Abstract-Non-perturbative terahertz high-harmonic generation in the three-dimensional Dirac semimetal Cd3As2

Sergey Kovalev, Renato M. A. Dantas, Semyon Germanskiy, Jan-Christoph Deinert, Bertram Green, Igor Ilyakov, Nilesh Awari, Min Chen, Mohammed Bawatna, Jiwei Ling, Faxian Xiu, Paul H. M. van Loosdrecht, Piotr Surówka, Takashi Oka,  Zhe Wang, 

https://www.nature.com/articles/s41467-020-16133-8

Harmonic generation is a general characteristic of driven nonlinear systems, and serves as an efficient tool for investigating the fundamental principles that govern the ultrafast nonlinear dynamics. Here, we report on terahertz-field driven high-harmonic generation in the three-dimensional Dirac semimetal Cd3As2 at room temperature. Excited by linearly-polarized multi-cycle terahertz pulses, the third-, fifth-, and seventh-order harmonic generation is very efficient and detected via time-resolved spectroscopic techniques. The observed harmonic radiation is further studied as a function of pump-pulse fluence. Their fluence dependence is found to deviate evidently from the expected power-law dependence in the perturbative regime. The observed highly non-perturbative behavior is reproduced based on our analysis of the intraband kinetics of the terahertz-field driven nonequilibrium state using the Boltzmann transport theory. Our results indicate that the driven nonlinear kinetics of the Dirac electrons plays the central role for the observed highly nonlinear response.

Abstract-THz excitations in α-RuCl3: Majorana fermions, rigid-plane shear and compression modes

S. Reschke, V. Tsurkan, S.-H. Do, K.-Y. Choi, P. Lunkenheimer, Zhe Wang, A. Loidl

https://arxiv.org/abs/1902.10453

Spin liquids may host emergent quasiparticles, collective excitations of the spin degrees of freedom with characteristic features of Majorana fermions, which experimentally are detectable by broad excitation continua due to spin fractionalization. The latter is predicted for the Kitaev spin liquid, an exactly solvable model with bond-dependent interactions on a two-dimensional honeycomb lattice. Here we report on detailed THz experiments in {\alpha}-RuCl3, identifying these characteristic fingerprints of Majorana fermions. The continuum intensity decreases and finally vanishes on increasing temperature. It partly overlaps with phonon modes representing characteristic sliding and compression modes of the van der Waals bonded molecular layers.

Abstract-Terahertz oscilloscope for recording time information of ultrashort electron beams

Lingrong Zhao, Zhe Wang, Heng Tang, Rui Wang, Yun Cheng, Chao Lu, Tao Jiang, Pengfei Zhu, Long Hu, Wei Song, Huida Wang, Jiaqi Qiu, Roman Kostin, Chunguang Jing, Sergey Antipov, Peng Wang, Jia Qi, Ya Cheng, Dao Xiang, and Jie Zhang

https://journals.aps.org/prl/accepted/d407dY16M5819b51b9d98708b359b7042e3e658c9

We propose and demonstrate a Terahertz (THz) oscilloscope for recording time information of an ultrashort electron beam. By injecting a laser-driven THz pulse with circular polarization into a dielectric tube, the electron beam is swept helically such that the time information is uniformly encoded into the angular distribution that allows one to characterize both the temporal profile and timing jitter of an electron beam. The dynamic range of the measurement in such a configuration is significantly increased compared to deflection with a linearly polarized THz pulse. With this THz oscilloscope, nearly 50-fold longitudinal compression of a relativistic electron beam to about 15 fs (rms) is directly visualized with its arrival time determined with 3 fs accuracy. This technique bridges the gap between streaking of photoelectrons with optical lasers and deflection of relativistic electron beams with radio-frequency deflectors, and should have wide applications in many ultrashort electron beam based facilities.

Abstract-Extremely efficient terahertz high-harmonic generation in graphene by hot Dirac fermions

Hassan A. Hafez, Sergey Kovalev, Jan-Christoph Deinert, Zoltán Mics, Bertram Green, Nilesh Awari, Min Chen, Semyon Germanskiy, Ulf Lehnert, Jochen Teichert, Zhe Wang, Klaas-Jan Tielrooij, Zhaoyang Liu, Zongping Chen, Akimitsu Narita, Klaus Müllen, Mischa Bonn, Michael Gensch,  Dmitry Turchinovich

https://www.nature.com/articles/s41586-018-0508-1

Multiple optical harmonic generation—the multiplication of photon energy as a result of nonlinear interaction between light and matter—is a key technology in modern electronics and optoelectronics, because it allows the conversion of optical or electronic signals into signals with much higher frequency, and the generation of frequency combs. Owing to the unique electronic band structure of graphene, which features massless Dirac fermions, it has been repeatedly predicted that optical harmonic generation in graphene should be particularly efficient at the technologically important terahertz frequencies. However, these predictions have yet to be confirmed experimentally under technologically relevant operation conditions. Here we report the generation of terahertz harmonics up to the seventh order in single-layer graphene at room temperature and under ambient conditions, driven by terahertz fields of only tens of kilovolts per centimetre, and with field conversion efficiencies in excess of 10−3, 10−4 and 10−5 for the third, fifth and seventh terahertz harmonics, respectively. These conversion efficiencies are remarkably high, given that the electromagnetic interaction occurs in a single atomic layer. The key to such extremely efficient generation of terahertz high harmonics in graphene is the collective thermal response of its background Dirac electrons to the driving terahertz fields. The terahertz harmonics, generated via hot Dirac fermion dynamics, were observed directly in the time domain as electromagnetic field oscillations at these newly synthesized higher frequencies. The effective nonlinear optical coefficients of graphene for the third, fifth and seventh harmonics exceed the respective nonlinear coefficients of typical solids by 7–18 orders of magnitude. Our results provide a direct pathway to highly efficient terahertz frequency synthesis using the present generation of graphene electronics, which operate at much lower fundamental frequencies of only a few hundreds of gigahertz.

Abstract-Terahertz Streaking of Few-Femtosecond Relativistic Electron Beams

Lingrong Zhao, Zhe Wang, Chao Lu, Rui Wang, Cheng Hu, Peng Wang, Jia Qi, Tao Jiang, Shengguang Liu, Zhuoran Ma, Fengfeng Qi, Pengfei Zhu, Ya Cheng, Zhiwen Shi, Yanchao Shi, Wei Song, Xiaoxin Zhu, Jiaru Shi, Yingxin Wang, Lixin Yan, Liguo Zhu, Dao Xiang, and Jie Zhan

https://journals.aps.org/prx/abstract/10.1103/PhysRevX.8.021061

Streaking of photoelectrons with optical lasers has been widely used for temporal characterization of attosecond extreme ultraviolet pulses. Recently, this technique has been adapted to characterize femtosecond x-ray pulses in free-electron lasers with the streaking imprinted by far-infrared and terahertz (THz) pulses. Here, we report successful implementation of THz streaking for time stamping of an ultrashort relativistic electron beam, whose energy is several orders of magnitude higher than photoelectrons. Such an ability is especially important for MeV ultrafast electron diffraction (UED) applications, where electron beams with a few femtosecond pulse width may be obtained with longitudinal compression, while the arrival time may fluctuate at a much larger timescale. Using this laser-driven THz streaking technique, the arrival time of an ultrashort electron beam with a 6-fs (rms) pulse width has been determined with 1.5-fs (rms) accuracy. Furthermore, we have proposed and demonstrated a noninvasive method for correction of the timing jitter with femtosecond accuracy through measurement of the compressed beam energy, which may allow one to advance UED towards a sub-10-fs frontier, far beyond the approximate 100-fs (rms) jitter.

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Abstract-Terahertz streaking of few-femtosecond relativistic electron beams

Lingrong Zhao, Zhe Wang, Chao Lu, Rui Wang, Cheng Hu, Peng Wang, Jia Qi, Tao Jiang, Shengguang Liu, Zhuoran Ma, Fengfeng Qi, Pengfei Zhu, Ya Cheng, Zhiwen Shi, Yanchao Shi, Wei Song, Xiaoxin Zhu, Jiaru Shi, Yingxin Wang, Lixin Yan, Liguo Zhu, Dao Xiang,  Jie Zhang,

https://journals.aps.org/prx/accepted/d8075K71A261f001129c7ce70c632d2221b6fd030

Streaking of photoelectrons with optical lasers has been widely used for temporal characterization of attosecond extreme ultraviolet pulses. Recently, this technique has been adapted to characterize femtosecond x-ray pulses in free-electron lasers with the streaking imprinted by far-infrared and Terahertz (THz) pulses. Here, we report successful implementation of THz streaking for time-stamping of an ultrashort relativistic electron beam of which the energy is several orders of magnitude higher than photoelectrons. Such ability is especially important for MeV ultrafast electron diffraction (UED) applications where electron beams with a few femtosecond pulse width may be obtained with longitudinal compression while the arrival time may fluctuate at a much larger time scale. Using this laser-driven THz streaking technique, the arrival time of an ultrashort electron beam with 6 fs (rms) pulse width has been determined with 1.5 fs (rms) accuracy. Furthermore, we have proposed and demonstrated a non-invasive method for correction of the timing jitter with femtosecond accuracy through measurement of the compressed beam energy, which may allow one to advance UED towards sub-10 fs frontier far beyond the $\sim$100 fs (rms) jitter.

Abstract-Sub-gap optical response across the structural phase transition in van der Waals layered α-RuCl3

S. Reschke, F. Mayr, S. Widmann, H.-A. Krug von Nidda, V. Tsurkan, M. V. Eremin, Seung-Hwan Do, K.-Y. Choi, Zhe Wang, A. Loidl

https://arxiv.org/abs/1803.04887

We report on magnetic, thermodynamic, thermal expansion, and optical experiments on the layered compound \alpha-RuCl3 focusing on the sub-gap optical response across the structural phase transition from the monoclinic high-temperature to the rhombohedral low-temperature structure, where mainly the stacking sequence of the molecular layers is changed. The temperature dependence of the complex dielectric response, including symmetry changes via the phase transition should allow the identification of the microscopic origin of the recorded phonon and spin-orbital excitations. In addition, this type of phase transition seems to be characteristic for a variety of tri-halides crystallizing in a layered honeycomb-type structure and so far is unique, as the low-temperature phase has the higher symmetry. We document a number of highly unusual findings: A characteristic two-step hysteresis of the structural phase transition, accompanied by a dramatic change of the reflectivity. An electronic excitation, which only appears in a narrow temperature range just across the structural phase transition, and a complex dielectric loss spectrum in the THz regime, which could indicate some remnants of Kitaev physics. Despite the significant structural effects across the monoclinic to rhombohedral phase transition, phonon eigenfrequencies and the majority of spin-orbital excitations are not strongly influenced. Obviously, symmetry and binding forces of the single molecular layers only determine the eigenfrequencies of most of these excitations. Finally, from a detailed and combined terahertz, far- and mid-infrared study we try to shed some light on the so far unsolved low energy (< 1eV) electronic structure of the ruthenium 4d5 electrons in \alpha-RuCl3.

Abstract-Excitations and relaxation dynamics in multiferroic GeV 4 S 8 studied by terahertz and dielectric spectroscopy

S. Reschke, Zhe Wang, F. Mayr, E. Ruff, P. Lunkenheimer, V. Tsurkan, and A. Loidl

https://journals.aps.org/prb/abstract/10.1103/PhysRevB.96.144418

We report on THz time-domain spectroscopy on multiferroic ${\mathrm{GeV}}_4{S}_8$, which undergoes orbital ordering at a Jahn-Teller transition at 30.5 K and exhibits antiferromagnetic order below 14.6 K. The THz experiments are complemented by dielectric experiments at audio and radio frequencies. We identify a low-lying excitation close to 0.5 THz, which is only weakly temperature dependent and probably corresponds to a molecular excitation within the electronic level scheme of the $V_4$ clusters. In addition, we detect complex temperature-dependent behavior of a low-lying phononic excitation, closely linked to the onset of orbitally driven ferroelectricity. In the high-temperature cubic phase, which is paramagnetic and orbitally disordered, this excitation is of relaxational character becomes an overdamped Lorentzian mode in the orbitally ordered phase below the Jahn-Teller transition, and finally appears as well-defined phonon excitation in the antiferromagnetic state. Abrupt changes in the real and imaginary parts of the complex dielectric permittivity show that orbital ordering appears via a structural phase transition with strong first-order character and that the onset of antiferromagnetic order is accompanied by significant structural changes, which are of first-order character, too. Dielectric spectroscopy documents that at low frequencies, significant dipolar relaxations are present in the orbitally ordered, paramagnetic phase only. In contrast to the closely related ${\mathrm{GaV}}_4{S}_8$, this relaxation dynamics that most likely mirrors coupled orbital and polar fluctuations does not seem to be related to the dynamic processes detected in the THz regime.

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Abstract-Electronic and phonon excitations in α − RuC l 3

S. Reschke, F. Mayr, Zhe Wang, Seung-Hwan Do, K.-Y. Choi, and A. Loi

https://journals.aps.org/prb/abstract/10.1103/PhysRevB.96.165120

We report on terahertz (THz), infrared reflectivity, and transmission experiments for wavenumbers from 10 to $8000c{m}^{-1}$ ($\sim 1\mathrm{meV}-1\mathrm{eV}$) and for temperatures from 5 to 295 K on the Kitaev candidate material $\alpha -\mathrm{RuC}{l}_3$. As reported earlier, the compound under investigation passes through a first-order structural phase transition, from a monoclinic high-temperature to a rhombohedral low-temperature phase. The phase transition shows an extreme and unusual hysteretic behavior, which extends from 60 to 166 K. In passing this phase transition, in the complete frequency range investigated, we found a significant reflectance change, which amounts to almost a factor of two. We provide a broadband spectrum of dielectric constant, dielectric loss, and optical conductivity from the THz to the mid-infrared regime and study in detail the phonon response and the low-lying electronic density of states. We provide evidence for the onset of an optical energy gap, which is on the order of 200 meV, in good agreement with the gap derived from measurements of the dc electrical resistivity. Remarkably, the onset of the gap exhibits a strong blue shift on increasing temperatures.

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Abstract-Magnetic Excitations and Continuum of a Field-Induced Quantum Spin Liquid in α-RuCl3

Zhe Wang, S. Reschke, D. Hüvonen, S.-H. Do, K.-Y. Choi, M. Gensch, U. Nage, T. Rõõm, A. Loidl

(Submitted on 19 Jun 2017)

https://arxiv.org/abs/1706.06157

We report on terahertz spectroscopy of quantum spin dynamics in α-RuCl3, a system proximate to the Kitaev honeycomb model, as a function of temperature and magnetic field. An extended magnetic continuum develops below the structural phase transition at Ts2=62K. With the onset of a long-range magnetic order at TN=6.5K, spectral weight is transferred to a well-defined magnetic excitation at ℏω1=2.48meV, which is accompanied by a higher-energy band at ℏω2=6.48meV. Both excitations soften in magnetic field, signaling a quantum phase transition at Bc=7T where we find a broad continuum dominating the dynamical response. Above Bc, the long-range order is suppressed, and on top of the continuum, various emergent magnetic excitations evolve. These excitations follow clear selection rules and exhibit distinct field dependencies, characterizing the dynamical properties of the field-induced quantum spin liquid.