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Topological nature of nonlinear optical effects in solids

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Science Advances  20 May 2016:
Vol. 2, no. 5, e1501524
DOI: 10.1126/sciadv.1501524


  • Fig. 1 Schematic picture of the Floquet two band model.

    Under the drive of monochromatic light, energy bands evolve into Floquet bands, which describe Bloch states dressed with photons. When two Floquet bands cross, they show an anticrossing. The nonequilibrium steady state (and hence, NLORs) can be captured by studying this anticrossing of two Floquet bands.

  • Fig. 2 Vector field Embedded Imagefor the 1D model, which preserves TRS and breaks inversion symmetry.

    We plot (Embedded Image) in the parameter space (k, Q2) with Q1 = 1, Embedded Image = 0. Inset is a plot of distribution of the “flux” Embedded Image defined in the text, which is related to the third-order nonlinear responses.

  • Fig. 3 Vector fields Embedded Image for the 1D model, which break both TRS and inversion symmetry.

    (A and B) We plot (Embedded Image) with Q1 = 1, Embedded Image = 0.1 (A) and (Embedded Image) with Q1 = 1, Q2 = 0.4 (B).

  • Fig. 4 Transformation laws of Berry connection and Berry curvature.

    We consider the geometry in the space spanned by the momentum k and the parameter Q quantifying the inversion breaking and the geometry in the momentum space with kx and ky (or Embedded Image). Here, Q is even under T, whereas k and Embedded Image are odd under T. All Q, Embedded Image and k are odd under P.

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