Terahertz signatures of ultrafast Dirac fermion relaxation at the surface of topological insulators

Topologically protected surface states present rich physics and promising spintronic, optoelectronic, and photonic applications that require a proper understanding of their ultrafast carrier dynamics. Here, we investigate these dynamics in topological insulators (TIs) of the bismuth and antimony chalcogenide family, where we isolate the response of Dirac fermions at the surface from the response of bulk carriers by combining photoexcitation with below-bandgap terahertz (THz) photons and TI samples with varying Fermi level, including one sample with the Fermi level located within the bandgap. We identify distinctly faster relaxation of charge carriers in the topologically protected Dirac surface states (few hundred femtoseconds), compared to bulk carriers (few picoseconds). In agreement with such fast cooling dynamics, we observe THz harmonic generation without any saturation effects for increasing incident fields, unlike graphene which exhibits strong saturation. This opens up promising avenues for increased THz nonlinear conversion efficiencies, and high-bandwidth optoelectronic and spintronic information and communication applications.Parts of this research were carried out at ELBE at the Helmholtz-Zentrum Dresden-Rossendorf e.V., a member of the Helmholtz Association. The films are grown in IRE RAS within the framework of the state task. This work was supported by the RFBR grants Nos. 18-29-20101, 19-02-00598. N.A., S.K., and I.I. acknowledge support from the European Union’s Horizon 2020 research and innovation program under grant agreement No. 737038 (TRANSPIRE). T.V.A.G.O. and L.M.E. acknowledge the support by the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter (ct.qmat). K.-J.T. acknowledges funding from the European Union’s Horizon 2020 research and innovation program under Grant Agreement No. 804349 (ERC StG CUHL) and financial support through the MAINZ Visiting Professorship. ICN2 was supported by the Severo Ochoa program from Spanish MINECO Grant No. SEV-2017-0706

Electrical tunability of terahertz nonlinearity in graphene

Graphene is conceivably the most nonlinear optoelectronic material we know. Its nonlinear optical coefficients in the terahertz frequency range surpass those of other materials by many orders of magnitude. Here, we show that the terahertz nonlinearity of graphene, both for ultrashort single-cycle and quasi-monochromatic multicycle input terahertz signals, can be efficiently controlled using electrical gating, with gating voltages as low as a few volts. For example, optimal electrical gating enhances the power conversion efficiency in terahertz third-harmonic generation in graphene by about two orders of magnitude. Our experimental results are in quantitative agreement with a physical model of the graphene nonlinearity, describing the time-dependent thermodynamic balance maintained within the electronic population of graphene during interaction with ultrafast electric fields. Our results can serve as a basis for straightforward and accurate design of devices and applications for efficient electronic signal processing in graphene at ultrahigh frequencies.D.T. and H.A.H. acknowledge funding from the European Union’s Horizon 2020 Framework Programme under grant agreement no. 964735 (EXTREME-IR). M.G. and B.G. acknowledge support from the European Cluster of Advanced Laser Light Sources (EUCALL) project that has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement no. 654220. K.-J.T. acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement no. 804349 (ERC StG CUHL) and financial support through the MAINZ Visiting Professorship. ICN2 was supported by the Severo Ochoa program from Spanish MINECO (grant no. SEV-2017-0706). Parts of this research were carried out at ELBE at the Helmholtz-Zentrum Dresden-Rossendorf e.V., a member of the Helmholtz Association. F.H.L.K. acknowledges support from the Government of Spain (FIS2016-81044; Severo Ochoa CEX2019-000910-S), Fundació Cellex, Fundació Mir-Puig, and Generalitat de Catalunya (CERCA, AGAUR, and SGR 1656). Furthermore, the research leading to these results has received funding from the European Union’s Horizon 2020 under grant agreement no. 881603 (Graphene Flagship Core 3)

Grating-graphene metamaterial as a platform for terahertz nonlinear photonics

Nonlinear optics is an increasingly important field for scientific and technological applications, owing to its relevance and potential for optical and optoelectronic technologies. Currently, there is an active search for suitable nonlinear material systems with efficient conversion and small material footprint. Ideally, the material system should allow for chip-integration and room-temperature operation. Two-dimensional materials are highly interesting in this regard. Particularly promising is graphene, which has demonstrated an exceptionally large nonlinearity in the terahertz regime. Yet, the light-matter interaction length in two-dimensional materials is inherently minimal, thus limiting the overall nonlinear-optical conversion efficiency. Here we overcome this challenge using a metamaterial platform that combines graphene with a photonic grating structure providing field enhancement. We measure terahertz third-harmonic generation in this metamaterial and obtain an effective third-order nonlinear susceptibility with a magnitude as large as 3$\cdot$10$^{-8}$m$^2$/V$^2$, or 21 esu, for a fundamental frequency of 0.7 THz. This nonlinearity is 50 times larger than what we obtain for graphene without grating. Such an enhancement corresponds to third-harmonic signal with an intensity that is three orders of magnitude larger due to the grating. Moreover, we demonstrate a field conversion efficiency for the third harmonic of up to $\sim$1% using a moderate field strength of $\sim$30 kV/cm. Finally we show that harmonics beyond the third are enhanced even more strongly, allowing us to observe signatures of up to the 9$^{\rm th}$ harmonic. Grating-graphene metamaterials thus constitute an outstanding platform for commercially viable, CMOS compatible, room temperature, chip-integrated, THz nonlinear conversion applications

Inertial spin dynamics in ferromagnets

The understanding of how spins move and can be manipulated at pico- and femtosecond timescales has implications for ultrafast and energy-efficient data-processing and storage applications. However, the possibility of realizing commercial technologies based on ultrafast spin dynamics has been hampered by our limited knowledge of the physics behind processes on this timescale. Recently, it has been suggested that inertial effects should be considered in the full description of the spin dynamics at these ultrafast timescales, but a clear observation of such effects in ferromagnets is still lacking. Here, we report direct experimental evidence of intrinsic inertial spin dynamics in ferromagnetic thin films in the form of a nutation of the magnetization at a frequency of ~0.5 THz. This allows us to reveal that the angular momentum relaxation time in ferromagnets is on the order of 10 ps

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

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. © 2020, The Author(s)

Research data: Electrical tunability of terahertz nonlinearity in graphene

This research data publications contains the sorted pulse-resolved data and metadata corresponding to the linked publication: Electrical tunability of terahertz nonlinearity in graphene. The final data evaluation and preparation of figures was done externally by Dr. Hassan Hafez, who should be contacted in terms of assigning raw data to data shown in publication

Electrical tunability ofterahertz nonlinearity in graphene

Graphene is conceivably the most nonlinear optoelectronic material we know. Its nonlinear optical coefficients in the terahertz frequency range surpass those of other materials by many orders of magnitude. Here, we show that the terahertz nonlinearity of graphene, both for ultrashort single-cycle and quasi-monochromatic multicycle input terahertz signals, can be efficiently controlled using electrical gating, with gating voltages as low as a few volts. For example, optimal electrical gating enhances the power conversion efficiency in terahertz third-harmonic generation in graphene by about two orders of magnitude. Our experimental results are in quantitative agreement with a physical model of the graphene nonlinearity, describing the time-dependent thermodynamic balance maintained within the electronic population of graphene during interaction with ultrafast electric fields. Our results can serve as a basis for straightforward and accurate design of devices and applications for efficient electronic signal processing in graphene at ultrahigh frequencies.Peer ReviewedPostprint (published version

Phase-resolved Higgs response in superconducting cuprates

In high energy physics, the Higgs field couples to gauge bosons and fermions and gives mass to their elementary excitations. Experimentally, such couplings can be verified from the decay product of the Higgs boson, the scalar (amplitude) excitation of the Higgs field. In superconductors, Cooper pairs bear a certain analogy to the Higgs field. Coulomb interactions between the Cooper pairs give mass to the electromagnetic field, which leads to the Meissner effect. Additional coupling with other types of interactions or collective modes is foreseeable, and even highly probable for high-Tc superconductors, where multiple degrees of freedom are intertwined. The superconducting Higgs mode may reveal such couplings spectroscopically and uncover interactions directly relevant to Cooper pairing. To this end, we investigate the Higgs mode of several cuprate thin films using phase-resolved terahertz third harmonic generation (THG) to. In addition to the heavily damped Higgs mode itself, we observe a universal jump in the phase of the driven Higgs oscillation as well as a non-vanishing THG above Tc. These findings indicate coupling of the Higgs mode to other collective modes and a nonzero pairing amplitude above Tc. Our study demonstrates a new approach for investigating unconventional superconductivity. We foresee a fruitful future for phase-resolved spectroscopy in various superconducting systems

Phase-resolved Higgs response in superconducting cuprates

In high energy physics, the Higgs field couples to gauge bosons and fermions and gives mass to their elementary excitations. Experimentally, such couplings can be verified from the decay product of the Higgs boson, the scalar (amplitude) excitation of the Higgs field. In superconductors, Cooper pairs bear a certain analogy to the Higgs field. Coulomb interactions between the Cooper pairs give mass to the electromagnetic field, which leads to the Meissner effect. Additional coupling with other types of interactions or collective modes is foreseeable, and even highly probable for high-Tc superconductors, where multiple degrees of freedom are intertwined. The superconducting Higgs mode may reveal such couplings spectroscopically and uncover interactions directly relevant to Cooper pairing. To this end, we investigate the Higgs mode of several cuprate thin films using phase-resolved terahertz third harmonic generation (THG) to. In addition to the heavily damped Higgs mode itself, we observe a universal jump in the phase of the driven Higgs oscillation as well as a non-vanishing THG above Tc. These findings indicate coupling of the Higgs mode to other collective modes and a nonzero pairing amplitude above Tc. Our study demonstrates a new approach for investigating unconventional superconductivity. We foresee a fruitful future for phase-resolved spectroscopy in various superconducting systems