Exciton polaritons in transition-metal dichalcogenides and their direct excitation via energy transfer

Physical Review B - Condensed Matter and Materials Physics

Volumn 92, Issue 7, 2015, Pages

  Gartstein, Yuri N ^a   Li, Xiao ^a,b   Zhang, Chuanwei ^a  

^a UNIVERSITY OF TEXAS AT DALLAS   (United States)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84941131049     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.92.075445     Document Type: Article

References (52)

1. A. K. Geim and I. V. Grigorieva, Van der Waals heterostructures, Nature 499, 419 (2013). NATUAS 0028-0836 10.1038/nature12385
2. X. Xu, W. Yao, D. Xiao, and T. F. Heinz, Spin and pseudospins in layered transition metal dichalcogenides, Nat. Phys. 10, 343 (2014). 1745-2473 10.1038/nphys2942
3. K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, Atomically Thin (Equation presented): A New Direct-Gap Semiconductor, Phys. Rev. Lett. 105, 136805 (2010). PRLTAO 0031-9007 10.1103/PhysRevLett.105.136805
4. D. Xiao, G.-B. Liu, W. Feng, X. Xu, and W. Yao, Coupled Spin and Valley Physics in Monolayers of (Equation presented) and Other Group-VI Dichalcogenides, Phys. Rev. Lett. 108, 196802 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.108.196802
5. H. Zeng, J. Dai, W. Yao, D. Xiao, and X. Cui, Valley polarization in (Equation presented) monolayers by optical pumping, Nat. Nanotech. 7, 490 (2012). 1748-3387 10.1038/nnano.2012.95
6. K. F. Mak, K. He, J. Shan, and T. F. Heinz, Control of valley polarization in monolayer (Equation presented) by optical helicity, Nat. Nanotech. 7, 494 (2012). 1748-3387 10.1038/nnano.2012.96
7. T. Cao, G. Wang, W. Han, H. Ye, C. Zhu, J. Shi, Q. Niu, P. Tan, E. Wang, B. Liu, and J. Feng, Valley-selective circular dichroism of monolayer molybdenum disulphide, Nat. Commun. 3, 887 (2012). 2041-1723 10.1038/ncomms1882
8. J. S. Ross, S. Wu, H. Yu, N. J. Ghimire, A. M. Jones, G. Aivazian, J. Yan, D. G. Mandrus, D. Xiao, W. Yao, and X. Xu, Electrical control of neutral and charged excitons in a monolayer semiconductor, Nat. Commun. 4, 1474 (2013). 2041-1723 10.1038/ncomms2498
9. Y. Zhang, T.-R. Chang, B. Zhou, Y.-T. Cui, H. Yan, Z. Liu, F. Schmitt, J. Lee, R. Moore, Y. Chen, H. Lin, H.-T. Jeng, S.-K. Mo, Z. Hussain, A. Bansil, and Z.-X. Shen, Direct observation of the transition from indirect to direct bandgap in atomically thin epitaxial (Equation presented), Nat. Nanotech 9, 111 (2014). 1748-3387 10.1038/nnano.2013.277
10. K. F. Mak, K. He, C. Lee, G. H. Lee, J. Hone, T. F. Heinz, and J. Shan, Tightly bound trions in monolayer (Equation presented), Nat. Mater. 12, 207 (2013). 1476-1122 10.1038/nmat3505
11. J. Feng, X. Qian, C.-W. Huang, and J. Li, Strain-engineered artificial atom as a broad-spectrum solar energy funnel, Nat. Photon. 6, 866 (2012). 1749-4885 10.1038/nphoton.2012.285
12. D. Lagarde, L. Bouet, X. Marie, C. R. Zhu, B. L. Liu, T. Amand, P. H. Tan, and B. Urbaszek, Carrier and Polarization Dynamics in Monolayer (Equation presented), Phys. Rev. Lett. 112, 047401 (2014). PRLTAO 0031-9007 10.1103/PhysRevLett.112.047401
13. K. F. Mak, K. L. McGill, J. Park, and P. L. McEuen, The Valley Hall effect in (Equation presented) transistors, Science 344, 1489 (2014). SCIEAS 0036-8075 10.1126/science.1250140
14. B. W. H. Baugher, H. O. H. Churchill, Y. Yang, and P. Jarillo-Herrero, Intrinsic electronic transport properties of high-quality monolayer and bilayer (Equation presented), Nano Lett. 13, 4212 (2013). NALEFD 1530-6984 10.1021/nl401916s
15. X. Li, F. Zhang, and Q. Niu, Unconventional Quantum Hall Effect and Tunable Spin Hall Effect in Dirac materials: Application to an Isolated (Equation presented) Trilayer, Phys. Rev. Lett. 110, 066803 (2013). PRLTAO 0031-9007 10.1103/PhysRevLett.110.066803
16. R.-L. Chu, X. Li, S. Wu, Q. Niu, W. Yao, X. Xu, and C. Zhang, Valley-splitting and valley-dependent inter-Landau-level optical transitions in monolayer (Equation presented) quantum Hall systems, Phys. Rev. B 90, 045427 (2014). PRBMDO 1098-0121 10.1103/PhysRevB.90.045427
17. A. M. Jones, H. Yu, J. S. Ross, P. Klement, N. J. Ghimire, J. Yan, D. G. Mandrus, W. Yao, and X. Xu, Spin-layer locking effects in optical orientation of exciton spin in bilayer (Equation presented), Nat. Phys. 10, 130 (2014). 1745-2473 10.1038/nphys2848
18. G. Aivazian, Z. Gong, A. M. Jones, R.-L. Chu, J. Yan, D. G. Mandrus, C. Zhang, D. Cobden, W. Yao, and X. Xu, Magnetic control of valley pseudospin in monolayer (Equation presented), Nat. Phys. 11, 148 (2015). 1745-2473 10.1038/nphys3201
19. A. M. Jones, H. Yu, N. J. Ghimire, S. Wu, G. Aivazian, J. S. Ross, B. Zhao, J. Yan, D. G. Mandrus, D. Xiao, W. Yao, and X. Xu, Optical generation of excitonic valley coherence in monolayer (Equation presented), Nat. Nanotech. 8, 634 (2013). 1748-3387 10.1038/nnano.2013.151
20. S. Wu, J. S. Ross, G.-B. Liu, G. Aivazian, A. Jones, Z. Fei, W. Zhu, D. Xiao, W. Yao, D. Cobden, and X. Xu, Electrical tuning of valley magnetic moment through symmetry control in bilayer (Equation presented), Nat. Phys. 9, 149 (2013). 1745-2473 10.1038/nphys2524
21. D. Y. Qiu, F. H. da Jornada, and S. G. Louie, Optical Spectrum of (Equation presented): Many-Body Effects and Diversity of Exciton States, Phys. Rev. Lett. 111, 216805 (2013). PRLTAO 0031-9007 10.1103/PhysRevLett.111.216805
22. F. Hüser, T. Olsen, and K. S. Thygesen, How dielectric screening in two-dimensional crystals affects the convergence of excited-state calculations: Monolayer (Equation presented), Phys. Rev. B 88, 245309 (2013). PRBMDO 1098-0121 10.1103/PhysRevB.88.245309
23. H. Yu, G. Liu, P. Gong, X. Xu, and W. Yao, Bright excitons in monolayer transition metal dichalcogenides: From Dirac cones to Dirac saddle points, Nat. Commun. 5, 3876 (2014). 10.1038/ncomms4876
24. G.-B. Liu, W.-Y. Shan, Y. Yao, W. Yao, and D. Xiao, Three-band tight-binding model for monolayers of group-VIB transition metal dichalcogenides, Phys. Rev. B 88, 085433 (2013). PRBMDO 1098-0121 10.1103/PhysRevB.88.085433
25. T. C. Berkelbach, M. S. Hybertsen, and D. R. Reichman, Theory of neutral and charged excitons in monolayer transition metal dichalcogenides, Phys. Rev. B 88, 045318 (2013). PRBMDO 1098-0121 10.1103/PhysRevB.88.045318
26. G. Berghauser and E. Malic, Analytical approach to excitonic properties of (Equation presented), Phys. Rev. B 89, 125309 (2014). PRBMDO 1098-0121 10.1103/PhysRevB.89.125309
27. A. Ramasubramaniam, Large excitonic effects in monolayers of molybdenum and tungsten dichalcogenides, Phys. Rev. B 86, 115409 (2012). PRBMDO 1098-0121 10.1103/PhysRevB.86.115409
28. F. Wu, F. Qu, and A. H. MacDonald, Exciton band structure of monolayer (Equation presented), Phys. Rev. B 91, 075310 (2015). PRBMDO 1098-0121 10.1103/PhysRevB.91.075310
29. H. Yu, X. Cui, X. Xu, and W. Yao, Valley excitons in two-dimensional semiconductors, Natl. Sci. Rev. 2, 57 (2015). 2095-5138 10.1093/nsr/nwu078
30. P. K. Basu, Theory of Optical Processes in Semiconductors, Bulk and Microstructures (Clarendon, Oxford, 1997).
31. H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors (World Scientific, Singapore, 2004).
32. X. Liu, T. Galfsky, Z. Sun, F. Xia, E. Lin, Y. Lee, S. K. éna-Cohen, and V. M. Menon, Strong light-matter coupling in two-dimensional atomic crystals, Nat. Photon. 9, 30 (2015). 1749-4885 10.1038/nphoton.2014.304
33. L. C. Andreani and F. Bassani, Exchange interaction and polariton effects in quantum-well excitons, Phys. Rev. B 41, 7536 (1990). PRBMDO 0163-1829 10.1103/PhysRevB.41.7536
34. R. Girlanda, S. Savasta, and B. Azzerboni, Quantum description of the electromagnetic field in a confined polarizable medium, Riv. Nuovo Cim. 21, 1 (1998). 1826-9850 10.1007/BF02874617
35. A shorter version of this paper is available as an eprint: Y. N. Gartstein, X. Li, and C. Zhang, Exciton polaritons in transition-metal dichalcogenides and their direct excitation via energy transfer, arXiv:1502.00905.
36. V. M. Agranovich and V. L. Ginzburg, Crystal Optics with Spatial Dispersion, and Excitons (Springer, Berlin, 1984).
37. V. M. Agranovich, Excitations in Organic Solids (Oxford University, Oxford, 2009).
38. F. Prins, A. J. Goodman, and W. A. Tisdale, Reduced dielectric screening and enhanced energy transfer in single- and few-layer (Equation presented), Nano Lett. 14, 6087 (2014). NALEFD 1530-6984 10.1021/nl5019386
39. D. Prasai, A. R. Klots, A. K. M. Newaz, J. S. Niezgoda, N. J. Orfield, C. A. Escobar, A. Wynn, A. Efimov, G. K. Jennings, S. J. Rosenthal, and K. I. Bolotin, Electrical control of near-field energy transfer between quantum dots and two-dimensional semiconductors, Nano Lett. 15, 4374 (2015). NALEFD 1530-6984 10.1021/acs.nanolett.5b00514
40. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).
41. Y. N. Gartstein and V. M. Agranovich, Excitons in long molecular chains near the reflecting interface, Phys. Rev. B 76, 115329 (2007). PRBMDO 1098-0121 10.1103/PhysRevB.76.115329
42. The real part of the diagonal elements (Equation presented) in integral (11) would formally diverge with interaction (12) due to the short-distance (Equation presented) behavior of the electrostatic dipole-dipole coupling. There is no divergence, however, in the off-diagonal elements. Of course, at short distances the point-dipole description does not apply, whereas the actual short-range Coulomb interactions would be determined by the detailed behavior of electron wave functions. The divergent electrostatic term needs therefore to be separated in the calculation. The separated term corresponds to a (Equation presented) shift (Equation presented) in the self-energy matrix and represents an overall renormalization of the exciton energies due to short-range interactions that we are not interested in.
43. G. Moody, C. K. Dass, K. Hao, C. Chen, L. Li, A. Singh, K. Tran, G. Clark, X. Xu, G. Bergauser, E. Malic, A. Knorr, and X. Li, Intrinsic exciton linewidth in monolayer transition metal dichalcogenides, arXiv:1410.3143.
44. We restrict our attention here to the layer with the in-plane polarizability only. When taking into account the polarizability perpendicular to the layer, the expression for the reflection coefficient (Equation presented) is more involved than Eq. (19).
45. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, Cambridge, England, 2006).
46. M. R. Philpott, Effect of surface plasmons on transitions in molecules, J. Chem. Phys. 62, 1812 (1975). JCPSA6 0021-9606 10.1063/1.430708
47. R. R. Chance, A. Prock, and R. Silbey, Molecular fluorescence and energy transfer near interfaces, in Advances in Chemical Physics, Vol. 37, edited by S. A. Rice and I. Prigogine (Wiley, New York, 1978), p. 1.
48. J. M. Gordon and Y. N. Gartstein, Dielectric polarization, anisotropy and nonradiative energy transfer into nanometre-scale thin semiconducting films, J. Phys.: Condens. Matter 25, 425302 (2013). JCOMEL 0953-8984 10.1088/0953-8984/25/42/425302
49. L. Gaudreau, K. J. Tielrooij, G. E. D. K. Prawiroatmodjo, J. Osmond, F. J. G. de Abajo, and F. H. L. Koppens, Universal distance-scaling of nonradiative energy transfer to graphene, Nano Lett. 13, 2030 (2013). NALEFD 1530-6984 10.1021/nl400176b
50. V. M. Agranovich, Y. N. Gartstein, and M. Litinskaya, Hybrid resonant organic-inorganic nanostructures for optoelectronic applications, Chem. Rev. 111, 5179 (2011). CHREAY 0009-2665 10.1021/cr100156x
51. J. Feldmann, G. Peter, E. O. Göbel, P. Dawson, K. Moore, C. Foxon, and R. J. Elliott, Linewidth Dependence of Radiative Exciton Lifetimes in Quantum Wells, Phys. Rev. Lett. 59, 2337 (1987). PRLTAO 0031-9007 10.1103/PhysRevLett.59.2337
52. Surface Polaritons, edited by V. M. Agranovich and D. L. Mills (North Holland, Amsterdam, 1982).