Role of virtual band population for high harmonic generation in solids

Rapid Communication

Role of virtual band population for high harmonic generation in solids

Yasuyuki Sanari, Hideki Hirori, Tomoko Aharen, Hirokazu Tahara, Yasushi Shinohara, Kenichi L. Ishikawa, Tomohito Otobe, Peiyu Xia, Nobuhisa Ishii, Jiro Itatani, Shunsuke A. Sato, and Yoshihiko Kanemitsu

Phys. Rev. B 102, 041125(R) – Published 30 July 2020

Abstract

We study the sub-band-gap high harmonic generation (HHG) in a methylammonium lead trichloride single crystal. Anisotropy in the crystal orientation dependence of the high harmonic yield is observed, and the yield varies substantially with the electric field strength of the midinfrared laser pulse used for excitation. Our real-time ab initio simulations reproduce the experimental results well and also show that the HHG is independent of the interband decoherence time. Based on a microscopic analysis of the intraband current, we reveal that the orientation dependence of the HHG in this perovskite semiconductor is governed by the virtual band population, rather than the anharmonicity of the electronic band structure.

Received 23 October 2019
Revised 1 May 2020
Accepted 13 July 2020

DOI:https://doi.org/10.1103/PhysRevB.102.041125

Physics Subject Headings (PhySH)

High-order harmonic generation Nonlinear optical susceptibility Ultrafast optics

Crystal structures Perovskites Semiconductors

High-harmonic generation Optical absorption spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yasuyuki Sanari¹, Hideki Hirori ^1,*, Tomoko Aharen¹, Hirokazu Tahara ¹, Yasushi Shinohara ^2,3, Kenichi L. Ishikawa ^2,3,4, Tomohito Otobe ⁵, Peiyu Xia⁶, Nobuhisa Ishii ⁶, Jiro Itatani ⁶, Shunsuke A. Sato ^7,8, and Yoshihiko Kanemitsu ^1,*

¹Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan
²Photon Science Center, Graduate School of Engineering, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan
³Department of Nuclear Engineering and Management, Graduate School of Engineering, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan
⁴Research Institute for Photon Science and Laser Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
⁵Kansai Photon Science Institute, National Institutes for Quantum and Radiological Science and Technology, Kizugawa, Kyoto 619-0615, Japan
⁶Institute for Solid State Physics, The University of Tokyo, Kashiwa, Chiba 277-8581, Japan
⁷Center for Computational Sciences, University of Tsukuba, Tsukuba 305-8577, Japan
⁸Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany

^*Corresponding authors: hirori@scl.kyoto-u.ac.jp; kanemitu@scl.kyoto-u.ac.jp

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 102, Iss. 4 — 15 July 2020

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Schematics of experimental setup for HHG measurement and the perovskite $A B X_{3}$ crystal structure where $A = C H_{3} N {H_{3}}^{+}$ (MA), $B = Pb$ , and $X = Cl$ . The schematic atomic arrangement next to the $A B X_{3}$ crystal structure illustrates the electron wave functions of the Cl $3 p$ (light green) and Pb $6 s$ orbitals (light blue). The yellow arrow shows how we define the direction of the fundamental excitation field. (b) HHG spectra of a bulk $MAPbC l_{3}$ single crystal for $E = 10 MV / cm$ . (c) Measured (open circles) and calculated (solid lines) harmonic yields as a function of the peak electric field $E$ inside the sample for harmonic orders $h = 3, 5, 7$ , and 9. The dashed lines are proportional to $E^{2 h}$ and serve as guides for the eye. (d) Right-handed circularly polarized (RCP) and left-handed circularly polarized (LCP) components of the HHG spectrum under LCP excitation (blue dashed and red solid lines, respectively). The data are offset for clarity.
Reuse & Permissions
Figure 2
Measured θ dependences of HH yields obtained for $E = 6, 8$ , and 10 MV/cm (shown with blue, green, and red lines, respectively). The harmonic orders are indicated on the left upper corners of each data set and the maximum peak intensities are normalized.
Reuse & Permissions
Figure 3
(a) Electronic band structure and DOS for $CsPbC l_{3}$ calculated using first-principles DFT. (b) Calculated θ dependences of the HHG yield for $E = 5, 8$ , and 10 MV/cm are shown with the blue, green, and red curves, respectively. The data for the third-, fifth-, seventh-, and ninth-order harmonics are provided and the data are normalized for clarity. The calculations shown are for an interband decoherence time $τ = \infty$ .
Reuse & Permissions
Figure 4
(a) Calculated total current $J_{total}$ and (b) population change $Δ n_{VBs}$ of the nine uppermost VBs in the time domain. Three data sets corresponding to three different interband decoherence times τ ( $= \infty$ , 100 fs, 10 fs) are provided. All calculations use a 10 MV/cm excitation pulse as shown in the upper panel of (b). (c) The spectra of $J_{total}$ and $J_{VBs}$ for the three τ values and (d) the spectra of the oscillating components in the population change $Δ n_{VBs}$ . Here, we analyzed the contribution of the virtual population change by subtracting the real population from the total population in the time domain shown in (b).
Reuse & Permissions
Figure 5
(a)–(c) Fourier spectra of current, population change, and velocity averaged over the nine uppermost VBs in the time domain, $J_{VBs} (ω), Δ n_{VBs} (ω)$ , and $V_{VBs} (ω)$ , for $E = 10 MV / cm$ . (d) Comparison of the harmonic intensity ratios of $J_{VBs} (ω), Δ n_{VBs} (ω)$ , and $V_{VBs} (ω)$ for $θ = 0^{\circ}$ to those for $θ = 45^{\circ}$ . The three types of ratios are shown with the red, blue, and green bars, respectively. (e) Calculated population changes $Δ n_{VBs} (t)$ for $θ = 0^{\circ}$ [these data are the same as those shown in Fig. 4 for $τ = \infty$ ] and 45° are shown with the red and blue curves, respectively. (f) Electric field dependences of the calculated $Δ n_{VBs} (ω)$ for the second, fourth, sixth, and eighth order for $θ = 0^{\circ}$ (red solid curves) and $θ = 45^{\circ}$ (blue dashed curves). The black lines are proportional to $E^{2 h}$ and serve as guides for the eye. The data are offset for clarity.
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics