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Microscopic theory for the light-induced anomalous Hall effect in graphene

S. A. Sato, J. W. McIver, M. Nuske, P. Tang, G. Jotzu, B. Schulte, H. Hübener, U. De Giovannini, L. Mathey, M. A. Sentef, A. Cavalleri, and A. Rubio
Phys. Rev. B 99, 214302 – Published 10 June 2019
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  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    We employ a quantum Liouville equation with relaxation to model the recently observed anomalous Hall effect in graphene irradiated by an ultrafast pulse of circularly polarized light. In the weak-field regime, we demonstrate that the Hall effect originates from an asymmetric population of photocarriers in the Dirac bands. By contrast, in the strong-field regime, the system is driven into a nonequilibrium steady state that is well described by topologically nontrivial Floquet-Bloch bands. Here, the anomalous Hall current originates from the combination of a population imbalance in these dressed bands together with a smaller anomalous velocity contribution arising from their Berry curvature. This robust and general finding enables the simulation of electrical transport from light-induced Floquet-Bloch bands in an experimentally relevant parameter regime and creates a pathway to designing ultrafast quantum devices with Floquet-engineered transport properties.

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    • Received 20 January 2019

    DOI:https://doi.org/10.1103/PhysRevB.99.214302

    ©2019 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Anomalous Hall effectUltrafast phenomena
    1. Physical Systems
    Floquet systemsGraphene
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    S. A. Sato1,2,*, J. W. McIver2, M. Nuske3, P. Tang2, G. Jotzu2, B. Schulte2, H. Hübener2, U. De Giovannini2, L. Mathey3,4, M. A. Sentef2, A. Cavalleri2, and A. Rubio2,5,†

    • 1Center for Computational Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, Japan
    • 2Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
    • 3Zentrum für Optische Quantentechnologien and Institut für Laserphysik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
    • 4The Hamburg Centre for Ultrafast Imaging, University of Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
    • 5Center for Computational Quantum Physics (CCQ), Flatiron Institute, 162 Fifth Avenue, New York, New York 10010, USA

    • *ssato@ccs.tsukuba.ac.jp
    • †angel.rubio@mpsd.mpg.de

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    Issue

    Vol. 99, Iss. 21 — 1 June 2019

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    Images

    • Figure 1
      Figure 1

      Light-induced Hall conductivity in the weak-field regime, EMIR=1 MV/m: (a) Theoretical Hall conductivity σxy as a function of μ. The full simulation result (red) and the population contribution (green) are shown. (b) The experimental Hall conductivity with the peak laser fluence of 0.01mJ/cm2 as shown in Ref. [36]. (c) Electronic structure of the Dirac Hamiltonian. Black-dashed lines show the original Dirac bands, while blue-solid lines show the tilted Dirac bands under a source-drain field with strength 0.2a.u. (d) Pump dichroism of conduction-band populations under source-drain bias along the y direction.

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    • Figure 2
      Figure 2

      Light-induced Hall conductivity in the strong field regime, EMIR=20 MV/m: (a) The theoretical Hall conductivity σxy as a function of μ. The full simulation result (red), the population contribution in the original Dirac band (green), and the natural-orbital population contribution (blue) are shown. (b) The experimental Hall conductivity with the peak laser fluence of 0.23mJ/cm2 as shown in Ref. [36]. (c) Floquet bands (red) and the original Dirac cone (black dashed). Outer (inner) edges of the resonant gap are indicated by blue (red) arrows. (d) Pump dichroism of natural-orbital population with source-drain bias along y direction.

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    • Figure 3
      Figure 3

      Relation of the steady state orbitals and the Floquet states: (a) Floquet fidelity, Sk, at the Dirac point, k=0, as a function of the driving field strength. The inset shows the Floquet fidelity in the BZ in the strong field regime where EMIR=20MV/m. (b) Comparison between the full conductivity σxy and the Berry curvature contribution σxyT. (c) The Berry curvature of the steady-state natural orbitals in the strong field regime. (d) The Berry curvature of the corresponding Floquet states.

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    • Figure 4
      Figure 4

      The Hall conductivity σxy as a function of chemical potential μ in the weak field regime. The results with different relaxation times, T1 and T2, are shown.

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    • Figure 5
      Figure 5

      The Hall conductivity σxy as a function of chemical potential μ in the strong field regime. The results with different relaxation times, T1 and T2, are shown.

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    • Figure 6
      Figure 6

      The Hall conductivity σxy as a function of chemical potential μ in the weak field regime. The results computed with the laser pulse (red solid) and the continuous-wave laser (blue dashed) are shown.

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    • Figure 7
      Figure 7

      The Hall conductivity σxy as a function of chemical potential μ in the weak field regime. The results computed with the laser pulse (red solid) and the continuous-wave laser (blue dashed) are shown.

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    • Figure 8
      Figure 8

      The Hall conductivity σxy as a function of applied field strength. The total conductivity is shown as the red line, while the topological contribution is shown as the blue line.

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