Defect-induced helicity dependent terahertz emission in Dirac semimetal PtTe2 thin films

Nonlinear transport enabled by symmetry breaking in quantum materials has aroused considerable interest in condensed matter physics and interdisciplinary electronics. However, achieving a nonlinear optical response in centrosymmetric Dirac semimetals via defect engineering has remained a challenge. Here, we observe the helicity dependent terahertz emission in Dirac semimetal PtTe2 thin films via the circular photogalvanic effect under normal incidence. This is activated by a controllable out-of-plane Te-vacancy defect gradient, which we unambiguously evidence with electron ptychography. The defect gradient lowers the symmetry, which not only induces the band spin splitting but also generates the giant Berry curvature dipole responsible for the circular photogalvanic effect. We demonstrate that the THz emission can be manipulated by the Te-vacancy defect concentration. Furthermore, the temperature evolution of the THz emission features a minimum in the THz amplitude due to carrier compensation. Our work provides a universal strategy for symmetry breaking in centrosymmetric Dirac materials for efficient nonlinear transport.

The interaction of ultrafast laser with topological materials has attracted significant attention in ultrafast optoelectronics, which not only provides an efficient way to characterize the band structures and spin textures 1,2 , but also serves as a control knob to dynamically induce topological phase transitions [3][4][5] and nonlinear optical responses 6- 8 .These intriguing quantum phenomena are closely associated with the topological characteristics of linear band dispersion 6 , Berry curvature 7 , and their inherent symmetries [3][4][5] .However, centrosymmetric Dirac materials can hardly produce spontaneous photocurrents via a second-order coupling with a pulsed electrical field owing to the symmetry requirements 5,9 .Thus, it is highly desirable to develop effective approaches to engineer the material symmetry breakings, thereby generating emergent nonlinear optical phenomena.
The circular photogalvanic effect (CPGE), as a second-order nonlinear effect, has been observed in a myriad of non-centrosymmetric materials/heterostructures [10][11][12][13][14][15][16][17][18][19][20] .The direction of the CPGE photocurrent can be switched by reversing the chirality of the light via the spin-flip transitions 10,18,19 or the nontrivial Berry curvature contribution 11,15,20 .To date, considerable efforts have been devoted to exploring multiple excitations in topological Weyl semimetals in the vicinity of Weyl nodes, which provides a static measurement of the chirality of Weyl fermions 7,21 .However, such electrical means seriously suffer from the limited time domain and spurious effects 22,23 .In this regard, polarized terahertz (THz) emission spectroscopy based on ultrafast femtosecond lasers is a powerful optical tool for generating and detecting ultrafast spin photocurrents 24,25 .Very recently, THz emission has been observed in centrosymmetric Dirac semimetal PtSe2 films due to the photon drag effect 26,27 and a second nonlinearity from a structural asymmetry 28  As an emerging type-II Dirac semimetal, PtTe2 exhibits high conductivity, high mobility, and good air stability, providing an ideal platform to explore novel physical properties for various applications [29][30][31][32] .Type-II Dirac semimetals feature the Lorentz variance and linear dispersion at a tilted Dirac cone, which could lead to anisotropic transport properties 29 .Strong interlayer interactions in PtTe2 could also lead to the thickness-dependent semimetal-semiconductor transitions 31,32 .Recently, defect engineering has been shown to break the inversion symmetry for inducing the intriguing Rashba effect in PtSe2 33,34 , which offers a promising opportunity to produce nonlinear transport in centrosymmetric Dirac semimetals.
In this article, we report the defect-gradient-induced helicity-dependent THz

Evidence of a defect gradient in PtTe 2 films revealed by electron ptychography
PtTe2 is a stacked structure of quasi 2D Te-Pt-Te layers formed through the van der Waals force.It belongs to the C3v symmetry point group with an inversion center, which is required for stabilizing type-II Dirac nodes 35 .In this work, large-area PtTe2 films with the intentionally created VTe defect are obtained by a controllable modified twostep CVD process (for details see Method and Supplementary Note 1 and Supplementary Figs. 1 and 2) [36][37][38] .The tellurization of pre-deposited Pt films is considered as a diffusion process with a finite Te concentration gradient, which is controlled by the thermodynamic conditions 36 .The X-ray diffraction (XRD) patterns, Raman spectra, Raman mapping images, and high-resolution scanning transmission electron microscopy (HR-STEM) images in a high-angle annular dark-field (HAADF) mode not only show the large-area uniformity of the as-grown films, but also consistently reflect the 1T-phase crystal structure of as-grown PtTe2 thin films without additional impurities (see Supplementary Figs.3-8).
With the unique deep-sub-angstrom resolution and low-electron doses, electron ptychography is a powerful tool to obtain images of single-atom defects and their depthdependent distribution in various material systems, such as MoS2, PrScO3, zeolites, and SrTiO3 [39][40][41][42] .To image defects at the sub-nanometer precision in PtTe2 films, multislice electron ptychography with adaptive-propagator (Fig. 1a) is also carried out.The original cross-sectional HR-STEM image of multilayer PtTe2 films grown on sapphire (Al2O3) substrates exhibits that d-spacing of the periodically arranged Pt atoms is approximately 0.53 nm (Supplementary Fig. 8b), perfectly matching the PtTe2 (001) 1T-phase structure.The corresponding ptychographic phase image (Supplementary Fig. 8c) is used for the examination of the vacancy defect.The enlarged phase images in four boxed, coloured areas are displayed in Fig. 1b,c, respectively.The intensity contrast at different Te atomic sites clearly demonstrates the presence of VTe, as reflected by the weaker intensity columns.We plot the intensity profile along the c-axis in Fig. 1d.The intensity of these Te peaks does decrease at these sites along the depth orientation.More electron ptychography observations of other slices show the consistent results (see Supplementary Figs. 9 and 10).
The inversion symmetry of the system can be broken by artificially introducing an organized defect distribution, which has been observed in van der Waals PtSe2 layers 33,34 .To visualize the depth distribution of VTe in our PtTe2 films, we perform the depth-profile mapping of a selected 29-layer PtTe2 film in Te sites (Fig. 1e).The obvious difference of mapping results along the depth orientation indicates that the distribution of VTe is inhomogeneous.The VTe-rich region is primarily concentrated in the midst of thin films.The relative phase intensity profile of Te/Pt in each layer shows the exact gradient-like rather than random distribution of VTe (Fig. 1f).Albeit the relatively large scatter, the experimental result from Layer 5 to 29 is largely consistent with density functional theoretical (DFT) calculations based on the growth dynamics (Supplementary Fig. 2d), indicating that the systematic gradient-like trend does exist in PtTe2 system.The corresponding Te/Pt relative phase mapping further affirm that the VTe defect is mainly concentrated in the midst of films (Supplementary Fig. 11).By contrast, the electron ptychography for Te-passivated PtTe2 films (i.e., post-annealing under the Te vapor to mostly eliminate VTe) shows the uniform out-of-plane distribution of Te (Supplementary Fig. 12).Moreover, the presence of VTe in the as-grown PtTe2 films is also revealed by the temperature-dependent Raman spectroscopy.As compared with the Te-passivated PtTe2 films, the defective sample containing VTe has a significant blue-shift for the Raman vibrational peak of Eg mode at low temperatures especially below 150 K, while the Raman peak of A1g mode keeps largely unshifted (Supplementary Note 2 and Supplementary Fig. 5c, d).This is due to the fact that the Eg mode and A1g mode are associated with in-plane and out-of-plane vibrations, respectively.The existence of VTe has the larger impact on the phonon frequency shift of the Eg mode 43 .The out-of-plane defect gradient naturally breaks the out-of-plane inversion symmetry.Meantime, the defect-gradient film can be considered as vertical collection of heterostructures composed of a myriad of PtTe2 monolayers with different VTe defect concentrations.The discrepancy in adjacent monolayers naturally breaks the in-plane inversion symmetry (reduced from C3v to C1).To this end, we provide the sufficient evidence of the out-of-plane defect gradient that induces in-plane symmetry breaking in PtTe2 films through high spatial-resolution structural characterization.

THz emission in symmetry-broken PtTe 2 films
Ultrafast-laser-induced THz emission based on second-order nonlinear effects has been recognized as a versatile probe of the symmetry breaking 44 .Figure 2a shows the schematic of the THz emission setup with a transmission configuration.The laser pulses have a duration of 100 fs at a central wavelength of 800 nm (1.55 eV) and a repetition rate of 1 kHz; the beam is normally incident on the PtTe2 films along the z-axis.The excitation by near-infrared light enables to investigate the unique nonlinear optical properties of type-II Dirac fermions, although the observed type-II Dirac point in PtTe2 resides far below the Fermi energy (~0.8 eV) 29 .
To demonstrate the symmetry breaking in PtTe2 films, first we investigate the THz emission under linear polarization (LP) of laser, and the various THz emission is observed under LP excitation by rotating the half-wave plate (HWP) with an angle ϕ /2 in defective PtTe2 films (Fig. 2b).Note that the THz emission efficiency of our PtTe2 films is three order magnitude larger than that of the standard ZnTe (Supplementary Fig. 13 and Supplementary Table 1), and it is comparable to those of topological semimetals 13,27 .The linear pump-fluence dependence of THz emission indicates that the emitted THz signals are dominated by a second-order nonlinear effect (Supplementary Fig. 14).The amplitude of THz emission exhibits a cosinoidal dependence on the ϕ /2 with a period of 180 o .Such a THz radiation is derived from the linear photogalvanic effect (LPGE) (i.e., shift current) owing to a real-space shift of the charge centers between initial and final electron states 45 .It is noticeable that the current has a geometrical origin that can be described by the Berry phase connection 46 .In contrast, no THz signals can be detected from the Te-passivated samples without the defect gradient (see bottom panel of Fig. 2c).Hence, the symmetry-broken PtTe2 films can serve as an attractive platform to study the exotic nonlinear optical phenomena.
As a further THz emission measurement, the as-grown PtTe2 films are subjected to left/right circularly polarized (LCP/RCP) excitations under normal incidence.
Notably, the THz radiation and its uniformity are clearly observed in the as-grown PtTe2 films (Fig. 2c and Supplementary Fig. 15).Likewise, no THz signals of helicity are detected from the Te-passivated sample (Fig. 2c).Together with the identical THz radiation intensity from the defective PtTe2 films grown on other substrates of MgO and quartz (Supplementary Fig. 16), the genuine defect-gradient-induced effect is thus nailed down.The emitted THz signals are linearly polarized under the LCP or RCP excitation (Supplementary Fig. 17).The difference between the THz radiation under the LCP and RCP excitation can be attributed to a second-order nonlinear CPGE, which can also be observed in other PtTe2 films with different thicknesses.The CPGE amplitude (the difference between the LCP and RCP excitations, Fig. 2d) can be modulated by the VTe contribution (equation ( 2)) from the thickness-dependent experiments (Supplementary Fig. 18 and Table 2).The polarity of the emitted THz signals switches when the pump laser changes between the LCP and RCP excitation.It could be considered as an asymmetry in the transient carrier population in the momentum space, as determined by the helicity-dependent optical selection rules (Fig. 3a) 15,47 .Other mechanisms for the THz emission are excluded according to our measurement geometry (Supplementary Note 3 and Supplementary Fig. 19).
To systematically investigate the helicity-dependent THz emission, we change the helicity of the elliptically polarized light by rotating the angle of the quarter-wave plate (QWP, θ /4 ). Figure 2d  (Supplementary Fig. 20), which is distinct from φ-independent CPGE observed in materials with the C3 rotational symmetry 49 .The detailed symmetry analysis further proves that symmetry point group of defect-gradient PtTe2 system is lowered from C3v to C1 (Supplementary Note 4 and Supplementary Fig. 21).The modulation of the CPGE with the helicity of the laser pump shows that the ultrafast spin photocurrent is more pronounced along the inversion-symmetry axis (i.e., φ = 0 o ) for opto-spintronic applications.As a complementary tool to the THz emission, the optical second harmonic generation is further measured to confirm the inversion symmetry breaking in defect-gradient PtTe2 films (Supplementary Fig. 22).

First-principles calculations for band structures of PtTe 2
As mentioned above, the observed helicity-dependent THz radiation is attributed to the optical selection rule.A spin splitting arising from the intrinsically broken inversion symmetry and the strong spin-orbit coupling should occur in the defect-gradient PtTe2 (schematically shown in Fig. 3a).To elucidate the influence of the VTe gradient on the PtTe2 band structure for the helicity-dependent THz emission, DFT-based firstprinciples calculations are performed.The band structure of the bulk defect-free PtTe2 sample near the Dirac point shows no spin splitting at all because the system has the spatial inversion symmetry (Fig. 3b).To understand the CPGE induced by the VTe defect gradient in the experiment, we use the average defect gradient between two Te sub-lattices within a minimum approximation model of the bulk PtTe2 sample, which roughly capture the key band variation (Fig. 3c).Compared to the band structure of PtTe2 without defects (Fig. 3b), a considerable gap does open near the Dirac point and the momentum-dependent spin splitting happens.It can be further verified from the different directions (see Supplementary Fig. 23 and Fig. 4e,f).The band spin splitting energy ( = 15±5 meV at  point and  = 70±5 meV at K point) is comparable to the other typical materials (note that at K point is larger than those of Weyl semimetals 16,59 , Supplementary Table 3).The upshift of the Dirac point, closer to the Fermi level, is more favorable for the photoexcitation.Furthermore, we also compare the band structure in samples with the uniform defects and a defect gradient along the depth (Supplementary Fig. 24), and find that the presence of the defect gradient is critical to achieve the selective excitation with respect to the uniform defects.
A previous experiment demonstrated that PtTe2 films with more than three layers exhibited the bulk band features 32 .To precisely explore the VTe gradient in the as-grown films, we further choose an 8-layer-thick PtTe2 sample (corresponds to the thickness of 4 nm with the THz emission shown in Supplementary Fig. 18a) and provide the DFTcalculated band structures with and without a defect gradient.A slab geometry composed of 8 layers of PtTe2 and 20 Å vacuum is adopted to describe the genuine experimental situation (Fig. 3d).Notably, spin degeneracy is preserved in the stoichiometric sample because the inversion symmetry is protected even by decreasing the thickness of the film from bulk to 8 layers (or any other number of layers) (Fig. 3e).
Very remarkably, spin splitting does occur in the VTe-gradient sample containing a larger number of subbands owing to the inversion symmetry breaking (Fig. 3f).It is seen that band structures are quite different between defect-free and defective PtTe2, leading to the dramatic changes of the band structure of the defect-free material.These theoretical results further consolidate that the spin splitting induced by the symmetry breaking is a prerequisite for the experimentally observed emergent THz emission.

Defect engineering of the helicity-dependent THz emission
As shown above, the VTe defect gradient breaks both the C3 rotational symmetry and the inversion symmetry, which may lead to the asymmetric distribution of Berry curvature ( ( )) and non-vanishing BCD ( ), namely the dipole moment of Berry curvature over the occupied states 50 .Berry curvature is an important geometrical property of Bloch bands, which plays a dominant role in the nonlinear transport in timereversal-invariant materials [51][52][53] .It has been theoretically shown that the CPGE is directly proportional to the BCD 47,[54][55][56] .
We investigate the dependence of the CPGE amplitude extracted from THz emission on the tunable VTe-defect concentration in 18-nm-thick PtTe2 films under invacuo annealing.The VTe formation is thermodynamically favorable since it has a lower formation energy under a Te-poor annealing environment.As seen from the annealingtime-dependent THz emission (Fig. 4a), we find that the THz emission intensity first increases until it reaches a maximum around one hour of annealing, and then decreases with time evolution.The micro-Raman spectra taken from all annealed films ensure the where is the carrier relaxation time and ( ) = √ ( , ± , 0) describes the electric field of the normal incident RCP and LCP light.As long as the BCD is nonzero (i.e., ≠ 0), the CPGE photocurrent can be observed under normal incidence in the symmetry-broken PtTe2.In right panels of Fig. 4d-f, it is seen that the BCD ( ) becomes more dominant when the VTe gradient is larger.The larger VTe gradient, the more VTe contribution.Hence, the BCD's trend is entirely consistent with our experimental observation (Fig. 4c).Notably, the BCD value is giant, which can reach the order of 10 nm with a maximum value up to ~64 nm (Supplementary Fig. 26a), typically larger than that (~8 Å) calculated in monolayer WTe2 11 .Importantly, the carrier relaxation time () will become short once the VTe concentration is excessively high upon the elongation of the annealing time.Consequently, the CPGE amplitude drops after one-hour annealing and reaches a minimum value according to equation ( 4).
We thus obtain the quantitative relationship between the CPGE and the BCD through the defect engineering.

Temperature-dependent THz emission in defect-gradient PtTe 2 films
It should be noted that the contribution of defects becomes more pronounced as the temperature decreases, as manifested by the temperature-dependent Raman spectra (Supplementary Fig. 5).Therefore, it is highly desirable to reveal the influence of defects on THz radiation at low temperatures.The 35-nm-thick PtTe2 films were cryogenically cooled during measurements.Intriguingly, with decreasing temperature, both THz amplitudes under LCP and RCP in principle decrease monotonously and then increase (Fig. 5b), featuring a minimum near 120 K (green-shaded area).Given that the carrier compensation effect destroys the spin photocurrent generation 59 , we then measure the temperature-dependent Hall behaviors of the PtTe2 films (Fig. 5c).Above 120 K, the Hall coefficient is negative, suggesting the electron-type carriers dominate the transport behavior.As the temperature decreases, the Hall coefficient remains negative at low fields, but the slope decreases at the higher fields, indicating the presence of multiband effects in PtTe2.The temperature dependence of the carrier density and mobility is plotted in Fig. 5d.The extracted carrier density shows an electron-rich case at high temperatures and a nearly compensated carrier concentration below 120 K, which exactly coincides with the minimum of the THz amplitudes (Fig. 5b).As temperature reaches 120 K, the excited electrons and holes compensate each other, resulting in a diminished photocurrent.When temperature is lower than 120 K, the increasing mobility of electrons leads to an increase in photocurrent, although carrier compensation is still maintained.When temperature is above 120 K, the carrier compensation gradually decreases, and electron carriers increase dominantly (the inset of Fig. 5d), thus enhancing the photocurrent.Consequently, the minimum of the THz amplitude observed near 120 K can be attributed to the electron-hole compensation.
This provides a profound insight into the temperature-dependent THz emission via VTeinduced Hall nonlinear characteristic.It should be noted that albeit the strong THz emission amplitude, the CPGE amplitude is relatively weak, i.e., the helicity-dependent THz emission is not remarkable from 50 to 300 K (Fig. 5b), which is attributed to the fact that when the film is thick it is difficult to control VTe gradient-like distribution throughout the depth orientation.The relatively prominent CPGE amplitude at 50 K is attributed to the more VTe contribution at low temperatures (Supplementary Fig. 5).

Discussion
We have demonstrated the generation of vacancy-defect-gradient-induced helicitydependent THz emission via CPGE in PtTe2 thin films.The high spatial resolution of adaptive-propagator ptychography enables us not only to directly observe the subangstrom VTe, but also to provide its depth distribution.These results affirm our claim that the out-of-plane vacancy gradient breaks the inversion symmetry, inducing the considerable band spin splitting and the anisotropic CPGE photocurrent.The CPGE is activated by the giant BCD due to the vacancy-defect gradient along the depth orientation, as corroborated by the theoretical calculations.The CPGE amplitude can be largely tunable by the defect concentration using the in-vacuo annealing.The temperature evolution of the helicity-dependent THz emission reveals that the minimum of the THz emission amplitude is attributed to the compensated electron and hole carriers.Furthermore, the helicity-dependent THz emission is also observed in the Se-vacancy-gradient PtSe2 films under normal incidence, indicating the universality of our unique strategy of the symmetry engineering in Dirac semimetals (see Supplementary Fig. 27).Our work provides an alternative pathway to manipulate spin photocurrents that are otherwise unavailable in centrosymmetric Dirac semimetals, which facilitates the development of nonlinear optical devices and integrated THz spintronic devices based on quantum materials.

Growth of PtTe 2 films
Large-area PtTe2 films with the various thickness were grown by a modified two-step CVD process on the (0001)-oriented Al2O3 substrate (Shanghai Institute of Optics and Fine Mechanics).First, Pt films with controlled thickness of 1-10 nm were deposited on clean Al2O3 substrates by magnetron sputtering at a fixed rate of 1.25 Å s -1 .Second, the pre-deposited Pt films were tellurized to form large-area and high-quality PtTe2 films (for details see Supplemental Note 1).Te powder, as a reaction source, was placed in a quartz tube with an inner diameter of 10 mm and two open ends.In addition, the furnace was heated to a growth temperature of 400 °C at a rate of 13.3 °C min -1 and maintained for 30-120 minutes, followed by a forming gas (95% Ar and 5% H2) delivered at a rate of 100 standard cubic centimeters per minute.Subsequently, it was cooled down to room temperature naturally after the growth.During the growth process, the carrier gas was maintained to prevent the samples from oxidation.Control samples were prepared by post annealing under Te vapor to mostly eliminate the VTe defect gradient, which is regarded as Te-passivated.The PtTe2 films grown on other substrates of MgO (111) and quartz glass were also prepared by the same procedure.The in-vacuo annealed samples with thickness of 18 nm were heated to 300 o C for duration from 20 to 100 mins, with the flowing forming gas applied to accelerate the VTe formation.
Additionally, the low-temperature THz emission measurements were conducted only on the 35-nm-thick PtTe2 films.

Magnetotransport measurements
Prior to transport measurements, the Hall-bar contacts with eight-probe configuration were fabricated by silver paste on films, as schematically shown in the inset of Fig. 4b.
Magnetotransport measurements were measured using a Cryogenic cryogen-free measurement system (CFMS-12).The perpendicular magnetic field up to 12 T was applied to the film surface.

Second harmonic generation measurements
The second harmonic generation measurements were performed using a Ti:sapphire oscillator (duration: 70 fs, repetition rate: 80 MHz, central wavelength: 810 nm).The laser pulse was focused to a spot size of ~1 μm on the films by a 40× objective lens.
The generated second harmonic light was detected by a photomultiplier tube, and the harmonic generation signal was collected in the reflection mode.

First-principles DFT calculations
All the band structures were calculated using the Vienna Ab-Initio Simulation Package (VASP) 60,61 within DFT in the regime of local density approximation (LDA) implemented by a projector-augmented wave.Spin-orbit coupling was included in all calculations.We used lattice constants a = b = 4.03 Å and c = 5.22 Å for the PtTe2 crystal 31 , and test k-point meshes and energy cutoff for the convergence to stabilize the structure.The plane wave basis energy cutoff and the force convergence standard were set to 500 eV and 0.01 eV Å -1 , respectively.The self-consistent convergence criterion was set to 10 -6 eV.Here, we mainly showed the DFT band structures of the bulk PtTe2 sample and 8-layer thick sample, where the 8 × 8 × 6 grid of k-points was used for the former and the 13 × 13 × 1 grid point sampling with Γ-centered Monkhorst-Pack adopted for the latter.To eliminate the interaction of adjacent slab calculations, vacuum spacing (16 Å) was added above the topmost layer of the 8-layer thick sample.To simulate the VTe of the experimental samples, we employed the virtual crystal approximation (VCA) method 62 , which was proven to be valid in studying the topological phase transition 63 and the Rashba physics 34 .Average defects within a minimum approximation model were used to roughly capture the key band variation, where the vacancy defect gradient was set between two Te sub-lattices.In addition, we further used the widely-used open source Wannier90 codes to fit the DFT band structures.Meanwhile, we developed the home-made codes to obtain the corresponding effective Hamiltonian and then calculated the subband-dependent Berry curvature and the energy-dependent BCD (see Supplementary Note 6 for details).
Nonlinear transport enabled by symmetry breaking in quantum materials has aroused considerable interest in condensed matter physics and interdisciplinary electronics.However, the nonlinear optical response in centrosymmetric Dirac semimetals via the defect engineering has remained highly challenging.Here, we observe the helicity-dependent terahertz (THz) emission in Dirac semimetal PtTe 2 thin films via circular photogalvanic effect (CPGE) under normal incidence.This is activated by artificially controllable out-of-plane Te-vacancy defect gradient, which is unambiguously evidenced by the electron ptychography.The defect gradient lowers the symmetry, which not only induces the band spin splitting, but also generates the giant Berry curvature dipole (BCD) responsible for the CPGE.Such BCD-induced helicity-dependent THz emission can be manipulated by the Te-vacancy defect concentration.Furthermore, temperature evolution of the THz emission features the minimum of the THz amplitude due to the carrier compensation.Our work provides a universal strategy for symmetry breaking in centrosymmetric Dirac materials for efficient nonlinear transport and facilitates the promising device applications in integrated optoelectronics and spintronics.
. Remarkably, Luo et al. observed the light-induced transient phase transition and hence giant photocurrent (i.e., THz emission) in bulk Dirac semimetal ZrTe5 5 .However, THz emission in Dirac semimetals with intrinsic inversion symmetry breaking has rarely been seen.
emission in PtTe2 thin films grown by a modified two-step chemical vapor deposition (CVD) method.The main Te-vacancy (VTe) defect is created during crystal growth along the depth orientation, as evidenced by adaptive-propagator ptychography with deep-sub-angstrom resolution.The inversion-symmetry-broken PtTe2 shows a remarkable CPGE based on the polarized THz emission spectroscopy.Combing firstprinciples calculations and defect engineering, we unambiguously demonstrate that the helicity-dependent THz emission originates from the band spin splitting and the predominantly giant Berry curvature dipole (BCD).Moreover, temperature-dependent THz emission shows the THz amplitude reaches a minimum at about 120 K due to the carrier compensation.Our findings may provide the great potential for the realization of nonlinear optical devices based on Dirac materials containing a defect gradient.
photocurrents have a strong in-plane anisotropy.It is noticeable that C shows a significant dependence on the sample azimuthal angle φ due to the lowered symmetry

Fig. 1 |
Fig. 1 | Out-of-plane vacancy-defect gradient visualized by electron ptychography.a, Schematic illustration of the multislice electron ptychography for depth sectioning of a PtTe2 sample.During ptychographic reconstruction, the sample is divided into 15 slices and each slice is ~2 nm in thickness.b,c, The summed phase images of [001] PtTe2 over 15 slices taken from orange, blue, grey, and green rectangles of Supplementary Fig. 8c, respectively.The scale bar is 5 Å.The yellow arrows marked in c denote the VTe due to a relatively weak mapping intensity.d, The corresponding profiles of phase intensity taken from atomic columns marked with blue, grey and green rectangles in c, respectively.e, Te phase mapping in the selected 29-layer PtTe2 film from near the substrate to near the top surface.Light and dark colours denote the low and high VTe concentration, respectively.The substrate is schematically shown.The scale bar is 1 nm.f, The relative phase intensity variation of the Te/Pt in each PtTe2 layer, which is extracted from Supplementary Fig. 11.The intensity is normalized by the maximum intensity.

Fig. 2 |
Fig. 2 | Helicity-dependent THz emission observed in symmetry-broken PtTe 2 films with the thickness of 10 nm.a, Schematic illustration of the experimental setup for THz emission measurements.The HWP and QWP are placed before the PtTe2 films to change the polarization of normally incident laser pulses by varying the angles of ϕ /2 and θ /4, respectively.The coordinate system (xyz) is adapted for the laboratory frame.The sample is set in the x-y plane and the azimuthal angle is denoted by φ with respect to the y-axis.The normal incidence is realized through the observation of the reflected light going back along its original optical path.b, The THz amplitudes under different LP excitations.c, Transient THz waveforms from the as-grown PtTe2 film (top panel) and Te-passivated PtTe2 films (bottom panel) under the RCP and LCP excitations at φ = 0 o , respectively.The THz emission of the annealed sample under the LP excitation is also included.The inset of c shows the schematic diagrams of the distribution of VTe for the as-grown and passivated samples, respectively.d, THz peak amplitudes at φ = 0 o (blue) and φ = 90 o (orange) as functions of θ /4, where the solid line represents the fitting.Arrows atop the panels indicate the polarization sequences, where the red and blue circles represent LCP and RCP, respectively, and the black double arrows represent LP.The red double arrow shows the difference between the LCP and RCP excitations, which is defined as the CPGE amplitude.The insets show the normalized fitting parameters extracted from the THz emission.

Fig. 3 |
Fig. 3 | Band spin splitting enabled by a defect gradient.a, The band diagram of the optical selection rules for the symmetry-broken PtTe2.The dashed line denotes the Fermi level (EF).The blue and red arrows denote the electronic states with the opposite spins.b,c, Band structures for the bulk samples without defects and with a defect gradient, respectively.The high-symmetry points Γ, M, and K in the (kx, ky) plane of the reciprocal space are shown in the inset of b. d, Schematic diagram of an 8-layerthick PtTe2 film with a defect gradient.The VTe gradient is indicated by the colour scheme on the right.e,f, Band structures for a concrete 8-layer-thick PtTe2 sample without defects and with a defect gradient, respectively.Notably, spin degeneracy is preserved in both defect-free bulk in b and defect-free 8-layer-thick PtTe2 sample in e.However, a band spin splitting occurs in c,f where the number of subbands increases.The colours denote the proportion  contributed by the upper and lower surface layers.

Fig. 4 |
Fig. 4 | Microscopic origin of THz emission through defect engineering.a, The transient THz waveforms of PtTe2 films with various in-vacuo annealing time under LCP and RCP at φ = 0 o , respectively.b, Hall curves of PtTe2 films with various invacuo annealing time under the perpendicular field at 5 K.The inset shows a schematic of Hall bar device structure.c, The extracted CPGE amplitude from a and extracted VTe contribution from b as a function of the annealing time.The thickness of PtTe2 films is 18 nm.d-f, Band structures and Berry curvatures of PtTe2 obtained within the homemade codes.DFT bands are fitted for the defect-free sample in d and the defective samples with VTe concentration difference of 18% in e and 22% in f between two Te atoms in the minimum model, respectively.The right panels in d-f show the x component of BCD ( ) for the defect-free and defective samples, respectively.No BCD is found in the defect-free sample.

Fig. 5 |
Fig. 5 | Temperature-dependent THz emission and its correlation with carrier compensation.a, Temperature-dependent transient THz waveforms at φ= 0 o under LCP and RCP, as shown in the top and bottom panel, respectively.b, The THz amplitudes as a function of temperature, which is extracted from a. c, The temperaturedependent Hall curves of PtTe2 films under the perpendicular field.d, The extracted carrier concentration and mobility at various temperatures.Note that the PtTe2 film shows the Hall transition from nonlinearity to linearity within the temperature of the light green region (~120 K), coinciding with the minimum of THz amplitude shown in b.The inset of d shows the temperature dependence of ne/nh ratio.The thickness of PtTe2 films is 35 nm.