Dominant role of two-photon vertex in nonlinear response in two-dimensional Dirac systems
Source abstract
Abstract
Abstract We show that the standard concepts of nonlinear response to electromagnetic fields break down in two-dimensional Dirac systems, like graphene, in the quantum regime close to the Dirac point. We present a compelling many-body theory for nonlinear transport focusing on disorder scattering as a benchmark example. We show that, although the diamagnetic two-photon vertex is absent at the non-interacting level, disorder effects give rise to a self-generation of such two-photon vertex surviving even in the clean limit. We predict that the two-photon vertex self-generation is present only in two dimensions. The impact of such a striking scenario on the nonlinear quantum transport is discussed, predicting a huge enhancement of third-order dc conductivity comparing to the common models.
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Research context
OpenAlex topics: Topological Materials and Phenomena · Graphene research and applications · Quantum and electron transport phenomena
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References (61)
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1. Castro Neto, A. H., Guinea, F., Peres, N. M. R., Novoselov, K. S. & Geim, A. K. The electronic properties of graphene. Rev. Mod. Phys. 81, 109–162 (2009).10.1103/RevModPhys.81.109 ↗
2. Wehling, T., Black-Schaffer, A. & Balatsky, A. Dirac materials. Adv. Phys. 63, 1–76 (2014).10.1080/00018732.2014.927109 ↗
3. Armitage, N. P., Mele, E. J. & Vishwanath, A. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 90, 015001 (2018).10.1103/RevModPhys.90.015001 ↗
4. Katsnelson, M. Graphene: Carbon in Two Dimensions (Cambridge University Press, 2012).10.1017/CBO9781139031080 ↗
5. Das Sarma, S., Adam, S., Hwang, E. H. & Rossi, E. Electronic transport in two-dimensional graphene. Rev. Mod. Phys. 83, 407–470 (2011).10.1103/RevModPhys.83.407 ↗
6. Peres, N. M. R. Colloquium: The transport properties of graphene: an introduction. Rev. Mod. Phys. 82, 2673–2700 (2010).10.1103/RevModPhys.82.2673 ↗
7. Hendry, E., Hale, P. J., Moger, J., Savchenko, A. K. & Mikhailov, S. A. Coherent nonlinear optical response of graphene. Phys. Rev. Lett. 105, 097401 (2010).10.1103/PhysRevLett.105.097401 ↗
8. Zhang, H. et al. Z-scan measurement of the nonlinear refractive index of graphene. Opt. Lett. 37, 1856–1858 (2012).10.1364/OL.37.001856 ↗
9. Kumar, N. et al. Third harmonic generation in graphene and few-layer graphite films. Phys. Rev. B 87, 121406(R) (2013).10.1103/PhysRevB.87.121406 ↗
10. Woodward, R. I. et al. Characterization of the second- and third-order nonlinear optical susceptibilities of monolayer MoS2using multiphoton microscopy. 2D Materials 4, 011006 (2016).10.1088/2053-1583/4/1/011006 ↗
11. Soavi, G. et al. Broadband, electrically tunable third-harmonic generation in graphene. Nat. Nanotechnol. 13, 583–588 (2018).10.1038/s41565-018-0145-8 ↗
12. Hafez, H. A. et al. Extremely efficient terahertz high-harmonic generation in graphene by hot Dirac fermions. Nature 561, 507–511 (2018).10.1038/s41586-018-0508-1 ↗
13. Soavi, G. et al. Hot electrons modulation of third-harmonic generation in graphene. ACS Photon. 6, 2841–2849 (2019).10.1021/acsphotonics.9b00928 ↗
14. Ma, Q. et al. Observation of the nonlinear hall effect under time-reversal-symmetric conditions. Nature 565, 337–342 (2019).10.1038/s41586-018-0807-6 ↗
15. Ma, J. et al. Nonlinear photoresponse of type-II Weyl semimetals. Nat. Mater. 18, 476–481 (2019).10.1038/s41563-019-0296-5 ↗
16. de Juan, F., Grushin, A. G., Morimoto, T. & Moore, J. E. Quantized circular photogalvanic effect in Weyl semimetals. Nature Communications 8, 15995 (2017).10.1038/ncomms15995 ↗
17. Rostami, H. & Polini, M. Nonlinear anomalous photocurrents in Weyl semimetals. Phys. Rev. B 97, 195151 (2018).10.1103/PhysRevB.97.195151 ↗
18. Ma, J. et al. Nonlinear photoresponse of type-II Weyl semimetals. Nat. Mater. 18, 476–481 (2019).10.1038/s41563-019-0296-5 ↗
19. Cheng, B. et al. Efficient terahertz harmonic generation with coherent acceleration of electrons in the dirac semimetal cd3as2. Phys. Rev. Lett. 124, 117402 (2020).10.1103/PhysRevLett.124.117402 ↗
20. Cheng, J. L., Sipe, J. E. & Wu, S. W. Third-order optical nonlinearity of three-dimensional massless Dirac fermions. ACS Photon. 7, 2515–2526 (2020).10.1021/acsphotonics.0c00836 ↗
21. Sukhachov, P. O. & Rostami, H. Acoustogalvanic effect in Dirac and Weyl semimetals. Phys. Rev. Lett. 124, 126602 (2020).10.1103/PhysRevLett.124.126602 ↗
22. Mikhailov, S. A. Non-linear electromagnetic response of graphene. Europhys. Lett. 79, 27002 (2007).10.1209/0295-5075/79/27002 ↗
23. Cheng, J. L., Vermeulen, N. & Sipe, J. E. Third order optical nonlinearity of graphene. N J. Phys. 16, 053014 (2014).10.1088/1367-2630/16/5/053014 ↗
24. Cheng, J. L., Vermeulen, N. & Sipe, J. E. Numerical study of the optical nonlinearity of doped and gapped graphene: From weak to strong field excitation. Phys. Rev. B 92, 235307 (2015).10.1103/PhysRevB.92.235307 ↗
25. Cheng, J. L., Vermeulen, N. & Sipe, J. E. Third-order nonlinearity of graphene: effects of phenomenological relaxation and finite temperature. Phys. Rev. B 91, 235320 (2015).10.1103/PhysRevB.91.235320 ↗
26. Mikhailov, S. A. Quantum theory of the third-order nonlinear electrodynamic effects of graphene. Phys. Rev. B 93, 085403 (2016).10.1103/PhysRevB.93.085403 ↗
27. Rostami, H. & Polini, M. Theory of third-harmonic generation in graphene: a diagrammatic approach. Phys. Rev. B 93, 161411(R) (2016).10.1103/PhysRevB.93.161411 ↗
28. Rostami, H., Katsnelson, M. I. & Polini, M. Theory of plasmonic effects in nonlinear optics: the case of graphene. Phys. Rev. B 95, 035416 (2017).10.1103/PhysRevB.95.035416 ↗
29. Mikhailov, S. A. Theory of the strongly nonlinear electrodynamic response of graphene: a hot electron model. Phys. Rev. B 100, 115416 (2019).10.1103/PhysRevB.100.115416 ↗
30. Principi, A., Bandurin, D., Rostami, H. & Polini, M. Pseudo-Euler equations from nonlinear optics: Plasmon-assisted photodetection beyond hydrodynamics. Phys. Rev. B 99, 075410 (2019).10.1103/PhysRevB.99.075410 ↗
31. Hafez, H. A. et al. Terahertz nonlinear optics of graphene: from saturable absorption to high-harmonics generation. Adv. Opt. Mater. 8, 1900771 (2020).10.1002/adom.201900771 ↗
32. Rostami, H. & Juričić, V. Probing quantum criticality using nonlinear hall effect in a metallic Dirac system. Phys. Rev. Res. 2, 013069 (2020).10.1103/PhysRevResearch.2.013069 ↗
33. Giuliani, G. & Vignale, G. Quantum Theory of the Electron Liquid (Cambridge University Press, Cambridge, 2005).10.1017/CBO9780511619915 ↗
34. Goldman, S. P. & Drake, G. W. F. Relativistic sum rules and integral properties of the Dirac equation. Phys. Rev. A 25, 2877–2881 (1982).10.1103/PhysRevA.25.2877 ↗
35. Cenni, R. On the f sum rule and its extensions. Nuclear Phys. A 696, 605–622 (2001).10.1016/S0375-9474(01)01151-4 ↗
36. Sabio, J., Nilsson, J. & Castro Neto, A. H. f-sum rule and unconventional spectral weight transfer in graphene. Phys. Rev. B 78, 075410 (2008).10.1103/PhysRevB.78.075410 ↗
37. Bistritzer, R. & MacDonald, A. H. Hydrodynamic theory of transport in doped graphene. Phys. Rev. B 80, 085109 (2009).10.1103/PhysRevB.80.085109 ↗
38. Sun, Z., Basov, D. N. & Fogler, M. M. Third-order optical conductivity of an electron fluid. Phys. Rev. B 97, 075432 (2018).10.1103/PhysRevB.97.075432 ↗
39. Sun, Z., Basov, D. N. & Fogler, M. M. Universal linear and nonlinear electrodynamics of a Dirac fluid. Proc. Natl Acad. Sci. USA 115, 3285–3289 (2018).10.1073/pnas.1717010115 ↗
40. Parker, D. E., Morimoto, T., Orenstein, J. & Moore, J. E. Diagrammatic approach to nonlinear optical response with application to weyl semimetals. Phys. Rev. B 99, 045121 (2019).10.1103/PhysRevB.99.045121 ↗
41. Avetissian, H. K. & Mkrtchian, G. F. Impact of electron-electron coulomb interaction on the high harmonic generation process in graphene. Phys. Rev. B 97, 115454 (2018).10.1103/PhysRevB.97.115454 ↗
42. Cheng, J. L., Sipe, J. E. & Guo, C. Third harmonic generation of undoped graphene in hartree-fock approximation. Phys. Rev. B 100, 245433 (2019).10.1103/PhysRevB.100.245433 ↗
43. Shen, Y. The Principles of Nonlinear Optics (Wiley, New York, 1984).
44. Boyd, R. Nonlinear Optics (Academic Press, Cambridge, 2008).
45. Shon, N. H. & Ando, T. Quantum transport in two-dimensional graphite system. J. Phys. Soc. Jpn. 67, 2421–2429 (1998).10.1143/JPSJ.67.2421 ↗
46. Ando, T., Zheng, Y. & Suzuura, H. Dynamical conductivity and zero-mode anomaly in honeycomb lattices. J. Phys. Soc. Jpn. 71, 1318–1324 (2002).10.1143/JPSJ.71.1318 ↗
47. Rostami, H. & Cappelluti, E. Impurity effects and bandgap closing in massive Dirac systems. Phys. Rev. B 96, 054205 (2017).10.1103/PhysRevB.96.054205 ↗
48. Aleiner, I. L. & Efetov, K. B. Effect of disorder on transport in graphene. Phys. Rev. Lett. 97, 236801 (2006).10.1103/PhysRevLett.97.236801 ↗
49. Castro Neto, A. H., Guinea, F., Peres, N. M. R., Novoselov, K. S. & Geim, A. K. The electronic properties of graphene. Rev. Mod. Phys. 81, 109–162 (2009).10.1103/RevModPhys.81.109 ↗
50. González, J., Guinea, F. & Vozmediano, M. A. H. Marginal-fermi-liquid behavior from two-dimensional coulomb interaction. Phys. Rev. B 59, R2474–R2477 (1999).10.1103/PhysRevB.59.R2474 ↗
51. Vozmediano, M. A. H. Renormalization group aspects of graphene. Philos. Trans. R. Soc. A 369, 2625–2642 (2011).10.1098/rsta.2010.0383 ↗
52. Mishchenko, E. G. Effect of electron-electron interactions on the conductivity of clean graphene. Phys. Rev. Lett. 98, 216801 (2007).10.1103/PhysRevLett.98.216801 ↗
53. Leibbrandt, G. Introduction to the technique of dimensional regularization. Rev. Mod. Phys. 47, 849–876 (1975).10.1103/RevModPhys.47.849 ↗
54. Peskin, M. E. An Introduction To Quantum Field Theory, 1st edn. (CRC Press, 1995).
55. Baym, G. & Kadanoff, L. P. Conservation laws and correlation functions. Phys. Rev. 124, 287–299 (1961).10.1103/PhysRev.124.287 ↗
56. Kadanoff, L. P. & Baym, G. Quantum Statistical Mechanics, 1st edn. (W.A. Benjamin, 1962).
57. Cappelluti, E. & Benfatto, L. Vertex renormalization in dc conductivity of doped chiral graphene. Phys. Rev. B 79, 035419 (2009).10.1103/PhysRevB.79.035419 ↗
58. Dorgan, V. E., Behnam, A., Conley, H. J., Bolotin, K. I. & Pop, E. High-field electrical and thermal transport in suspended graphene. Nano Letters 13, 4581–4586 (2013).10.1021/nl400197w ↗
59. Berciaud, S. et al. Electron and optical phonon temperatures in electrically biased graphene. Phys. Rev. Lett. 104, 227401 (2010).10.1103/PhysRevLett.104.227401 ↗
60. Meric, I. et al. Current saturation in zero-bandgap, top-gated graphene field-effect transistors. Nat. Nanotechnol. 3, 654–659 (2008).10.1038/nnano.2008.268 ↗
61. Horng, J. et al. Drude conductivity of Dirac fermions in graphene. Phys. Rev. B 83, 165113 (2011).10.1103/PhysRevB.83.165113 ↗