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Microwave-induced transitions between weak localization and weak antilocalization in graphene

Jorge Navarro-Giraldo1,*, Vinicius T. Santana1, Oleksii Laguta1, Dominik Bloos2, Anastasia Bauernfeind3, Marc Scheffler3, Valentyn Laguta4, D. Kurt Gaskill5, and Petr Neugebauer1,†

  • *Contact author: jorge.navarro@ceitec.vutbr.cz
  • †Contact author: petr.neugebauer@ceitec.vutbr.cz

Phys. Rev. B 113, 125408 – Published 4 March, 2026

DOI: https://doi.org/10.1103/8nz6-xgg5

Abstract

Weak localization (WL) and weak antilocalization (WAL) of electrons in a disordered conductor refer to the decrease or increase of the conductivity caused by the quantum interference of the electronic motion. In graphene, the nontrivial Berry phase and the chiral nature of the charge carriers imply that both phenomena can be observed, as it has been firmly established in direct current (DC) magnetotransport experiments. However, studies of alternating current (AC) magnetoconductivity at frequencies comparable to, and much higher than, the dephasing rate (τϕ−1) remain unexplored. Using a combination of transport and spectroscopic measurements at low (ω/2π<20GHz) and high (ω/2π=90–350GHz) frequencies compared to the dephasing rate, we demonstrate a frequency dependence in the optical magnetoconductivity of graphene in the limit ωτϕ≫1. We prove that spectroscopic measurements at low frequencies are well reproduced by the WL theory in the static limit (ω=0), with no appreciable changes in the magnetoconductivity at different frequencies as long as the condition ωτϕ<1 holds. At higher frequencies, the spectra exhibit transitions between WL and WAL induced solely by the external electromagnetic field, as they occur at constant temperature and carrier density. By analyzing the results with a WL model extended to finite frequencies, we observe that the usual decoherence mechanisms of inelastic scattering, in addition to the elastic processes of intervalley and long-range scattering, do not explain the observed behavior. Our results point to the need for a revised model for the decoherence dynamics in the limit ωτϕ≫1.

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References (61)

  1. E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, Scaling theory of localization: Absence of quantum diffusion in two dimensions, Phys. Rev. Lett. 42, 673 (1979).
  2. P. W. Anderson, E. Abrahams, and T. V. Ramakrishnan, Possible explanation of nonlinear conductivity in thin-film metal wires, Phys. Rev. Lett. 43, 718 (1979).
  3. D. J. Thouless, Maximum metallic resistance in thin wires, Phys. Rev. Lett. 39, 1167 (1977).
  4. Y. B. Vasilyev, G. Y. Vasileva, Y. L. Ivanov, S. Novikov, and S. N. Danilov, Temperature-dependent terahertz photoconductivity in epitaxial graphene, Appl. Phys. Lett. 105, 171105 (2014).
  5. S. Lara-Avila, A. Danilov, D. Golubev, H. He, K. H. Kim, R. Yakimova, F. Lombardi, T. Bauch, S. Cherednichenko, and S. Kubatkin, Towards quantum-limited coherent detection of terahertz waves in charge-neutral graphene, Nat. Astron. 3, 983 (2019).
  6. D. Wang, L. Yang, Z. Hu, F. Wang, Y. Yang, X. Pan, Z. Dong, S. Tian, L. Zhang, L. Han, M. Jiang, K. Tang, F. Dai, K. Zhang, W. Lu, X. Chen, L. Wang, and W. Hu, Antiferromagnetic semimetal terahertz photodetectors enhanced through weak localization, Nat. Commun. 16, 25 (2025).
  7. B. L. Altshuler, D. Khmel'nitzkii, A. I. Larkin, and P. A. Lee, Magnetoresistance and Hall effect in a disordered two-dimensional electron gas, Phys. Rev. B 22, 5142 (1980).
  8. L. P. Gor'kov, A. I. Larkin, and D. E. Khmel'nitskii, Particle conductivity in a two-dimentional random potential, JETP Lett. 30, 228 (1970).
  9. A. I. Larkin and D. E. Khmel'nitskй, Anderson localization and anomalous magnetoresistance at low temperatures, Sov. Phys. Usp. 25, 185 (1982).
  10. E. McCann, K. Kechedzhi, V. I. Fal'ko, H. Suzuura, T. Ando, and B. L. Altshuler, Weak-localization magnetoresistance and valley symmetry in graphene, Phys. Rev. Lett. 97, 146805 (2006).
  11. V. I. Fal'ko, K. Kechedzhi, E. McCann, B. L. Altshuler, H. Suzuura, and T. Ando, Weak localization in graphene, Solid State Commun. 143, 33 (2007).
  12. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, Two-dimensional gas of massless Dirac fermions in graphene, Nature (London) 438, 197 (2005).
  13. H. Suzuura and T. Ando, Crossover from symplectic to orthogonal class in a two-dimensional honeycomb lattice, Phys. Rev. Lett. 89, 266603 (2002).
  14. S. Hikami, A. I. Larkin, and Y. Nagaoka, Spin-orbit interaction and magnetoresistance in the two dimensional random system, Prog. Theor. Phys. 63, 707 (1980).
  15. D. K. Ki, D. Jeong, J. H. Choi, H. J. Lee, and K. S. Park, Inelastic scattering in a monolayer graphene sheet: A weak-localization study, Phys. Rev. B 78, 125409 (2008).
  16. F. V. Tikhonenko, D. W. Horsell, R. V. Gorbachev, and A. K. Savchenko, Weak localization in graphene flakes, Phys. Rev. Lett. 100, 056802 (2008).
  17. F. V. Tikhonenko, A. A. Kozikov, A. K. Savchenko, and R. V. Gorbachev, Transition between electron localization and antilocalization in graphene, Phys. Rev. Lett. 103, 226801 (2009).
  18. S. Lara-Avila, A. Tzalenchuk, S. Kubatkin, R. Yakimova, T. J. B. M. Janssen, K. Cedergren, T. Bergsten, and V. Fal'ko, Disordered Fermi liquid in epitaxial graphene from quantum transport measurements, Phys. Rev. Lett. 107, 166602 (2011).
  19. A. M. R. Baker, J. A. Alexander-Webber, T. Altebaeumer, T. J. B. M. Janssen, A. Tzalenchuk, S. Lara-Avila, S. Kubatkin, R. Yakimova, C. T. Lin, L. J. Li, and R. J. Nicholas, Weak localization scattering lengths in epitaxial, and CVD graphene, Phys. Rev. B 86, 235441 (2012).
  20. C. I. Liu, P. Wang, J. Mi, H. Y. Lee, Y. T. Wang, I. F. Ho, C. Zhang, X. Lin, R. E. Elmquist, and C. T. Liang, Weak localization and microwave-irradiated transport in multilayer epitaxial graphene grown on SiC, Mater. Res. Express 2, 115002 (2015).
  21. A. Drabińska, A. Wołoś, M. Kamińska, W. Strupinski, and J. M. Baranowski, Contactless microwave studies of weak localization in epitaxial graphene, Phys. Rev. B 86, 045421 (2012).
  22. A. Drabinska, M. K. Kami´nska, A. W. Woło´s, W. Strupinski, A. Wysmołek, W. Bardyszewski, R. Bo˙ Zek, and J. M. Baranowski, Enhancement of elastic and inelastic scattering lengths in quasi-free-standing graphene measured with contactless microwave spectroscopy, Phys. Rev. B 88, 165413 (2013).
  23. A. Wolos and A. Drabinska, Application of microwave spectroscopy to studies of electron transport properties, J. Cryst. Growth 401, 314 (2014).
  24. H. Linke, P. Omling, P. Ramvall, B. K. Meyer, M. Drechsler, C. Wetzel, R. Rudeloff, and F. Scholz, Application of microwave detection of the Shubnikov-de Haas effect in two-dimensional systems, J. Appl. Phys. 73, 7533 (1993).
  25. D. Bloos, J. Kunc, L. Kaeswurm, R. L. Myers-Ward, K. Daniels, M. Dejarld, A. Nath, J. V. Slageren, D. K. Gaskill, and P. Neugebauer, Contactless millimeter wave method for quality assessment of large area graphene, 2D Mater. 6, 035028 (2019).
  26. B. Altshuller, A. Aronov, and D. Khmelnitsky, Suppression of localization effects by the high frequency field and the Nyquist noise, Solid State Commun. 39, 619 (1981).
  27. V. I. Fal'ko, Effect of a microwave field on the quantum correction to the conductivity, Zh. Eksp. Teor. Fiz. 92, 704 (1987) [Sov. Phys. JETP 65, 397 (1987)].
  28. S. Wang and P. E. Lindelof, Microwave-enhanced phase-relaxation observed in weak-localization experiments, Phys. Rev. Lett. 59, 1156 (1987).
  29. S. Vitkalov, G. Gusyev, Z. Kvon, G. Leviev, and V. Falko, Dynamic action of microwave field on weak localization, Zh. Eksp. Teor. Fiz. 94, 376 (1988) [Sov. Phys. JETP 67, 1080 (1988)].
  30. A. A. Bykov, G. M. Gusev, and Z. D. Kvon, Dynamical suppression of weak localisation in silicon polycrystalline films by microwave radiation, J. Phys. C 21, L585 (1988).
  31. J. Liu and N. Giordano, Effect of an ac electric field on phase coherence in thin metal films, Phys. Rev. B 39, 9894 (1989).
  32. B. I. Belevtsev, J. Hasse, A. S. Anopchenko, and E. Y. Beliayev, Effect of an ac electric field on weak electron localization in Bi films, Low Temp. Phys. 22, 58 (1996).
  33. J. Wei, S. Pereverzev, and M. E. Gershenson, Microwave-induced dephasing in one-dimensional metal wires, Phys. Rev. Lett. 96, 086801 (2006).
  34. V. Eless, T. Yager, S. Spasov, S. Lara-Avila, R. Yakimova, S. Kubatkin, T. J. B. M. Janssen, A. Tzalenchuk, and V. Antonov, Phase coherence and energy relaxation in epitaxial graphene under microwave radiation, Appl. Phys. Lett. 103, 093103 (2013).
  35. G. U. Sumanasekera, B. D. Williams, D. V. Baxter, and J. P. Carini, Effects of weak localization and superconducting fluctuations on the frequency dependence of the conductivity in copper-semiconductor sandwiches, Phys. Rev. B 50, 2606 (1994).
  36. S. A. Vitkalov, High-frequency conductivity of two-dimensional electrons under weak-localization conditions, Zh. Eksp. Teor. Fiz. 109, 1846 (1996) [J. Exp. Theor. Phys. 82, 994 (1996)].
  37. S. A. Vitkalov, Microwave conductivity of 2D electron gas in AlGaAs/GaAs heterojunction in weak localization regime, Czech. J. Phys. 46, 2505 (1996).
  38. J. B. Pieper, J. C. Price, and J. M. Martinis, Measurement of the weak-localization complex conductivity at 1 GHz in disordered Ag wires, Phys. Rev. B 45, 3857 (1992).
  39. See Supplemental Material at http://link.aps.org/supplemental/10.1103/8nz6-xgg5 for details on DC transport, X-band spectroscopy, AC conductivity, and sub-THz spectroscopy characterization of various samples, which includes Refs. [40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50].
  40. E. N. Adams and T. D. Holstein, Quantum theory of transverse galvano-magnetic phenomena, J. Phys. Chem. Solids 10, 254 (1959).
  41. J. M. Schneider, M. Orlita, M. Potemski, and D. K. Maude, Consistent interpretation of the low-temperature magnetotransport in graphite using the Slonczewski-Weiss-McClure 3D band-structure calculations, Phys. Rev. Lett. 102, 166403 (2009).
  42. A. V. Kretinin, Y. Cao, J. S. Tu, G. L. Yu, R. Jalil, K. S. Novoselov, S. J. Haigh, A. Gholinia, A. Mishchenko, M. Lozada, T. Georgiou, C. R. Woods, F. Withers, P. Blake, G. Eda, A. Wirsig, C. Hucho, K. Watanabe, T. Taniguchi, A. K. Geim, et al., Electronic properties of graphene encapsulated with different two-dimensional atomic crystals, Nano Lett. 14, 3270 (2014).
  43. A. Ghirri, C. Bonizzoni, D. Gerace, S. Sanna, A. Cassinese, and M. Affronte, YBa2Cu3O7 microwave resonators for strong collective coupling with spin ensembles, Appl. Phys. Lett. 106, 184101 (2015).
  44. Z. Velluire-Pellat, E. Maréchal, N. Moulonguet, G. Saïz, G. C. Ménard, S. Kozlov, F. Couëdo, P. Amari, C. Medous, J. Paris, R. Hostein, J. Lesueur, C. Feuillet-Palma, and N. Bergeal, Hybrid quantum systems with high-Tc superconducting resonators, Sci. Rep. 13, 14366 (2023).
  45. W. Voesch, M. Thiemann, D. Bothner, M. Dressel, and M. Scheffler, On-chip ESR measurements of DPPH at mK temperatures, Phys. Procedia 75, 503 (2015).
  46. N. G. Ebensperger, M. Thiemann, M. Dressel, and M. Scheffler, Superconducting Pb stripline resonators in parallel magnetic field and their application for microwave spectroscopy, Supercond. Sci. Technol. 29, 115004 (2016).
  47. M. Javaheri Rahim, T. Lehleiter, D. Bothner, C. Krellner, D. Koelle, R. Kleiner, M. Dressel, and M. Scheffler, Metallic coplanar resonators optimized for low-temperature measurements, J. Phys. D 49, 395501 (2016).
  48. D. S. Rausch, M. Thiemann, M. Dressel, D. Bothner, D. Koelle, R. Kleiner, and M. Scheffler, Superconducting coplanar microwave resonators with operating frequencies up to 50 GHz, J. Phys. D 51, 465301 (2018).
  49. E. Silva, R. Marcon, R. Fastampa, M. Giura, S. Sarti, and G. Ghigo, Field dependent microwave resistivity in YBa2Cu3O7−δ, J. Low Temp. Phys. 131, 871 (2003).
  50. D. Bothner, T. Gaber, M. Kemmler, D. Koelle, R. Kleiner, S. Wünsch, and M. Siegel, Magnetic hysteresis effects in superconducting coplanar microwave resonators, Phys. Rev. B 86, 014517 (2012).
  51. J. C. Kotsakidis, G. M. Stephen, M. DeJarld, R. L. Myers-Ward, K. M. Daniels, D. K. Gaskill, M. S. Fuhrer, R. E. Butera, A. T. Hanbicki, and A. L. Friedman, Charged impurity scattering and electron–electron interactions in large-area hydrogen intercalated bilayer graphene, ACS Applied Materials & Interfaces 16, 61194 (2024).
  52. M. Scheffler, K. Schlegel, C. Clauss, D. Hafner, C. Fella, M. Dressel, M. Jourdan, J. Sichelschmidt, C. Krellner, C. Geibel, and F. Steglich, Microwave spectroscopy on heavy‐fermion systems: Probing the dynamics of charges and magnetic moments, Physica Status Solidi (b) 250, 439 (2013).
  53. O. Laguta, A. Sojka, A. Marko, and P. Neugebauer, Rapid scan ESR: A versatile tool for the spin relaxation studies at (sub)THz frequencies, Appl. Phys. Lett. 120, 120502 (2022).
  54. A. Sojka, M. Sedivy, A. Lagin, A. Gabris, T. Laznicka, V. T. Santana, O. Laguta, and P. Neugebauer, Sample holders for sub-THz electron spin resonance spectroscopy, IEEE Trans. Instrum. Meas. 71, 1 (2022).
  55. L. A. Pardi, J. Krzystek, J. Telser, and L.-C. Brunel, Multifrequency EPR spectra of molecular oxygen in solid air, J. Magn. Reson. 146, 375 (2000).
  56. C. Riedl, C. Coletti, and U. Starke, Structural and electronic properties of epitaxial graphene on SiC(0 0 0 1): A review of growth, characterization, transfer doping and hydrogen intercalation, J. Phys. D 43, 374009 (2010).
  57. J. A. Robinson, M. Hollander, M. LaBella, K. A. Trumbull, R. Cavalero, and D. W. Snyder, Epitaxial graphene transistors: Enhancing performance via hydrogen intercalation, Nano Lett. 11, 3875 (2011).
  58. L. Nyakiti, V. Wheeler, N. Garces, R. Myers-Ward, C. Eddy, and D. Gaskill, Enabling graphene-based technologies: Toward wafer-scale production of epitaxial graphene, MRS Bull. 37, 1149 (2012).
  59. K. M. Daniels, M. M. Jadidi, A. B. Sushkov, A. Nath, A. K. Boyd, K. Sridhara, H. D. Drew, T. E. Murphy, R. L. Myers-Ward, and D. K. Gaskill, Narrow plasmon resonances enabled by quasi-freestanding bilayer epitaxial graphene, 2D Mater. 4, 025034 (2017).
  60. P. Neugebauer, D. Bloos, R. Marx, P. Lutz, M. Kern, D. Aguilà, J. Vaverka, O. Laguta, C. Dietrich, R. Clérac, and J. V. Slageren, Ultra-broadband EPR spectroscopy in field and frequency domains, Phys. Chem. Chem. Phys. 20, 15528 (2018).
  61. J. Navarro-Giraldo, V. Santana, O. Laguta, D. Bloos, A. Bauernfeind, M. Scheffler, V. Laguta, D. K. Gaskill, and P. Neugebauer, Dataset: Microwave-induced transitions between weak localization and weak antilocalization in graphene, Zenodo (2025),https://doi.org/10.5281/zenodo.17395915.

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