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  • Letter
  • Open Access

Coherent forward scattering peak and multifractality

Maxime Martinez1, Gabriel Lemarié1,2,3, Bertrand Georgeot1, Christian Miniatura2,3,4,5,6, and Olivier Giraud7

  • 1Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS, Toulouse, France
  • 2MajuLab, CNRS-UCA-SU-NUS-NTU International Joint Research Unit, Singapore
  • 3Centre for Quantum Technologies, National University of Singapore, 117543 Singapore, Singapore
  • 4Université Côte d'Azur, CNRS, INPHYNI, Nice, France
  • 5Department of Physics, National University of Singapore, 117542 Singapore, Singapore
  • 6School of Physical and Mathematical Sciences, Nanyang Technological University, 637371 Singapore, Singapore
  • 7Université Paris-Saclay, CNRS, LPTMS, 91405 Orsay, France

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Phys. Rev. Research 3, L032044 – Published 13 August, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L032044

Abstract

It has recently been shown that interference effects in disordered systems give rise to two nontrivial structures: the coherent backscattering (CBS) peak, a well-known signature of interference effects in the presence of disorder, and the coherent forward scattering (CFS) peak, which emerges when Anderson localization sets in. We study here the CFS effect in the presence of quantum multifractality, a fundamental property of several systems, such as the Anderson model at the metal-insulator transition. We focus on Floquet systems, and find that the CFS peak shape and its peak height dynamics are generically controlled by the multifractal dimensions D1 and D2, and by the spectral form factor. We check our results using a one-dimensional Floquet system whose states have multifractal properties controlled by a single parameter. Our predictions are fully confirmed by numerical simulations and analytic perturbation expansions on this model. Our results, which we believe to be generic, provide an original and direct way to detect and characterize multifractality in experimental systems.

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Outline

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Phys. Rev. Research 3, L032044– Published 13 August, 2021
  • Received 5 November 2020
  • Revised 2 July 2021
  • Accepted 28 July 2021
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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