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Ferroicity-driven nonlinear photocurrent switching in time-reversal invariant ferroic materials

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Science Advances  16 Aug 2019:
Vol. 5, no. 8, eaav9743
DOI: 10.1126/sciadv.aav9743
  • Fig. 1 Microscopic interpretation of SC and CC using a two-band model.

    δ⟨ra⟩ is the variation of the mean value of position operator indicating the shift of electron wave packet in real space. Photoexcitation induces the shift of the electron wave packet in real space. SC comes from the displacement of wave packet upon photoabsorption, while CC stems from the asymmetric motion of electrons and holes and the self-rotation of the wave packet. The latter induces itinerant orbital magnetic momentum coupled with the circularly polarized light. Transition rate W of SC is proportional to the linear optical absorption strength under the linearly polarized light at frequency ω, while transition rate F of CC is proportional to the local Berry curvature under the circularly polarized light at frequency ω.

  • Fig. 2 SC and its microscopic origin in 2D ferroelastic-ferroelectric monolayer group IV monochalcogenide GeS.

    (A) Crystal structure of monolayer group IV monochalcogenides MX, where M = (Ge, Sn) and X = (S, Se). (B) 2D electronic band structure near the Fermi level. (C and D) Frequency-dependent nonlinear SC response to incoming linearly x- and y-polarized light, respectively. (E and F) Reciprocal vector k-resolved SC susceptibility under linearly y-polarized light at the first two peaks (2.0 and 2.8 eV). (G to L) k-resolved SC strength (G and J), k-resolved dipole transition strength (H and K), and k-resolved topological shift vector of 2D GeS in 2D Brillouin zone under linearly x- and y-polarized light, respectively (I and L).

  • Fig. 3 CC and its microscopic origin in 2D ferroelastic-ferroelectric monolayer group IV monochalcogenide GeS.

    (A and B) Two opposite CC susceptibility tensor elements induced by the circularly polarized light. (C and D) Evolution of reciprocal vector k-resolved CC susceptibility under the circularly polarized light at two different frequencies (2.3 and 2.8 eV). (E and F) Group velocity difference and Berry curvature between the highest valence band and the lowest conduction band. The white arrows in (E) denote the calculated group velocity difference at specific k point, and the black curves indicate the associated stream lines.

  • Table 1 Transformation of interband Berry connection rmn, shift vector Rmn, group velocity difference Δmn, and Berry curvature Ωmn under space inversion I and time reversal T symmetry operation.

    Rmn(k) is odd under I and even under T in moment space. Ωmn(k) is even under I and odd under T in moment space. These transformation rules govern the coupling between ferroelectric polarization and nonlinear SC and CC photocurrent: JSCy,(Py)=JSCy,(Py), JSCy,(Py)=JSCy,(Py), JCCx,(Py)=JCCx,(Py), and JCCx,(Py)=JCCx,(Py).

    QuantitySymmetry operationGauge dependency
    Space inversion (I)Time reversal (T)
    rmn(k)rmn( −k)rmn*(k)Yes
    Rmn(k)Rmn( −k)Rmn( −k)No
    Δmn(k)Δmn( −k)Δmn( −k)No
    Ωmn(k)Ωmn( −k)Ωmn( −k)No
  • Table 2 Ferroicity-driven nonlinear photocurrent switching.

    Second-order nonlinear photocurrent SC and CC responses are directly correlated with the intrinsic ferroic orders (±P, ±ϵ) of 2D MX materials and external linear (↔ , ↕) and circular ( ⟲ , ⟳) polarization of incoming light. A total of 16 types of in-plane nonlinear photocurrents can be generated by controlling four ferroic states and four types of light polarizations.

    Nonlinear photocurrent
    (Jx, Jy)
    Ferroelectric order
    +PP
    +Px
    if ϵxx > 0
    +Py
    if ϵyy > 0
    Px
    if ϵxx > 0
    Py
    if ϵyy > 0
    Ferroelastic orderϵxx < 0 and ϵyy > 0(JCC,,JSC,)(JCC,,JSC,)
    −ϵϵxx > 0 and ϵyy < 0(JSC,,JCC,)(JSC,,JCC,)

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/8/eaav9743/DC1

    Table S1. Character table for C2v and D3h.

    Table S2. Second-order nonlinear photocurrent responses under different polarized light.

    Fig. S1. SC and CC in monolayer MX (C2v) and 1H-MX2 (D3h) without SOC.

    Fig. S2. SC and CC in monolayer MX (C2v) and 1H-MX2 (D3h) with SOC.

    Fig. S3. Microscopic distribution and frequency-dependent shift photocurrent susceptibility in monolayer 1H-MoSe2 with D3h point group.

    Fig. S4. SC and its microscopic origin in monolayer 1H-MoSe2.

    Fig. S5. Group velocity vx distribution in monolayer GeS.

    Fig. S6. Group velocity vy distribution in monolayer GeS.

    Fig. S7. Berry curvature distribution in monolayer 1H-MoSe2.

    Fig. S8. SC susceptibility tensor elements (σyxx(2), σyyy(2)) and CC susceptibility tensor elements (ηxyx(2), ηxxy(2)) of monolayer GeS with and without the scissor operator.

  • Supplementary Materials

    This PDF file includes:

    • Table S1. Character table for C2v and D3h.
    • Table S2. Second-order nonlinear photocurrent responses under different polarized light.
    • Fig. S1. SC and CC in monolayer MX (C2v) and 1H-MX2 (D3h) without SOC.
    • Fig. S2. SC and CC in monolayer MX (C2v) and 1H-MX2 (D3h) with SOC.
    • Fig. S3. Microscopic distribution and frequency-dependent shift photocurrent susceptibility in monolayer 1H-MoSe2 with D3h point group.
    • Fig. S4. SC and its microscopic origin in monolayer 1H-MoSe2.
    • Fig. S5. Group velocity vx distribution in monolayer GeS.
    • Fig. S6. Group velocity vy distribution in monolayer GeS.
    • Fig. S7. Berry curvature distribution in monolayer 1H-MoSe2.
    • Fig. S8. SC susceptibility tensor elements ( σyxx(2), σyyy(2)) and CC susceptibility tensor elements ( ηxyx(2), ηxxy(2)) of monolayer GeS with and without the scissor operator.

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