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Haotian Jiang, Tairan Xi, Jiangxu Li, Yangchen He, Hongrui Ma, Yulu Mao, [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), Daniel A. Rhodes, Yang Zhang, Jun Xiao, Ying Wang

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[Probing interplay of topological properties and electron correlation in TaIrTe4 via nonlinear Hall effect](https://mdr.nims.go.jp/datasets/777f11fd-0b5c-46bd-9c3d-187f28c42008)

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Probing interplay of topological properties and electron correlation in TaIrTe4 via nonlinear Hall effectArticle https://doi.org/10.1038/s41467-025-61347-3Probing interplay of topological propertiesand electron correlation in TaIrTe4 vianonlinear Hall effectHaotian Jiang1, TairanXi2, JiangxuLi 3,YangchenHe 2,HongruiMa1, YuluMao1,Takashi Taniguchi 4, Kenji Watanabe 5, Daniel A. Rhodes 2,6,Yang Zhang 3,7, Jun Xiao 1,2,6 & Ying Wang 1,2,6Studying the interplay of electron correlation and topology is crucial for dis-covering new quantum states, such as the fractional quantum spin Hall effectand topological superconductors. Unlike linear transport, nonlinear electricalresponses, which encode both symmetry and topological features remainlargely unexplored in systemswith electron correlation and topology. Herewereport that nonlinear Hall measurements reveal the emergence of a correlatedstate in few-layer topological semimetal TaIrTe₄ below a critical temperatureand bias current. This state, exhibiting ultra large nonlinear conductivity, isattributed to the formation of a charge density wave in TaIrTe4 that leads tosubstantial Berry curvature redistribution. This origin is further supported bythe observation of a Raman amplitude mode associated with the chargedensity wave, enhanced second harmonic generation, and first-principlescalculations. Our findings demonstrate that nonlinear electrical probes canaccess rich phase diagrams in topologicalmaterials and highlight the potentialof correlated topological systems for developing nonlinear electronics.Topological semimetals are materials characterized by gapless elec-tronic excitations and unique band crossings in their electronicstructure, leading to exotic phenomena such as the chiral anomaly andFermi arcs1–4. Many of these intriguing quantum phenomena are clo-sely related to their topological properties, including chiral Weylnodes and sizable Berry curvature in the momentum space1,2,4,5. Prob-ing how these topological properties evolve in different quantumorderings and quantum transitions is crucial for advancing theunderstanding of topological semimetals and paving the way for high-performance topological electronics. The recently discovered non-linearHall effect (NLHE) hasbeenutilized as a Berry curvatureprobe tocharacterize the asymmetric distribution of positive and negativeBerry curvature, namely the Berry curvature dipole (BCD), in themomentum space of topological semimetals with broken inversionsymmetry6–8. In a material with a nonzero BCD, an electric field, E,induces a second-order transverse current, whose magnitude quanti-tatively reveals the BCD near the Fermi level. The response of thisnonlinear transport is also sensitive to ordering symmetry6–9, making ita useful tool for probing order parameters of broken symmetry statesand their impact on topological properties.Beyond non-interacting electronic structure studies, there is agrowing interest in exploring strong correlations in topological semi-metals to discover new quantum states of matter. This approachpromotes quantum fluctuations and induces rich correlated states,such as topological superconductors, axion charge density waves(CDW), and fractional quantum spin Hall3,10–14. Given the fact thatReceived: 25 October 2024Accepted: 18 June 2025Check for updates1Department of Electrical andComputer Engineering, University ofWisconsin-Madison,Madison,WI, USA. 2Department ofMaterials Science and Engineering,University of Wisconsin-Madison, Madison, WI, USA. 3Department of Physics and Astronomy, University of Tennessee, Knoxville, TN, USA. 4Research Centerfor Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan. 5Research Center for Electronic and Optical Materials, NationalInstitute for Materials Science, Tsukuba, Japan. 6Department of Physics, University of Wisconsin-Madison, Madison, WI, USA. 7Department of ElectricalEngineering and Computer Science, University of Tennessee, Knoxville, TN, USA. e-mail: y.wang@wisc.eduNature Communications |         (2025) 16:6351 11234567890():,;1234567890():,;http://orcid.org/0000-0002-4534-4208http://orcid.org/0000-0002-4534-4208http://orcid.org/0000-0002-4534-4208http://orcid.org/0000-0002-4534-4208http://orcid.org/0000-0002-4534-4208http://orcid.org/0000-0002-5518-5087http://orcid.org/0000-0002-5518-5087http://orcid.org/0000-0002-5518-5087http://orcid.org/0000-0002-5518-5087http://orcid.org/0000-0002-5518-5087http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0002-7651-3211http://orcid.org/0000-0002-7651-3211http://orcid.org/0000-0002-7651-3211http://orcid.org/0000-0002-7651-3211http://orcid.org/0000-0002-7651-3211http://orcid.org/0000-0003-4630-5056http://orcid.org/0000-0003-4630-5056http://orcid.org/0000-0003-4630-5056http://orcid.org/0000-0003-4630-5056http://orcid.org/0000-0003-4630-5056http://orcid.org/0000-0003-4248-8190http://orcid.org/0000-0003-4248-8190http://orcid.org/0000-0003-4248-8190http://orcid.org/0000-0003-4248-8190http://orcid.org/0000-0003-4248-8190http://orcid.org/0000-0002-5307-8384http://orcid.org/0000-0002-5307-8384http://orcid.org/0000-0002-5307-8384http://orcid.org/0000-0002-5307-8384http://orcid.org/0000-0002-5307-8384http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-61347-3&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-61347-3&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-61347-3&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-61347-3&domain=pdfmailto:y.wang@wisc.eduwww.nature.com/naturecommunicationsstrong correlations lead to instability and reconstruction of electronicbands near the Fermi surface, along with the change in topology, theassociated Berry curvature redistribution makes NLHE a potential toolfor exploring rich correlated phase transitions in topological semi-metals, which remains largely unexplored.TaIrTe4, as a type-II Weyl semimetal15, has attracted a lot ofinterest recently due to its remarkable topological properties in bothbulk and monolayer forms, such as Berry curvature enhanced photo-response and the quantum spin Hall effect16–18. NLHE has been studiedin bulk TaIrTe4, in which a sizable BCD is observed as a result of sub-stantial Berry curvature near Weyl points and broken inversionsymmetry19, but has remained unexplored in the atomically thin limitdue to the centrosymmetric structure of monolayer TaIrTe4, whichdiminishes any intrinsic BCD. The recent work of the dual quantumspin Hall effect in monolayer TaIrTe4 indicates the formation of astrongly correlated state, which could be a CDW, yet the directexperimental evidence is missing18. Therefore, few-layer topologicalsemimetal TaIrTe4 becomes a favorable candidate to study the inter-play of strongly correlated states and topological features by NLHE.In this work, we use NLHE to reveal an electronic phase diagram inlayered topological semimetal TaIrTe4 (from two layers to ten layers).Our findings reveal a two-orders-of-magnitude enhancement in NLHEbelow the critical temperature and current, indicative of the emer-gence of a correlated state. Transition to this state can exhibit tem-perature- and current-dependent hysteresis in NLHE, respectively.Through temperature-dependent low-frequency Raman spectroscopyand symmetry information extracted from angle-dependent NLHE andnonlinear optical measurements, we identify this state as a one-dimensional (1D) CDW along the Ta atom chain. Density functionaltheory (DFT) calculations further confirm the formation of this 1DCDW state arises from a strong electronic instability in few-layerTaIrTe₄, and results in the enhancement of BCD and NLHE.Results and discussionThe lattice structure of a few-layer TaIrTe4 is shown in Fig. 1a with amirror planeM â. As restricted by symmetry, NLHE is nonzero along theb̂-axis in response to a perpendicular driving current, Iω = I0 sinðωtÞ,with frequency ω along the â-axis, while NLHE is expected to be neg-ligible along the â-axis19 (See Supplementary Note 1). To accuratelydetermine the crystal orientation of anisotropic two-dimensional (2D)flakes, polarized Raman spectroscopy is employed in a parallelconfiguration20 (see “Methods”). Figure 1b displays the Raman spec-trum for two representative polarization directions with respect to thecrystal â-axis. The intensity of several modes depends strongly on thepolarization direction, especially the modes at 77 cm�1, 103 cm�1, and160 cm�1, which correspond to the A1 modes of Td-TaIrTe418. Specifi-cally, the polarization direction corresponding to the maximum of the103 cm�1 mode and the minimum of 77 cm�1 and 160 cm�1 modes isalong the â-axis of the crystal20, which helps to identify the â-axis forHall bar-shaped devices. Accordingly, high-quality TaIrTe4 Hall bardevices are fabricated with source-drain electrodes along the â-axisand encapsulated by hexagonal boron nitride (hBN) (Fig. 1c, seeTeIrTaaMabaca50 100 150 200 250−50050100200250300Intensity (arb. units)Raman Shift (cm-1 ) 0� 90�103 16077150bI������TaIrTe4BN10 �mabTaIrTe4c d0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0010203040I �aa (�A)2 K300 KV2� ab (�V)Fig. 1 | Crystal structure and basic characterization of thin film TaIrTe4. a Thelattice structure of TaIrTe4 from the top view (left) and side view (right). Thecrystalline directions are noted. b Angle-resolved Raman spectra intensity for thehBN-covered few-layer TaIrTe4 measured in a parallel-polarized configuration atstage rotation angles of 0° and 90°, the polarization is parallel with the crystallineâ-axis and b̂-axis, respectively. c Schematic andoptical imageof theHall bar-shapeddevice tomeasureNLHE. The second harmonicHall voltage ismaximized along theb̂-axis with alternating driving current along the â-axis. Scale bar, 10 µm. d Thetypical NLH response V 2ωab at temperatures of T = 2 K and T = 300 K. Dashed curvesrepresent quadratic fits to the V–I characteristics.Article https://doi.org/10.1038/s41467-025-61347-3Nature Communications |         (2025) 16:6351 2www.nature.com/naturecommunications“Methods” for more details). To quantify NLHE, transverse voltagealong the b̂-axis V2ωab ismeasured with the input AC along the â-axis Iωaa.Unconventional nonlinear conductivity enhancementFigure 1d shows the nonlinear Hall (NLH) measurements in a six-layersample at T =2 K and T =300 K. In both cases, V 2ωab exhibits a clearquadratic dependence on Iωaa, but with a striking difference in magni-tude. At 2 K, the NLH response is 350 times larger than at room tem-perature. We quantify this enhancement by extracting the second-order nonlinear conductivity χαββ from the nonlinear I-V curves usingthe relation j2ωβα = χαββEβEβ, where j2ωβα is the second-order currentdensity in the α direction, driven by the electric field, Eβ, in the βdirection6: Such observation distinctly differs from the temperature-dependent NLHE in bulk TaIrTe4, where both the nonlinear con-ductivity and BCD show no significant enhancement at low tempera-ture, other thanminor changes due to Fermi level shifts19. Additionally,in the few-layer limit, the absolute value of χbaa (�20 μmV�1Ω�1) issignificantly boosted bymore thanfive orders ofmagnitude comparedto previous studies on bulk19, suggesting an enhancement mechanismunique to ultrathin TaIrTe₄.Phase diagram probed by NLHETo understand the physics of the enhanced NLHE in few-layerTaIrTe4 at low temperature, we conduct systematic temperature-dependent NLH measurements on a 6-layer TaIrTe4, across a widerange of injected current, Iωaa, as shown in Fig. 2. In particular, V2ωab(Fig. 2a) and the corresponding phase θ2ωab (Fig. 2b) are probed. θ2ωab isexpected to be ±90°, depending on the direction of BCD, based onthe expression of the second-order NLH voltage7:V 2ωab =V0 sinð2ωt +θ2ωab Þ / ± Iωaa� �2jAC = 12 I20 sinð2ωt ± π2Þ. Interestingly,with varying Iωaa and temperature, we find two distinct states(marked as state I and state II, respectively) with clear NLH voltageand phase boundaries, separated by a critical temperature, TC � 60K and critical driving current, IC ≤ 20 μA. Within the dome enclosed4 8 12 16 20 24 28 32 36 40 44 48 52 56 60481216202428 (�A)I� aa−10−8−6−4−20246810(�V)V 2�ab80 100120140160180200220240260280300T (K)State IState IIa4 8 12 16 20 24 28 32 36 40 44 48 52 56 60481216202428 (�A)I� aa-90-70-50-30-10 10 30 50 70 90 (�)2�abθ80 100120140160180200220240260280300T (K)State IIState Ibc0 200 400 600 800 10000510152025309060300-30-60-90   260 K  220 K  300 K  180 K  140 K  100 K /  / / / / / /( )2 (�A2)I�aa (�)2 � abθ(�V)V 2 � ab 2�abθ V 2�ab0 5 10 15 20 25 30 35−15−10−509060300-30-60-90  56 K  44 K   32 K  20 K  8 K  2 K / / / / / / (�)2 � abθ(�V)V 2 � ab / 2�abθ V 2�ab( )2 (�A2)I�aad0 5 10 15 20 25 30 3503060901201501800 5 10 15 20 25 30 350102030    at 10 K  (     )   at 10 K  fitted quadratic curves�A (�)2�abθ2 � abθ(�V)V 2 � abswept upswept updown downV 2�abI �aae0 20 40 60 80 100100−10−20−30−40−50−60 State I (I > IC) State II (T swept Down) State II (T swept Up)T (K)�baa ~ -20 �m V-1�-1�baa ~ 0.1 �baa ~ 1.5 �m V-1�-1�m V-1�-1 (V-1)� abfFig. 2 | Phase transitionwith enhancedNLHE in few-layer TaIrTe4. a The 2Dmapof the NLH voltage V 2ωab as a function of temperature and input current.bCorrespondingmapof theNLHphase θ2ωab . Bothmaps indicate the onset of state IIbelow60K and low driving current below 20 μA. Crosscuts of V 2ωab and θ2ωab for stateI and state II are shown in c andd respectively. In both panel, dashed lines representlinear fits to the V 2ωab data and the solid lines are guides to the θ2ωab data. Phasetransitionbetween state I and state II with hysteresis window, driven by current andtemperature independently, are shown in e, f, respectively. In e the dashed curvesrepresent quadratic fits to the V–I characteristics. In f error bars represent thestandard error of ηab from quadratic fitting and the dashed line marks ηab = 0 as areference for the direction of the NLHE.Article https://doi.org/10.1038/s41467-025-61347-3Nature Communications |         (2025) 16:6351 3www.nature.com/naturecommunicationsby these thresholds (state II), relative to the outer region (state I),V 2ωab exhibits two orders’ enhancement and a sign reversal with a180° phase shift from −90° to 90°.In the following, we will take a closer look at each of state and thetransition between them. From 300K to 70K, TaIrTe4 shows a stan-dard NLH response as the temperature changes. As shown in Fig. 2c,line cuts of Iωaa versus V2ωab for 6 different isotherms all show a second-harmonic transverse voltage which scales quadratically with theapplied longitudinal current (V 2ωab / ðIωaaÞ2), maintaining a −90° phaseacross the whole current range. The value of the NLH generationefficiency21,22, ηab =V2ωabVωaað Þ2, shows a gradual shifting from 0.5 to 1 V�1 inthis region, which is attributed to the shifting of the chemical potentialwith temperature. The value of ηab of our few-layer sample in state I isalready four orders of magnitude higher than its bulk counterpart,since only the surface of the bulk contributes to NLHE19.Below 60K, TaIrTe4 exhibits a distinctly different NLHE, sug-gesting the formation of state II in the critical region (T <TC andIωaa < IC). By taking line cuts within this critical region (Fig. 2d), we findthatV 2ωab maintains a quadratic relationship below 5 µA and is enhancedby two orders of magnitude with respect to room temperature, with arelative shift ofπ for θ2ωab as compared to state I. When Iωaa is above 5 µA,the quadratic behavior diverges, suggesting that the large current candestroy state II. This effect is highlighted in Fig. 2e, where V 2ωab ismeasured at 10 Kby sweeping Iωaa. As shown, continuing to increase theIωaa above 20 µA restores the NLH response, where V 2ωab scales quad-ratically with Iωaa with θ2ωab flipping back to −90°, the same as state I. Thisobservation implies that the transition between state I and state II canbe driven by current.We also show the very slight change ofV2ωab = Iωaa� �2above IC over the whole temperature region from 300K to 2K (SeeSupplementary Note 2) and the linear resistance behavior across theentire temperature range, which is consistent with Fermi-liquid theoryfor currents exceeding IC (See Supplementary Note 3). Both observa-tions consolidate that TaIrTe4 has fully transitioned to state I above ICand there is a uniform state—state I—outside the critical region, whereTaIrTe4 displays normal NLH behavior with moderate strength, ascorroborated in other studies7,8,19. The 2D maps of the NLHE alsosuggest that the transition between state I and state II can be driven byeither temperature or incident current, where the Joule heating effectinduced by current has been excluded (See Supplementary Note 4). Apossiblemechanism for this current-induced phase transition could bethe depinning of charge order induced by current as discussed inSupplementary Note 5.First-order phase transition driven by current and temperatureMoreover, we observe a hysteresis of NLHE when sweeping either thecurrent or temperature. In Fig. 2e, NLH response ismeasured at 10Kbysweeping Iωaa. During the transition between the two states, hysteresiswindows between 7 µA and 20 µA are observed in both theNLH voltageV 2ωab and phase θ2ωab , plotted in black and red respectively. Similarly, inFig. 2f, a thermal hysteresis window, approximately 5 K wide, is alsoobserved in ηab during the temperature sweeps across state I and stateII, when measured at small driving currents (<5 µA). This hysteresisbehavior has been reproduced inmultiple devices, with an example ofa bilayer device shown in Supplementary Note 6, suggesting that theformation of state II undergoes a first-order transition.To further elucidate the NLH response across the transition, wecompare the behavior of ηab under different current amplitudes.Under large driving currents (>20 µA), ηab evolves smoothly from100K to 2 K, without a clear turning point (black line in Fig. 2f), indi-cating a gradual change contributed to the chemical potential shift. Incontrast, at small driving currents, ηab dramatically increases fromapproximately 0.7 V�1 at 100K to about 50 V�1 below 10K, with adistinct turning point near 60K. This is about a 2-orders-of-magnitudeenhancement of NLHE, primarily arising from a BCD increase inducedby the phase transition, as confirmed by the scaling law analysis (SeeSupplementary Note 7). The corresponding nonlinear conductivity atlow temperature is enhanced to 20 μm V�1Ω�1, which is the highestvalue reported among existing 2D material systems22–24 (See Supple-mentary Note 8).Optical features of correlated state IITo investigate the characteristic of state II in few-layer TaIrTe₄, weemploy temperature-dependent Raman spectroscopy, a sensitivetechnique for revealing lattice dynamics and possible collective exci-tations during phase transitions25–28. Figure 3a summarizes thetemperature-dependent Raman spectra of a typical TaIrTe4 thin film,captured from 55 cm−¹ to 115 cm−¹ between 2 K and 200K. Above thecritical temperature TC, the spectra exhibit one A2 mode near 68 cm−¹and three A1 modes around 79, 86, and 105 cm−¹, consistent with bothroom-temperature data and the previous report18. As the temperaturedrops below TC, a new peak emerges around 83 cm−¹, correspondingto an energy of 10.3meV, in addition to the existing modes at highertemperatures. The peak position and intensity of this new peak aredetermined using Voigt fitting, with examples at 5 K, 40K, and 100Kshown in Fig. 3b. Control fittings using only two peaks for the spectrabelow TC exhibit significant deviations from the experimental data,ruling out the possibility that the increase in intensity around 83 cm−¹is due to the broadening of nearby Raman modes (see SupplementaryFig. 9). Toquantify the evolutionof this newpeak at 83 cm−¹,weplot itsintegrated intensity as a function of temperature in Fig. 3c, whichincreases sharply below TC. The temperature dependence of this newpeak’s intensity is well-fitted by the mean-field theory (detailed inSupplementaryNote 9), as characteristic behavior of amplitudemodesin CDW systems, which suggests the state II below 60K is CDWphase29–31. And the energy peak’s energy (~10.3meV), which is a typicalenergy for the amplitude mode of a CDW, further supports thisinterpretation31–34. The fitting reveals a transition temperature of 60K,which is consistent with the critical temperature TC observed in NLHE.To further reveal the symmetry of state II, identified as CDW inRamanmeasurements, we employ second harmonic generation (SHG)microscopy and angle-resolved transport measurements, both ofwhichare sensitive to the crystal structure’s symmetry35–37.We conductSHG microscopy across different temperatures and compare the SHGpolarization pattern of our few-layer TaIrTe4 sample at 100K (state I)and 1.7 K (state II) (see “Methods” formore details). As shown inFig. 3d,both SHG patterns show four lobes and two-fold rotation symmetry,which belongs to the Pm space group. However, at 1.7 K, a strongeranisotropy in SHG intensity is observed along the crystalline â-axis,which is the Ta atom chain. By fitting both SHG patterns with thenonlinear susceptibility matrix in the Pm space group, we find a sig-nificant enhancement of ~25% in the nonlinear optical susceptibilityelementd11 from state I to state II, while the other elements, such asd12,remain nearly unchanged (See Supplementary Note 10). This suggeststhat the formation of the CDW state enhances the in-plane anisotropyof the orthorhombic TaIrTe₄ crystal without altering the space groupsymmetry. Moreover, temperature-dependent SHG intensity shows anotable increase below 60K, consistent with the onset temperatureidentified in our NLHE measurements (Fig. 3e). Given the substantiallyenhanced pattern elongation and nonlinear susceptibility value alongthe â-axiswithout further symmetrybreaking, theCDWstate is likely toexhibit a 1D electronic density modulation along the crystallineâ-axis38–40.The 1D electronic density modulation along the â-axis is furthersupported in the angle-dependent NLHE. We compare temperature-dependent NLH measurements with the current (below 20 μA) alongthe â-axis and the b̂-axis, respectively, in the Hall bar-shaped device, asshown in the inset of Fig. 3f. The strength of the NLHE along the â-axis,ηab, exhibits a two order of magnitude enhancement from roomArticle https://doi.org/10.1038/s41467-025-61347-3Nature Communications |         (2025) 16:6351 4www.nature.com/naturecommunicationstemperature to 2 K (red plot in Fig. 3f), in contrast to ηba along theb̂-axis, which remains near zero (black plot in Fig. 3f). This enhancedanisotropy in state II is consistent with the result shown in the SHGpolarization pattern, underscoring the transition’s 1D character, whereelectronic ordering occurs predominantly along the â-axis, supportinga 1D CDW.To explain the microscopic origin of the CDW phase and itsrelationship with BCD and the associated NLHE, we conduct first-principles calculations to model the phase instability and quantify theBCD. (“Methods” and Supplementary Note 11). Firstly, the electronicsusceptibility of conduction bands has been calculated, whose valuereflects the tendency of electronic instability. Indeed, we find a localelectronic susceptibility maximum at a nesting vector of Q* = (0:11, 0)Å�1, suggesting a strong tendency to form a CDW state at low tem-perature (see Fig. 4a top). In real space, such electronic ordering cor-responds to an electron density modulation along the 1D Ta chain(â-axis), with a relatively large period of about 15 atomic unit cells(Fig. 4a bottom). This 1D CDW phase scenario as the microscopic ori-gin for state II can well explain the observed anisotropic SHG andangle-resolved transport signatures: the proposed 1D CDWphase doesnot further break the mirror symmetry (M â) of pristine few-layerTaIrTe4 crystal in the Pm space group but results in larger SHG ani-sotropy andNLH transport anisotropywith the formation of additionalcharge ordering along the crystalline â-axis. As for the SHG intensityboost, this can be understood by considering the electronic density ofstate increment for related optical transitions due to the periodicCDW-induced band folding39,40. Taken together, the observed changesin both SHG polarization pattern and intensity are consistent with theformation of a 1D CDW state emerging in few-layer TaIrTe4.Given that the 1D CDW phase preserving mirror symmetry M â ishighly possible as the origin of state II, we further analyze how thiselectronic modulation can result in large BCD and correspondingenhanced nonlinear responses. By introducing the 1D superlatticepotential into the system, we have calculated both band structurechanges and the evolution of the BCD using an 8-band tight-bindingmodel. Comparing Fig. 4b, c, the CDW potential opens a gap betweenthe two lowest conduction bands. In the real case of our multilayerTaIrTe4 device, this band gap is shrunk but still exists. As shown in thecolor scale, a large Berry curvature, Ω, appears near the edges of theband gap. For the BCD distribution calculations, a 0.1 V/nm electricfield is employed to break the inversion symmetry and mimic theinversion symmetry breaking in thin-film TaIrTe4. It is noted that inTaIrTe4 films, only the component of BCD, Dac, is nonzero due to theabsence of the mirror plane M b̂. Next, we show the momentumresolved BCD maps in Fig. 4d (state I) and 4e (state II) at a chemicalpotential of 0.16 eV, which corresponds to the experimentally deter-mined Fermi level at TC extracted from the Hall measurement. Asillustrated in twomaps, the Dac hotspots are significantly enhanced bya factor of 20 near the CDW gap and exhibit opposite signs betweenstate I and state II. Both the magnitude enhancement and the signreversal match our observation in the experimental NLH response. Amore comprehensive analysis of the BCD as a function of chemicalpotential near the band gap, and its relevance to the NLHE enhance-ment, is provided in Supplementary Note 12.0 50 100 150 200 250 300100−10−20−30−40−50−60�αβ(V-1)100xleft configurationright configurationTemperature (K)1xTCV2�abV2�babaI�bbI�aaf0 20 40 60 80 100900100011001200130014001500SHG Intensity(arb. units) SHGTemperature (K)TCe−90−60−3003060901201501802102400.00.51.01.52.01.7 K100 K0.51.01.52.0SHG Intensity (arb. units)bad0 20 40 60 80 100 1200.00.20.40.6ExperimentMean Field TheoryNew Peak Intensity(arb.units)Temperature (K)TCcb60 70 80 90 100 1100.00.10.20.30.40.5Intensity (arb. units)  5K40 K 100 K Peak 1 New Peak Peak 2 Fitted PeakRaman Shift ( )60 70 80 90 100 11020406080100120140160180200Temperature(K)Raman Shift ( )0.040.050.060.070.080.090.10Raman Intensity (arb. units)TC New PeakaFig. 3 | Optical signature of the phase transition in few-layer TaIrTe4. a TheRaman spectra of TaIrTe₄ from 55 cm−¹ to 115 cm−¹ at temperatures between 2 Kand 200K. The rising of a new peak at ~83 cm−¹ emerging below 60K indicates theexcitation of the amplitudemode in the CDW phase. b Raman spectra at 5 K, 40K,and 100K,with Voigtfitting between75 and90 cm−¹. The newpeaks at 40K and 5Kare shown in the green dashed line and highlighted by the green arrow. c Thetemperature dependence of the new peak’s integrated intensity IA, with the solidline representing the mean-field theory fit, suggests the phase transition tem-perature at 60K. Error bars represent the standard error of Raman peak intensitiesobtained from Voigt fitting. d Polarized SHG patterns of TaIrTe4 at 100K and 1.7 Kwith normalized maximum. With normalized peak intensity along the b̂-axis, theintensity along the â-axis is greatly enhanced at 1.7 K. eTemperaturedependenceofthe SHG intensity. A significant enhancement of SHG intensity also emerges below60K. Error bars represent the standard error of themean of SHG intensities at eachtemperature point. fNLH generation efficiency ηαβ as a function of T from 300K to2 K for current applied along the â-axis and b̂-axis, respectively (the b̂-axis data aremultiplied by 100 times). Inset: two measurement configurations.Article https://doi.org/10.1038/s41467-025-61347-3Nature Communications |         (2025) 16:6351 5www.nature.com/naturecommunicationsIn summary, our results show that the NLHE can be used as asensitive probe for detecting correlated phases and constructing richphase diagrams in topological semimetals. The combination of non-linear transport and optical measurements points out the formation ofa 1D CDW in the few-layer topological semimetal TaIrTe4, which pro-vides a unique material platform to explore the interplay of stronglycorrelated states and topological properties. Moreover, its recorded-high nonlinear susceptibility at both cryogenic and room temperaturealso makes it competitive for nonlinear device development, such asenergy harvesters and infrared detectors.MethodsTaIrTe4 growthSingle crystals of TaIrTe4 were synthesized via a self-flux method. Tapowder (99.98%), Ir powder (99.99%), and Te chunks (99.9999%) wereloaded in a 1:1:20 ratio (Ta:Ir:Te) into an alumina Canfield crucible andsealed in a quartz ampoule under vacuum (10−6 Torr). The sealedampoule was then heated to 1100 °C over 24 h and dwelled for 5 days,before cooling to 600 °C at 1 °C/hr. The ampoule was then quicklycooled to 525 °C and centrifuged to remove excess Te. To remove anyresidual Te on the surface, the resulting crystals were sealed in anotherevacuated ampoule and placed in a tube furnace with a 200 °C tem-perature gradient and the crystals were placed at the hot end (425 °C)for 2 days.Raman measurementThe angle-resolved Raman spectra are obtained using a Horiba/AIST-NT LabRAM system. A linearly polarized laser beam with the wave-length of 633 nm is directed and focused onto the samples using a100× objective lens with a numerical aperture of 0.9. The same lenscaptures the scattered Raman signals and directs them back to thespectrometer. During the measurements, the sample is rotated on astage in 6° increments while keeping other experimental conditionsconsistent. Another low-frequency Raman measurement system withthree band notch filters designed for 5 cm−1 band stop of excitationbandwidth is used for the temperature-dependent Raman spectra.Raman spectra are obtained using the 1800 lines per mm grating in anAndor Shamrock 500i Spectrometer. A linearly polarized laser beamwith 633nm wavelength is directed and focused into the QuantumDesign OptiCool Cryostat on the samples using a 50× long workingdistance objective lens with a numerical aperture of 0.6.Device fabricationMulti- and few-layer TaIrTe4 exhibit high air sensitivity. Therefore, alldevice fabrication processes were conducted within a nitrogen-filledglove box. Initially, a layer of pre-patterned metal (2/10 nm Ti/Au) wasdeposited onto the Si/SiO2 chip using e-beam lithography and sub-sequent e-beamevaporation. Themetal contacts underwent a cleaningstep using a limited amount of O2 plasma for 25min before introduc-tion into the glove box. TaIrTe4 flakes were mechanically exfoliatedonto a polydimethylsiloxane stamp and then transferred onto Si/SiO2substrates. The specific layers (2–15 layers) were then identified basedon optical contrast observed on the Si/SiO2 substrates and furtherconfirmed by measuring step heights with an atomic force micro-scope. Subsequently, hBN (20–40nm thickness) was picked up using adry stacking method41. This hBN layer was then utilized to pick up thetargeted TaIrTe4 flake, and the whole hBN/TaIrTe4 stack was placedonto the pre-patterned metal contacts situated on the Si/SiO2 chip.Transport measurementTransport measurements were conducted within cryogenic systems(Physical Property Measurement System or the OptiCool system byQuantum Design), which provide temperature control from 1.7 K to300K and magnetic fields up to 14 Tesla. An AC excitationIωaa = I0 sinðωtÞ, whose frequency ω ranges from 17.7 to 1007.7 Hz wassourced using a lock-in amplifier (OE1022D by Sine Scientific Instru-ments), yielding consistent NLHE (See Supplementary Note 13). Bothfundamental and second-harmonic frequencies of longitudinal andtransverse voltages were captured by two dual-channel lock-in ampli-fiers (OE1022D by Sine Scientific Instruments).deaTaabaM−8×103−6×103−4×103−2×10302×1034×1036×1038×103kak bDac  Å  3��R−4×104−3×104−2×104−1×10401×1042×1043×1044×104kak bDac  Å  3��R−0.2 0.0 0.2−0.4−0.20.00.20.4 HighLow(0.11, 0)QaQQ b Å  -1 Å  -115ac−0.4−0.20.00.20.4Energy (eV)
 �� R−8 0 8 Å  2−0.4−0.20.00.20.4Energy (eV)
 �� R−40 0 40 Å  2bFig. 4 | Theoretical understanding of the phase transition and its impact onBerry curvature dipole in ultrathinTaIrTe4. aCalculated electronic susceptibilityof the conductionbandbasedonfirst-principles calculations (top). Thewhite arrowhighlights a local maximum of the electronic susceptibility at a wavevector Q*. Itcorresponds to a superlattice of about 15 unit cells along the one-dimensional Tachain direction (bottom). Band structures with Berry curvature (Ω) under an elec-trical field of 0.1 V/nm, b without, and c with superlattice potential with aperiodicity of 15 unit cells, show an enhanced Berry curvature near the CDW gaparound 0.2 eV. d, e Corresponding momentum-resolved Berry curvature dipole(Dac) at the energy level of 0.16 eV. Blue and red colors present positive andnegative BCD amplitudes indicating that the BCD magnitude in these hotspotsincreases from 2× 103 in state I to 4× 104 in state II, representing a 20-foldenhancement.Article https://doi.org/10.1038/s41467-025-61347-3Nature Communications |         (2025) 16:6351 6www.nature.com/naturecommunicationsNonlinear optical measurementThe measurements were performed based on an optical secondharmonic detection setup coupled with a cryogenic system (Opti-Cool by Quantum Design) with a temperature range from 1.7 K to300K. In particular, the excitation light at 1040 nm was extractedusing a tunable femtosecond laser (Discover NX by Coherent). Theexcitation laser was linearly polarized by a polarizing beamsplitter.The laser was focused by a 50× NIR objective on the sample with aspot size of around 3 μm. The SHG signal was detected in the back-scattering configuration and finally collected by photon-countingPMT modules. In the SHG polarization pattern study, we used a half-wave plate to control the incident light polarization, while theemitted by the sample was examined by a polarizer.DFT and model calculationsWe use the Vienna ab initio simulation package to determine the moststable structure and analyze the electronic properties of TaIrTe4. Theelectronic susceptibility was calculated by the Lindhard function. Theparameters ofDFT calculations andCDWsusceptibility canbe found inthe Supplementary Note 11.To simulate the superlattice band structure under a periodicmodulation of CDW potential, we use the Frohlich-Peierls method tointroduce an additional term in the Hamiltonian.H =H0ðrÞ+V cosðQ � r +ϕÞψðrÞyψðrÞWhere V is the amplitude of the CDW potential and Q is the wavevector corresponding to the periodicity of the CDW, r is the positionvector, and ϕ is the phase shift. The intrinsic part of the NLH con-ductivity χαββ can be described by the BCD, which can be calculatedfrom first principle method42 as follows:χαββ = � ϵαβγe3τ2ℏ2ð1 + iωτÞDβγDβγ =Zkf 0n ðkÞ∂Ωnγ∂kβWhereDβγ is the BCD, f0n ðkÞ is the equilibriumFermi-Dirac distribution,τ is the relaxation time, ϵαβγ is the third rank Levi-Civita symbol,α,β= a, b and γ = c in 2D. The Berry curvature Ωc in the 2D system canbe calculated by,ΩcðkÞ= � 2ImXm≠n<nj∂kaHjm> <mj∂kbjn>ðϵn � ϵmÞ2Where ϵn and jni are eigenvalues and eigenvectors, respectively. In 2D,the BCD is in a unit of length. Due to theM â reflection, only∂Ωc∂kais finite,and the χbaa is nonzero.Data availabilityThe source data underlying all main manuscript figures are providedwith this paper. All other data that support the findings of this studyare available from the corresponding authors upon request. Sourcedata are provided with this paper.Code availabilityThe codes used for the calculations are available from the corre-sponding authors on request.References1. Armitage, N. P., Mele, E. J. & Vishwanath, A. Weyl and Dirac semi-metals in three-dimensional solids. Rev. Mod. Phys. 90,015001 (2018).2. Burkov, A. A. Topological semimetals. Nat. Mater. 15,1145–1148 (2016).3. Yan, B. & Felser, C. Topological materials: Weyl semimetals. Annu.Rev. Condens. Matter Phys. 8, 337–354 (2017).4. Xu, S.-Y. et al. Discovery of a Weyl fermion semimetal and topolo-gical Fermi arcs. Science 349, 613–617 (2015).5. Chang, G. et al. Topological quantum properties of chiral crystals.Nat. Mater. 17, 978–985 (2018).6. Sodemann, I. & Fu, L. Quantum nonlinear Hall effect induced byBerry curvature dipole in time-reversal invariant materials. Phys.Rev. Lett. 115, 216806 (2015).7. Ma, Q. et al. Observation of the nonlinear Hall effect under time-reversal-symmetric conditions. Nature 565, 337–342 (2019).8. 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D.R., Y.H., and Y.M. are supported by National ScienceFoundation through the University of Wisconsin Materials ResearchScience and Engineering Center under grant No. DMR-2309000(Growth of TaIrTe4 crystal and device fabrication). K.W. and T.T.acknowledge support from the JSPS KAKENHI (grant No. 21H05233 and23H02052), the CREST (JPMJCR24A5), JST and World Premier Interna-tional Research Center Initiative (WPI), MEXT, Japan (Growth of BNcrystal).Author contributionsH.J. and Y.W. initiated and conceived the project; H.J. fabricated thedevices, carried out the transport measurements, and analyzed all thedata supervised by Y.W.; T.X. carried out the SHG measurement andanalyzed optical results with H.J., Y.W., and J.X.; J.L. carried out the first-principles calculations of the single-particle band and the CDW bandstructures under the guidance of Y.Z.; Y.H. grew the TaIrTe4 bulk crystalsunder the guidance of D.R.; H.M. carried out the low-frequency Ramanmeasurement under the guidance of H.J. and Y.W.; K.W. and T.T. grewthe BN bulk crystals. All authors jointly wrote or commented on themanuscript, with a main contribution from H.J., Y.M., J.X., and Y.W.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-025-61347-3.Correspondence and requests for materials should be addressed toYing Wang.Peer review information Nature Communications thanks Flavio Gior-gianni, Dushyant Kumar, and the other, anonymous, reviewer(s) for theircontribution to the peer review of this work. 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To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.© The Author(s) 2025Article https://doi.org/10.1038/s41467-025-61347-3Nature Communications |         (2025) 16:6351 8https://doi.org/10.1038/s41467-025-61347-3http://www.nature.com/reprintshttp://creativecommons.org/licenses/by-nc-nd/4.0/http://creativecommons.org/licenses/by-nc-nd/4.0/www.nature.com/naturecommunications Probing interplay of topological properties and electron correlation in TaIrTe4 via nonlinear Hall effect Results and discussion Unconventional nonlinear conductivity enhancement Phase diagram probed by NLHE First-order phase transition driven by current and temperature Optical features of correlated state II Methods TaIrTe4 growth Raman measurement Device fabrication Transport measurement Nonlinear optical measurement DFT and model calculations Data availability Code availability References Acknowledgments Author contributions Competing interests Additional information