
5	H. Wang Q., Kalantar-Zadeh K., Kis A., N. Coleman J., S. Strano M.. Electronics and optoelectronics of two-dimensional transition metal dichalcogenides. Nat. Nanotechnol., 2012, 7(11): 699 https://doi.org/10.1038/nnano.2012.193
6	Chernikov A., C. Berkelbach T., M. Hill H., Rigosi A., Li Y., Aslan B., R. Reichman D., S. Hybertsen M., F. Heinz T.. Exciton binding energy and nonhydrogenic Rydberg series in monolayer WS2. Phys. Rev. Lett., 2014, 113(7): 076802 https://doi.org/10.1103/PhysRevLett.113.076802
7	Y. Qiu D., H. da Jornada F., G. Louie S.. Optical spectrum of MoS2: Many-body effects and diversity of exciton states. Phys. Rev. Lett., 2013, 111(21): 216805 https://doi.org/10.1103/PhysRevLett.111.216805
8	L. Yang X., H. Guo S., T. Chan F., W. Wong K., Y. Ching W.. Analytic solution of a two-dimensional hydrogen atom (I): Nonrelativistic theory. Phys. Rev. A, 1991, 43(3): 1186 https://doi.org/10.1103/PhysRevA.43.1186
9	Cao T., Wang G., Han W., Ye H., Zhu C., Shi J., Niu Q., Tan P., Wang E., Liu B., Feng J.. Valley-selective circular dichroism of monolayer molybdenum disulphide. Nat. Commun., 2012, 3(1): 887 https://doi.org/10.1038/ncomms1882
10	L. Zeng H., Dai J., Yao W., Xiao D., Cui X.. Valley polarization in MoS2 monolayers by optical pumping. Nat. Nanotechnol., 2012, 7(8): 490 https://doi.org/10.1038/nnano.2012.95
11	F. Mak K., He K., Shan J., F. Heinz T.. Control of valley polarization in monolayer MoS2 by optical helicity. Nat. Nanotechnol., 2012, 7(8): 494 https://doi.org/10.1038/nnano.2012.96
12	M. Jones A., Yu H., J. Ghimire N., Wu S., Aivazian G., S. Ross J., Zhao B., Yan J., G. Mandrus D., Xiao D., Yao W., Xu X.. Optical generation of excitonic valley coherence in monolayer WSe. Nat. Nanotechnol., 2013, 8(9): 634 https://doi.org/10.1038/nnano.2013.151
13	Rivera P., Yu H., L. Seyler K., P. Wilson N., Yao W., Xu X.. Interlayer valley excitons in heterobilayers of transition metal dichalcogenides. Nat. Nanotechnol., 2018, 13(11): 1004 https://doi.org/10.1038/s41565-018-0193-0
14	Xiao D., C. Chang M., Niu Q.. Berry phase effects on electronic properties. Rev. Mod. Phys., 2010, 82(3): 1959 https://doi.org/10.1103/RevModPhys.82.1959
15	Xiao D., B. Liu G., Feng W., Xu X., Yao W.. Coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides. Phys. Rev. Lett., 2012, 108(19): 196802 https://doi.org/10.1103/PhysRevLett.108.196802
16	Aivazian G., Gong Z., M. Jones A., L. Chu R., Yan J., G. Mandrus D., Zhang C., Cobden D., Yao W., Xu X.. Magnetic control of valley pseudospin in monolayer WSe2. Nat. Phys., 2015, 11(2): 148 https://doi.org/10.1038/nphys3201
17	Srivastava A., Sidler M., V. Allain A., S. Lembke D., Kis A., Imamoğlu A.. Valley Zeeman effect in elementary optical excitations of monolayer WSe. Nat. Phys., 2015, 11(2): 141 https://doi.org/10.1038/nphys3203
18	MacNeill D., Heikes C., F. Mak K., Anderson Z., Kormányos A., Zólyomi V., Park J., C. Ralph D.. Breaking of valley degeneracy by magnetic field in monolayer MoSe2. Phys. Rev. Lett., 2015, 114(3): 037401 https://doi.org/10.1103/PhysRevLett.114.037401
19	Kormányos A., Zólyomi V., I. Fal’ko V., Burkard G.. Tunable Berry curvature and valley and spin Hall effect in bilayer MoS2. Phys. Rev. B, 2018, 98(3): 035408 https://doi.org/10.1103/PhysRevB.98.035408
20	F. Mak K., L. McGill K., Park J., L. McEuen P.. The valley Hall effect in MoS2 transistors. Science, 2014, 344(6191): 1489 https://doi.org/10.1126/science.1250140
21	Yu T., W. Wu M.. Valley depolarization dynamics and valley Hall effect of excitons in monolayer and bilayer MoS2. Phys. Rev. B, 2016, 93(4): 045414 https://doi.org/10.1103/PhysRevB.93.045414
22	Yao W., Xiao D., Niu Q.. Valley-dependent optoelectronics from inversion symmetry breaking. Phys. Rev. B, 2008, 77(23): 235406 https://doi.org/10.1103/PhysRevB.77.235406
23	Z. Zhu Q., W. Y. Tu M., Tong Q., Yao W.. Gate tuning from exciton superfluid to quantum anomalous Hall in van der Waals heterobilayer. Sci. Adv., 2019, 5(1): eaau6120 https://doi.org/10.1126/sciadv.aau6120
24	Y. Jiang C.Rasmita A.Ma H.Tan Q.Zhang Z. Huang Z.Lai S.Wang N.Liu S.Liu X. Yu T.Xiong Q. Gao W., A room-temperature gate-tunable bipolar valley Hall effect in molybdenum disulfide/tungsten diselenide heterostructures, Nat. Electron. 5(1), 23 (2021)
25	Onga M., Zhang Y., Ideue T., Iwasa Y.. Exciton Hall effect in monolayer MoS2. Nat. Mater., 2017, 16(12): 1193 https://doi.org/10.1038/nmat4996
26	Huang Z., Liu Y., Dini K., Tan Q., Liu Z., Fang H., Liu J., Liew T., Gao W.. Robust room temperature valley Hall effect of interlayer excitons. Nano Lett., 2020, 20(2): 1345 https://doi.org/10.1021/acs.nanolett.9b04836
27	Yao W., Niu Q.. Berry phase effect on the exciton transport and on the exciton Bose‒Einstein condensate. Phys. Rev. Lett., 2008, 101(10): 106401 https://doi.org/10.1103/PhysRevLett.101.106401
28	Y. Yu H., Yao W.. Electrically tunable topological transport of moire polaritons. Sci. Bull. (Beijing), 2020, 65(18): 1555 https://doi.org/10.1016/j.scib.2020.05.030
29	Ubrig N., Jo S., Philippi M., Costanzo D., Berger H., B. Kuzmenko A., F. Morpurgo A.. Microscopic origin of the valley Hall effect in transition metal dichalcogenides revealed by wavelength-dependent mapping. Nano Lett., 2017, 17(9): 5719 https://doi.org/10.1021/acs.nanolett.7b02666
30	Trushin M., O. Goerbig M., Belzig W.. Model prediction of self-rotating excitons in two-dimensional transition-metal dichalcogenides. Phys. Rev. Lett., 2018, 120(18): 187401 https://doi.org/10.1103/PhysRevLett.120.187401
31	Hichri A., Jaziri S., O. Goerbig M.. Charged excitons in two-dimensional transition metal dichalcogenides: Semiclassical calculation of Berry curvature effects. Phys. Rev. B, 2019, 100(11): 115426 https://doi.org/10.1103/PhysRevB.100.115426
32	Srivastava A., Imamoğlu A.. Signatures of Bloch-band geometry on excitons: Nonhydrogenic spectra in transition-metal dichalcogenides. Phys. Rev. Lett., 2015, 115(16): 166802 https://doi.org/10.1103/PhysRevLett.115.166802
33	H. Zhou J., Y. Shan W., Yao W., Xiao D.. Berry phase modification to the energy spectrum of excitons. Phys. Rev. Lett., 2015, 115(16): 166803 https://doi.org/10.1103/PhysRevLett.115.166803
34	Gong P., Yu H., Wang Y., Yao W.. Optical selection rules for excitonic Rydberg series in the massive Dirac cones of hexagonal two-dimensional materials. Phys. Rev. B, 2017, 95(12): 125420 https://doi.org/10.1103/PhysRevB.95.125420
35	Cao T., Wu M., G. Louie S.. Unifying optical selection rules for excitons in two dimensions: Band topology and winding numbers. Phys. Rev. Lett., 2018, 120(8): 087402 https://doi.org/10.1103/PhysRevLett.120.087402
36	O. Zhang X., Y. Shan W., Xiao D.. Optical selection rule of excitons in gapped chiral fermion systems. Phys. Rev. Lett., 2018, 120(7): 077401 https://doi.org/10.1103/PhysRevLett.120.077401
37	B. Liu G., Y. Shan W., Yao Y., Yao W., Xiao D.. Three-band tight-binding model for monolayers of group-VIB transition metal dichalcogenides. Phys. Rev. B, 2013, 88(8): 085433 https://doi.org/10.1103/PhysRevB.88.085433
38	C. Wu F., Y. Qu F., H. MacDonald A.. Exciton band structure of monolayer MoS2. Phys. Rev. B, 2015, 91(7): 075310 https://doi.org/10.1103/PhysRevB.91.075310
39	L. Ye Z., Cao T., O’Brien K., Zhu H., Yin X., Wang Y., G. Louie S., Zhang X.. Probing excitonic dark states in single-layer tungsten disulphide. Nature, 2014, 513(7517): 214 https://doi.org/10.1038/nature13734
40	Y. Qiu D., Cao T., G. Louie S.. Nonanalyticity, valley quantum phases, and lightlike exciton dispersion in monolayer transition metal dichalcogenides: Theory and first-principles calculations. Phys. Rev. Lett., 2015, 115(17): 176801 https://doi.org/10.1103/PhysRevLett.115.176801
41	K. Yong C., I. B. Utama M., S. Ong C., Cao T., C. Regan E., Horng J., Shen Y., Cai H., Watanabe K., Taniguchi T., Tongay S., Deng H., Zettl A., G. Louie S., Wang F.. Valley-dependent exciton fine structure and Autler‒Townes doublets from Berry phases in monolayer MoSe2. Nat. Mater., 2019, 18(10): 1065 https://doi.org/10.1038/s41563-019-0447-8
42	Chaudhary S., Knapp C., Refael G.. Anomalous exciton transport in response to a uniform in-plane electric field. Phys. Rev. B, 2021, 103(16): 165119 https://doi.org/10.1103/PhysRevB.103.165119
43	L. Cao J., A. Fertig H., Brey L.. Quantum geometric exciton drift velocity. Phys. Rev. B, 2021, 103(11): 115422 https://doi.org/10.1103/PhysRevB.103.115422
44	Q. Sui M., Chen G., Ma L., Y. Shan W., Tian D., Watanabe K., Taniguchi T., Jin X., Yao W., Xiao D., Zhang Y.. Gate-tunable topological valley transport in bilayer graphene. Nat. Phys., 2015, 11(12): 1027 https://doi.org/10.1038/nphys3485
45	Shimazaki Y., Yamamoto M., V. Borzenets I., Watanabe K., Taniguchi T., Tarucha S.. Generation and detection of pure valley current by electrically induced Berry curvature in bilayer graphene. Nat. Phys., 2015, 11(12): 1032 https://doi.org/10.1038/nphys3551
46	Ju L., Wang L., Cao T., Taniguchi T., Watanabe K., G. Louie S., Rana F., Park J., Hone J., Wang F., L. McEuen P.. Tunable excitons in bilayer graphene. Science, 2017, 358(6365): 907 https://doi.org/10.1126/science.aam9175
47	Y. Yu H., Yao W.. Luminescence anomaly of dipolar valley excitons in homobilayer semiconductor moire superlattices. Phys. Rev. X, 2021, 11(2): 021042 https://doi.org/10.1103/PhysRevX.11.021042
48	Y. Yu H., B. Liu G., Gong P., Xu X., Yao W.. Dirac cones and Dirac saddle points of bright excitons in monolayer transition metal dichalcogenides. Nat. Commun., 2014, 5(1): 3876 https://doi.org/10.1038/ncomms4876
49	H. He M., Rivera P., Van Tuan D., P. Wilson N., Yang M., Taniguchi T., Watanabe K., Yan J., G. Mandrus D., Yu H., Dery H., Yao W., Xu X.. Valley phonons and exciton complexes in a monolayer semiconductor. Nat. Commun., 2020, 11(1): 618 https://doi.org/10.1038/s41467-020-14472-0
50	Cudazzo P., V. Tokatly I., Rubio A.. Dielectric screening in two-dimensional insulators: Implications for excitonic and impurity states in graphane. Phys. Rev. B, 2011, 84(8): 085406 https://doi.org/10.1103/PhysRevB.84.085406
51	Danovich M., A. Ruiz-Tijerina D., J. Hunt R., Szyniszewski M., D. Drummond N., I. Fal’ko V.. Localized interlayer complexes in heterobilayer transition metal dichalcogenides. Phys. Rev. B, 2018, 97(19): 195452 https://doi.org/10.1103/PhysRevB.97.195452

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