Efficient Terahertz Harmonic Generation with Coherent Acceleration of Electrons in the Dirac Semimetal ${\mathrm{Cd}}_{3}{\mathrm{As}}_{2}$

Efficient Terahertz Harmonic Generation with Coherent Acceleration of Electrons in the Dirac Semimetal ${Cd}_{3} {As}_{2}$

Bing Cheng, Natsuki Kanda, Tatsuhiko N. Ikeda, Takuya Matsuda, Peiyu Xia, Timo Schumann, Susanne Stemmer, Jiro Itatani, N. P. Armitage, and Ryusuke Matsunaga

Phys. Rev. Lett. 124, 117402 – Published 19 March 2020

Abstract

We report strong terahertz ( $\sim 10^{12} Hz$ ) high harmonic generation at room temperature in thin films of ${Cd}_{3} {As}_{2}$ , a three-dimensional Dirac semimetal. Third harmonics are detectable with a tabletop light source and can be as strong as $100 V/ cm$ by applying a fundamental field of $6.5 kV / cm$ inside the film, demonstrating an unprecedented efficiency for terahertz frequency conversion. Our time-resolved terahertz spectroscopy and calculations also clarify the microscopic mechanism of the nonlinearity originating in the coherent acceleration of Dirac electrons in momentum space. Our results provide clear insights for nonlinear currents of Dirac electrons driven by the terahertz field under the influence of scattering, paving the way toward novel devices for high-speed electronics and photonics based on topological semimetals.

Received 19 December 2019
Revised 17 February 2020
Accepted 21 February 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.117402

Physics Subject Headings (PhySH)

High-order harmonic generation

Topological materials

Terahertz techniques

Condensed Matter, Materials & Applied PhysicsNonlinear Dynamics

Authors & Affiliations

Bing Cheng^1,†, Natsuki Kanda^2,†, Tatsuhiko N. Ikeda², Takuya Matsuda², Peiyu Xia², Timo Schumann³, Susanne Stemmer³, Jiro Itatani ², N. P. Armitage¹, and Ryusuke Matsunaga ^2,4,*

¹The Institute for Quantum Matter and Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218, USA
²The Institute for Solid State Physics, The University of Tokyo, Kashiwa, Chiba 277-8581, Japan
³Materials Department, University of California, Santa Barbara, California 93106-5050, USA
⁴PRESTO, Japan Science and Technology Agency, 4-1-8 Honcho Kawaguchi, Saitama 332-0012, Japan

^*matsunaga@issp.u-tokyo.ac.jp
^†These authors contributed equally to this work.

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Vol. 124, Iss. 11 — 20 March 2020

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Figure 1
(a) Schematic of the HHG in Dirac electron system. (b) Real- and imaginary-part THz conductivity spectra at 300 K. The dotted curves are the results of fitting. (c) Amplitude spectra of transmitted pump THz pulses for the ${Cd}_{3} {As}_{2}$ film, a reference substrate, and graphene on SiC with $E_{pump} = 31 kV / cm$ . (d) THG field amplitude as a function of $E_{pump}$ . The solid line for the ${Cd}_{3} {As}_{2}$ data is a fitted result with function $\propto E_{pump}^{α}$ with $α = 2.1$ for stronger field. The dashed lines are fitted with $\propto E_{pump}^{3}$ to show the perturbative regimes.
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Figure 2
(a) Schematic of broadband short THz pump-THz probe spectroscopy. (b) Probe pulse waveform $E_{probe}$ as a function of $t_{2}$ . (c) 2D plot of the change of the probe electric field $δ E_{probe}$ by the THz pump as functions of $t_{1}$ and $t_{2}$ . (d) $δ E_{probe}$ with a fixed delay of $t_{2}$ at the peak of the probe indicated by the broken line in (c). (e),(f) Open circles show the real and imaginary parts of the transient conductivity spectra at $t_{1} = 5 ps$ in comparison with data in equilibrium. The solid curves show the fitting with the Drude model. (g),(h) The carrier density $N$ and scattering time $τ$ obtained by the fitting in (e) and (f) as a function of the pump delay $t_{1}$ .
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Figure 3
(a) Schematic of quasimonochromatic THz pump-THz probe measurement. (b) The upper figure shows the pump THz waveform with $f = 0.8 THz$ . The lower figure shows $δ E_{probe}$ as a function of $t_{1}$ for the probe polarizations parallel and perpendicular to the pump. The data are normalized at the peak value of probe field and shown with offset for clarity. (c) Fourier components of $δ E_{probe}$ on the interband excitation signal in (b). The arrow indicates the oscillation component at $2 f = 1.6 THz$ . The peak at $f = 0.8 THz$ is ascribed to an artifact [14].
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Figure 4
(a) Calculated amplitude spectra from the thermodynamic (TD) model and the intraband acceleration model for $f = 0.8 THz$ . (b) THG amplitudes as a function of the field strength. The black and red curves show the results of the TD model and the intraband acceleration model and the circles show the experimental data. (c) THG amplitude as a function of $τ_{s}$ for $f = 0.8 THz$ and peak field of 3 and $6 kV / cm$ inside the film. The solid lines show power-law fittings to clearly see saturation. (d) 2D plot of the electron distribution in the momentum space parallel and perpendicular to the pump polarization, as denoted by $k_{pump}$ and $k_{⊥}$ , respectively. The top and bottom panels correspond to equilibrium and under the field of $6 kV / cm$ inside the film at $f = 0.8 THz$ .
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Physical Review Letters

Efficient Terahertz Harmonic Generation with Coherent Acceleration of Electrons in the Dirac Semimetal Cd3As2

Bing Cheng, Natsuki Kanda, Tatsuhiko N. Ikeda, Takuya Matsuda, Peiyu Xia, Timo Schumann, Susanne Stemmer, Jiro Itatani, N. P. Armitage, and Ryusuke Matsunaga

Phys. Rev. Lett. 124, 117402 – Published 19 March 2020

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Efficient Terahertz Harmonic Generation with Coherent Acceleration of Electrons in the Dirac Semimetal ${Cd}_{3} {As}_{2}$