Ultrafast terahertz emission from emerging symmetry-broken materials

Abstract

Nonlinear optical spectroscopies are powerful tools for investigating both static material properties and light-induced dynamics. Terahertz (THz) emission spectroscopy has emerged in the past several decades as a versatile method for directly tracking the ultrafast evolution of physical properties, quasiparticle distributions, and order parameters within bulk materials and nanoscale interfaces. Ultrafast optically-induced THz radiation is often analyzed mechanistically in terms of relative contributions from nonlinear polarization, magnetization, and various transient free charge currents. While this offers material-specific insights, more fundamental symmetry considerations enable the generalization of measured nonlinear tensors to much broader classes of systems. We thus frame the present discussion in terms of underlying broken symmetries, which enable THz emission by defining a system directionality in space and/or time, as well as more detailed point group symmetries that determine the nonlinear response tensors. Within this framework, we survey a selection of recent studies that utilize THz emission spectroscopy to uncover basic properties and complex behaviors of emerging materials, including strongly correlated, magnetic, multiferroic, and topological systems. We then turn to low-dimensional systems to explore the role of designer nanoscale structuring and corresponding symmetries that enable or enhance THz emission. This serves as a promising route for probing nanoscale physics and ultrafast light-matter interactions, as well as facilitating advances in integrated THz systems. Furthermore, the interplay between intrinsic and extrinsic material symmetries, in addition to hybrid structuring, may stimulate the discovery of exotic properties and phenomena beyond existing material paradigms.

Fig. 1. Time-resolved THz emission spectroscopy of symmetry-broken materials.

A general THz emission spectroscopy setup is shown in transmission configuration (readily reconfigured into reflection mode), along with a selection of mechanisms by which ultrafast photocurrents and THz radiation are generated. Mechanisms are grouped by the essential broken discrete symmetry, with the symmetry broken either within the material or at an interface, within the light-matter interaction, or via an applied static field. In all cases where only parity ($\mathcal{P}$) or time-reversal ($\mathcal{T}$) is broken, parity-time ($\mathcal{P}\mathcal{T}$) symmetry is broken generically

Fig. 2. THz emission from high-T_C superconductors.

a Schematic illustration of a superconducting dipole antenna. b Image of superconducting strip line before illumination (top), after illumination (middle), and following removal of the bias current (bottom). Note the formation of flux vortices following illumination, which subsequently revert to vortex/anti-vortex pairs upon removal of the bias. c Temperature phase diagram for the incommensurate stripe-ordered compound La_1.905Ba_0.095CuO₄. Here, $T_{\mathrm{CO}}$, $T_{\mathrm{SO}}$, and $T_{\mathrm{C}}$ represent the charge ordering, spin ordering, and the superconducting critical temperatures, respectively. d Emitted THz waveforms obtained for temperature intervals denoted by solid circles in (c). e Spectral amplitude of select time-domain traces in (d) fit to multi-Gaussian fit function. Inset: Schematic of the experimental geometry. Panel (a) adapted with permission from © 2019 Wiley-VCH Verlag GmbH. Panel (b) adapted with permission from ref. © 2005 The Japan Society of Applied Physics. Panels (c–e) reprinted from ref. © 2022 the Author(s), published by PNAS, under the terms of CC-BY 4.0

Fig. 3. Transient photocurrent-induced symmetry breaking in the Weyl semimetal TaAs.

a Schematic diagram of the net photocurrent contained within the (112) plane (yellow) of a TaAs unit cell, along with (b) a sketch of the experimental geometry used to realize current-induced second harmonic generation. c Changes in the transient second harmonic pattern ($\mathrm{\Delta }t=$ 0.1 ps) measured as a function of pump polarization relative to the [$1$,$1$,$\stackrel{\circledR }{1}$] axis (offset for clarity). The presence of enhanced (10–20%), polarization-dependent injection (panels d–f) and shift (panels g, h) currents along [$1$,$\stackrel{\circledR }{1}$,0] leads to a clear reduction in symmetry within the pattern. d False color plot and (e) select time-domain THz traces, illustrating the polarity reversal of the emitted THz waveform generated along the [$1$,$\stackrel{\circledR }{1}$,0] axis by injection photocurrents. Traces shown in panel e are obtained using quarter waveplate (QWP) angles of $\pm$45°, $\pm$22.5°, and 0°, which correspond to right/left circular, elliptical, and linear polarizations, respectively. f Peak-to-peak electric field amplitude plotted as a function of QWP angle. g Polarization independent shift currents generated along the [$1$,$1$,$\stackrel{\circledR }{1}$] axis following excitation by right-circular, linear, and left-circular polarized optical pulses. Detailed peak-to-peak E-field amplitude of the emitted THz radiation plotted as a function of (h) QWP (left) half waveplate (HWP; right) angle. Panels (a–c) adapted with permission from © 2021 the Author(s), under exclusive licence to Springer Nature. Panels (d–h) reprinted with permission from ref. © 2019 American Physical Society

Fig. 4. Inverse spin-Hall effect-based THz emission.

a Schematic of an ISHE-based THz emitter, which converts the ultrafast laser-induced spin current in the FM layer into a charge current in the NM layer. b Contrasting interfacial spin accumulation from Ru and Au metallic layers showing the comparatively rapid equilibration in the Au system. c THz radiation from Fe/Ru and Fe/Au emitters showing the dramatically larger emission bandwidth of the latter. d Schematic of THz emission from [Co/Pd]/Mn₂Au structure where the spin-polarized current is generated in the Co/Pd layer and the sublattice-mediated reorientation of spins in the AFM Mn₂Au generates a THz pulse polarized along the direction of magnetization. e Illustration of the spin-to-charge current conversion in an AFM, which drives a spin reorientation of out-of-plane polarized spins into antiparallel in-plane direction in the two magnetic sublattices yielding a charge current due to shifting of the Fermi contour. f THz transient from the [Co/Pd]/Mn₂Au emitter showing phase reversal under the change of external magnetic field orientation. Panels (b, c) reprinted with permission from ref. © 2013 Nature Publishing Group. Panels (d–f) reprinted with permission from ref. © 2022 Wiley-VCH GmbH

Fig. 5. Inverse Rashba-Edelstein effect-based THz emission.

a The effective field due to the Rashba interaction splits the electronic bands and leads to opposite winding of spin texture in the inner and outer Fermi contour. b Spin-polarized injection shifts the Fermi contours in the blue and red bands in (a) by $\mathrm{\Delta }\mathit{k\text{'}}$, leading to a charge current proportional to the injected spin current. c Schematic of an IREE-based THz emitter where a spin-polarized current from the FM is converted to a charge current at the NM1/NM2 interface due to the Fermi contour shift depicted in panel (b). d THz emission from CoFeB/Ag/Bi (red), CoFeB/Bi (green), CoFeB/Ag/Al (purple), CoFeB/Al (black), and MgO/Ag/Bi (cyan) heterostructures with the inset showing the reversal of the THz pulse phase under a 180 degree change in the magnetization direction of the FM layer. e Angle-resolved photoemission spectrum of the Rashba-mediated Dirac surface states in Bi/Bi₂Te₃ heterostructures. f THz emission from various heterostructures highlighting the increased response for Co/Bi/Bi₂Te₃ due to the presence of Rashba-mediated splitting of a Dirac surface state at the Bi/Bi₂Te₃ interface. Panel (d) reprinted with permission from © 2018 American Physical Society. Panels (e) and (f) reprinted with permission from ref. © 2020 American Chemical Society

Fig. 6. THz emission via inverse spin–orbit torque effect.

a Schematic of spin-orbit torques that can result from effective magnetic fields driven by an ultrafast pump pulse. b Pump helicity dependence of THz emission via ISOTE, where different circular polarization states give rise to different orientations of optically-induced effective magnetic fields and THz pulse phase reversal. c THz transient from a Co/Pt heterostructure showing phase reversal under interchange of pump helicity, sample, magnetization, and layer order. Panel (c) adapted with permission from ref. © 2016 Nature Publishing Group

Fig. 7. THz emission from rotationally symmetric magnetic systems.

a THz emission from (110) NiO driven by a near-infrared ultrafast pulse via ISRS and (b) the corresponding Fourier transform. c THz emission from (111) NiO driven by a near-infrared ultrafast pulse via ISRS (upper panel) and corresponding Fourier transform (lower panel). d Six-fold rotational symmetry of $x$- (upper panel) and $y$-polarized (lower panel) THz field components from (111) NiO under sample rotation, where red lobes correspond to a positive signed transient and blue lobes correspond to a negative signed transient. e ISRS selection rules for colinear scattering where the upward blue arrow indicated photon annihilation, the downward orange arrow indicates photon creation, and the downward red arrow indicates magnon excitation. f Six-fold symmetric THz emission from (111) NiO/Pt heterostructure (left panel) and (111) NiO (right panel) under sample rotation showing dramatic enhancement in the heterostructure. g THz transients from NiO/Pt heterostructures with various NiO crystal faces (left panel) and corresponding bare NiO response. Panels (a) and (b) reprinted with permission from © 2010 American Institute of Physics. Panels (c) and (d) reprinted from © 2011 American Physical Society, under the terms of CC-BY 3.0. Panels (f) and (g) reprinted with permission from © 2020 the Author(s), under exclusive licence to Springer Nature

Fig. 8. Terahertz emission from nanostructured metal surfaces and plasmonic nanocathodes.

a Localized and traveling plasmonic modes and illustrations of corresponding optical hot spots on (left to right) percolated ultrathin ($~$10 nm) films, nanogratings, and nanopatterned arrays. b Dependence of THz intensity on plasmon-enhanced near-field optical intensity for two different Ag nanostructure arrays, estimating a 7.5-fold near-field enhancement for the nanohole array (open circles) and 20-fold enhancement for the nanotriangle array (solid circles). Vertical offsets adjusted for clarity. Plasmonic c nanostructure, d nanoparticle, and e etched nanotip photocathodes with controlled photocurrent directionality and multiphoton to strong-field emission (along with post-emission ponderomotive dynamics). Panel a left inset (Ag thin film) and right inset (Ag nanotriangle array) adapted with permission from © 2011 American Chemical Society. Panel a middle inset (Au nanograting) adapted with permission from © 2011 Springer-Verlag. Panel b adapted with permission from © 2014 American Physical Society. Panel c adapted with permission from © 2013 American Chemical Society. Panel d adapted from © 2020 under the terms of CC-BY 4.0. Panel e adapted with permission from ref. © 2012 Nature Publishing Group

Fig. 9. THz emission from nanoplasmonic metasurfaces.

a THz pulse generated from an array of nanoplasmonic SRRs (bottom inset) excited at different resonance modes (top inset). b The field amplitude of the generated THz pulses versus pump power measured with different THz emitters, revealing comparable THz generation efficiency and the second-order nonlinearity. c Illustration of a few nanoplasmonic resonators with different symmetries, along with the polarization vectors at excitation (red arrows) and THz (cyan arrows) frequencies. d The rotation of THz linear polarization angle as a function of the excitation polarization angle. e Spatial separation of left- and right-handed circularly polarized THz radiation by implementing a linear PB phase gradient in the horizontal direction. Panels (a) and (b) adapted with permission from ref. © 2014 Nature Publishing Group. Panel (d) adapted from ref. © 2021 the Author(s) under the terms of CC-BY 4.0. Panel (e) adapted with permission from ref. © 2021 American Chemical Society

Fig. 10. Ultrafast dynamics in 1D materials.

a Semiconductor (InAs) nanowire forest with enhanced THz outcoupling relative to escape-cone-limited bulk InAs. b Exciton dynamics in chirality-enriched semiconducting carbon nanotube array. Superlinear bias dependence for the photocurrent readout indicates the long-timescale exciton multiplication (not present in the ultrafast THz emission signal). Panel (a) adapted with permission from ref. © 2011 American Physical Society. Panel (b) adapted from ref. © 2020 American Chemical Society under the terms of CC-BY. Panel (b) inset micrograph (nanotube array) adapted with permission from ref. © 2016 Nature Publishing Group

Fig. 11. On-chip and free-space THz emission from 2D materials and devices.

a Suspended graphene on a THz photoconductive strip line. b Ultrafast sub-nanometer heterojunction charge flow and THz emission following pulsed excitation, driven by the staggered (type-II) band alignment, with offsets of the same sign between the conduction and valence bands. Panel (a) adapted with permission from ref. © 2012 the Author(s). Panel (b) reprinted with permission from ref. © 2019 the Authors