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Yueshen Wu, Qi Wang, Xiang Zhou, Jinghui Wang, Peng Dong, Jiadian He, Yifan Ding, Bolun Teng, Yiwen Zhang, Yifei Li, Chenglong Zhao, Hongti Zhang, Jianpeng Liu, Yanpeng Qi, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Jun Li

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[Nonreciprocal charge transport in topological kagome superconductor CsV3Sb5](https://mdr.nims.go.jp/datasets/c153cbfb-edb7-40ee-bc77-8049ec64edb6)

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Nonreciprocal charge transport in topological kagome superconductor CsV3Sb5ARTICLE OPENNonreciprocal charge transport in topological kagomesuperconductor CsV3Sb5Yueshen Wu 1,2,8✉, Qi Wang1,2,8, Xiang Zhou 1,2, Jinghui Wang1,2, Peng Dong1,2, Jiadian He1,2, Yifan Ding1,2, Bolun Teng1,2,Yiwen Zhang1,2, Yifei Li1,2, Chenglong Zhao1, Hongti Zhang1, Jianpeng Liu 1,2, Yanpeng Qi 1,2,3✉, Kenji Watanabe 4,Takashi Taniguchi 5 and Jun Li 1,2,6,7✉Nonreciprocal charge transport phenomena are widely studied in two-dimensional superconductors, which demonstrateunidirectional-anisotropy magnetoresistances as a result of symmetry breaking. Here, we report a strong nonreciprocal transportphenomenon in superconducting CsV3Sb5 thin flakes. The second harmonic voltages, mainly originating from the rectificationeffect of vortex motion, are unambiguously developed with in-plane and out-of-plane magnetic fields, and their magnitudes arecomparable to those in noncentrosymmetric superconductors. The second harmonic magnetoresistances split into several peaksand some of them reverse their signs by ramping the magnetic field or the current within the superconducting transition. Thenonreciprocity suggests a strong asymmetry in CsV3Sb5. The centrosymmetric structure and symmetric electronic phases in CsV3Sb5can hardly induce the distinct nonreciprocal transport phenomenon, which could be correlated to a symmetry breaking from anunconventional superconducting order parameter symmetry.npj Quantum Materials           (2022) 7:105 ; https://doi.org/10.1038/s41535-022-00516-9INTRODUCTIONThe nonreciprocal charge transport phenomenon, also calledmagnetochiral anisotropy1 or unidirectional magnetoresistance2,results from inversion and time-reversal symmetry breaking thatcan modulate the energy dispersion with unequal electron energiesof opposite momentum k and −k or spin s and −s3. Based on thisphenomenon, a wide range of potential applications such asrectifiers, alternating-direct-current converters, and photodetectorscould be engineered4–7. In superconductors, the nonreciprocalsignal can be considerably enhanced in the superconducting stateby several orders of magnitude due to the significant differencebetween Fermi energy and superconducting energy gaps8–10, forwhich the nonreciprocal transport is related to the chirality ofsupercurrent or Cooper pairs. Up to now, nonreciprocal transportmeasurements have been performed in various superconductorssuch as the noncentrosymmetric MoS28,11, NbSe26, Nb/V/Ta super-lattice12, the polar superconductor SrTiO313, and the artificiallyengineered MoGe superconducting thin films14, all of which arebasically related to the symmetry breaking in structures, electronicstates, or even anisotropic friction forces on vortex flowing. On theother hand, the intrinsic vortex motion behavior correlated with thesuperconducting gap symmetry can also contribute to thenonreciprocity8. In addition, such nonreciprocal transport phenom-enon has been observed in the topological superconductingheterostructure of Bi2Te3/FeTe15. Thus, these nonreciprocalresponses can be studied as a probe to detect the chirality in ananisotropic superconducting states.Recently, a series of kagome metals AV3Sb5(A= K, Rb, Cs)16 haveattracted increasing attentions with the unique coexistence oftopological states, charge density wave (CDW), and multi-bandsuperconductivity. Among these crystals, CsV3Sb5 reveals thehighest of 2.5 K17. Up to now, fruitful experiments have beenactualized to understand the superconducting gap symmetry ofCsV3Sb5, including thermal conductivity18, scanning tunnelingspectroscopy measurements19, and penetration length measure-ments20. However, these results provided contradictory conclu-sions on the gap symmetry17–31. On the other hand, since thesuperconductivity coexists with CDW, their interplay should bealso taken into account. The investigation of these twocompetitive orders is one of research focuses in CsV3Sb5 super-conductor32–38. For instance, the observation of chiral CDWprovides a possible mechanism for unconventional superconduc-tivity28, which induces a pair density wave phase below thesuperconducting transition temperature39,40. Nevertheless, byapplying high pressure, an unusual observation of two super-conducting domes was found inside and outside the CDWphase41–45, indicating the competition between CDW and super-conductivity. In addition, CsV3Sb5 is also a Z2 topological metal inwhich the Dirac line locates between K and H points, and thetopological surface states were confirmed by the angle-resolvedphoton electron spectroscopy (ARPES)16,46. Moreover, evidence ofanomalous Hall effect has been observed in the CDW state, whichwas attributed to the symmetry breaking of the band struc-tures47–49. To address these issues, one of the most promisingpaths is investigating the possible chirality of Cooper pairs andvortex dynamics, which has not yet been reported.Here, we report the study of the nonreciprocal chargetransport of mechanically exfoliated CsV3Sb5 thin flakes. Asreducing the thickness, the superconducting transition tem-perature (Tc) is firstly enhanced but then suppressed, competing1School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China. 2ShanghaiTech Laboratory for Topological Physics, ShanghaiTechUniversity, Shanghai 201210, China. 3Shanghai Key Laboratory of High-resolution Electron Microscopy, ShanghaiTech University, Shanghai 201210, China. 4Research Center forFunctional Materials, National Institute for Materials Science, Tsukuba 305-0044, Japan. 5International Center for Materials Nanoarchitectonics, National Institute for MaterialsScience, Tsukuba 305-0044, Japan. 6State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, ChineseAcademy of Sciences, 865 Changning Road, Shanghai 200050, China. 7Wuhan National High Magnetic Field Center, Huazhong University of Science & Technology, Wuhan430074, China. 8These authors contributed equally: Yueshen Wu, Qi Wang. ✉email: wuysh@shanghaitech.edu.cn; qiyp@shanghaitech.edu.cn; lijun3@shanghaitech.edu.cnwww.nature.com/npjquantmatsPublished in partnership with Nanjing University1234567890():,;http://crossmark.crossref.org/dialog/?doi=10.1038/s41535-022-00516-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41535-022-00516-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41535-022-00516-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41535-022-00516-9&domain=pdfhttp://orcid.org/0000-0001-9462-2289http://orcid.org/0000-0001-9462-2289http://orcid.org/0000-0001-9462-2289http://orcid.org/0000-0001-9462-2289http://orcid.org/0000-0001-9462-2289http://orcid.org/0000-0002-1973-3736http://orcid.org/0000-0002-1973-3736http://orcid.org/0000-0002-1973-3736http://orcid.org/0000-0002-1973-3736http://orcid.org/0000-0002-1973-3736http://orcid.org/0000-0002-8564-0415http://orcid.org/0000-0002-8564-0415http://orcid.org/0000-0002-8564-0415http://orcid.org/0000-0002-8564-0415http://orcid.org/0000-0002-8564-0415http://orcid.org/0000-0003-2722-1375http://orcid.org/0000-0003-2722-1375http://orcid.org/0000-0003-2722-1375http://orcid.org/0000-0003-2722-1375http://orcid.org/0000-0003-2722-1375http://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/0000-0002-1467-3105http://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/0000-0002-6928-1256http://orcid.org/0000-0002-6928-1256http://orcid.org/0000-0002-6928-1256http://orcid.org/0000-0002-6928-1256http://orcid.org/0000-0002-6928-1256https://doi.org/10.1038/s41535-022-00516-9mailto:wuysh@shanghaitech.edu.cnmailto:qiyp@shanghaitech.edu.cnmailto:lijun3@shanghaitech.edu.cnwww.nature.com/npjquantmatswith the emergence of CDW. The nonreciprocal charge transportis observed when the magnetic field is aligned both within theab-plane and along the c-axis. The second harmonic magne-toresistance splits into several peaks and reverses their signs byramping the magnetic field or the current, suggesting a tunablerectification effect. Our results reveal detailed information aboutthe chirality and vortex dynamics.RESULTSSample characterizationCsV3Sb5 is a layered material with a V-kagome lattice located inthe middle of the unit cell shown in Fig. 1a. Thanks to the weaklybonding strength between Cs and Sb atoms, atomically thincrystals can be obtained by the mechanical exfoliation method.Thin flakes were covered by few-layer BN, and then transferredonto the pre-patterned gold leads as shown in Fig. 1b. Before thenonreciprocity measurements, we first examined the onset andzero resistance Tcs, and their thickness dependence is shown inFig. 1c. The onset Tc of bulk crystal is 3.5 K, and the Tc can beenhanced up to 4.25 K by shrinking the thickness of the crystalinto 80 nm, followed by a decrease in Tc to 2.5 K for the 10-nm-thick one. The Tc of zero-resistance behaves the similarly behavior.The nonmonotonically evolution of Tc with reducing layers maybe correlated to the competition with CDW order. Particularly, inthe 80-nm-thick sample, the transition temperature of CDW isreduced to 77 K, which can be confirmed by both Hall resistancesand dR/dT as shown in Fig. 1d. This phenomenon has been welldiscussed in recent reports50,51, in which the surface oxidationthat occurred during the sample fabrication process wasatrributed to additional carrier doping and Tc modification51. Inour present work, however, a piece of BN was covered onto thethin flakes to avoid oxidation, the Tc is generally related to thethickness, we can hardly ascribe to the sample degradation. Here,we focus on the samples with Tc of above 4 K (a 45-nm-thickdevice in the manuscript and others in Supplementary Figs. 1 and2) to study the vortex dynamics and the chirality of super-conductivity from the nonreciprocal charge transport by probingthe second harmonic response.Nonreciprocal magnetoresistanceThe first and second harmonic voltages (Vω and V2ω) weredetected using lock-in amplifier. According to the definition ofnonreciprocity, the total voltage V can be considered asV ¼ Vω þ V2ω ¼ Vω 1þ γBIð Þ, where, the coefficient γ is equal to2V2ω/VωBI. Since the electronic structure of CsV3Sb5 is quasi-two-dimensional, the nonreciprocal response could be anisotropicfrom in-plane to out-of-plane. We then measured and calculatedthe temperature dependence of the first and the secondharmonic resistances (Rωxx ¼ Vω=I0 and R2ωxx ¼ V2ω=I0) simulta-neously for both B//ab-plane and B//c-axis cases as shownin Fig. 2a, b. At low magnetic field limit for B//ab-plane case, thenonreciprocal resistance immediately develops when Rxx starts todecrease as marked in the green dashed line. On the other hand,the R2ωxx disappears at high magnetic field limit. Similar behavior isobserved for B//c-axis case as well. Another important feature isthat several times of sign reversals appear at both R2ωxx -T andR2ωxx -B curves, which will be discussed in detail below. It should benoted that the nonreciprocal magnetoresistance is detected justwithin the superconductivity transition region. Thus, we focus onthe investigation between nonreciprocal magnetoresistance andsuperconductivity.Generally, the superconducting transition of the type-II super-conductor consists of two regions, separated by a mean-fieldtransition temperature Tmc13,15. The Tmc can be determined asFig. 1 Characterization of superconductivity. a Crystal structure of CsV3Sb5. b Optical image of a sample covered with h-BN. Scale bar:20 μm. c Normalized resistance as a function of temperature with different thickness. d Temperature dependence of Hall resistance (red) anddifferential resistance (blue) of a 80-nm-thick sample under H= 2 T. Here the resistance is measured with direct current.Y. Wu et al.2npj Quantum Materials (2022)   105 Published in partnership with Nanjing University1234567890():,;shown in Fig. 2c by using the Aslamazov-Larkin termσ2D ¼ AðT � Tmc Þ�1, where σ2D is the two-dimensional conductiv-ity and A is a fitting parameter. Thus, we can confirm the Tmc isabout 4.00 K. Above the Tmc , the transport properties aredominated by the amplitude fluctuation of order parameterswhich causes a paraconductivity state. Below the Tmc , a phasefluctuation generates vortices motion, which takes charge of thetransport properties. It is worth noting that the resistance is stillnonzero until about 3.45 K due to the current-driven vortexmotion. Below 3.45 K, the vortices are frozen as the vortex solidstate (or vortex lattice for the type-II superconductors) and thesystem is in superconductivity state completely. Meanwhile, thetemperature-dependent R2ωxx curve demonstrates four character-istic regions as well, namely, normal state, paraconductivity, vortexmotion, and vortex solid state according to those of the Rωxx � Tcurve. For the magnetoresistance measurements, the Rωxx reveals atypical magnetic-field-dependent behavior as shown in Fig. 2d,while the R2ωxx curve demonstrates antisymmetric to the magneticfield, namely, a typical characteristic of nonreciprocity.To explore the magnetochiral properties correlated with thesuperconductivity, we investigated the field- and temperature-dependent R2ωxx . Figure 3a, b show the R2ωxx � B curves in differenttemperatures under magnetic fields in the ab-plane and along thec-axis, respectively. The phase diagrams of R2ωxx with respect to themagnetic field and the temperature are shown in Fig. 3c, d,respectively. The dashed lines are the contours of the firstharmonic resistance Rωxx at zero resistance 0RN, half of the normalstate resistance (0.5RN), three-quarters of the normal stateresistance (0.75RN), and the onset of transition. The nonreciprocalmagnetotransport mainly locates at the region between thecontours of 0RN and 0.5RN when the field is in the ab-plane andalong the c-axis. Therefore, the nonreciprocal response basicallyoccurs at the vortex flow regions, indicating that the vortexmotion could be the domination. Above the contour of R= 0.5RN,R2ωxx decays gradually because the magnetic field diminishes thepinning potentials and the vortices move more freely. Above thecontour of R= 0.75RN, the free flow regions continuously evolvedinto the amplitude fluctuation region and nonreciprocity is almostindiscernible as demonstrated in Fig. 3a, b. However, the R2ωxx didnot disappear until R reaches 0.95RN (Fig. 2d) at 3.8 K, where thecontribution of amplitude fluctuation of order parameter may notbe neglected.On the other hand, the R2ωxx under in-plane field is larger thanthat along the c-axis, suggesting an anisotropic nonreciprocalmagnetotransport. Since the crystal is in a quasi-two-dimensionalstructure, anisotropic superconducting properties should alsoaffect the vortex motion. We then examined the coherenceFig. 2 Anisotropic nonreciprocal magnetoresistance of a 45-nm-thick sample. a, b R− T curves of first (top) and second (bottom) harmonicsignal under B applied along the ab-plane and the c-axis, respectively. Scale bar: 2 mΩ. The dashed line is the guideline of onset temperatureof second harmonic signal. c The transition regions for R2ωxx � T curve under B= 0.1 T. Red dashed line is the Aslamazov-Larkin fitting curve ofparaconductivity contribution. d The R2ωxx � B and Rωxx � B curves at 3.8 K, where B is applied within the ab-plane.Y. Wu et al.3Published in partnership with Nanjing University npj Quantum Materials (2022)   105 lengths to estimate the size of the vortex from the anisotropicupper critical field Bc (at R= 0.99RN). According to the Ginzburg-Landau theory52, the in-plane and out-of-plane coherence lengthsare ξ2ab ¼ Φ02πBccand ξ2c ¼ Φ02πffiffiffiffiffiffiffiffiBccBabcp , which are given in Fig. 4a, whereΦ0 is flux quanta. Thus, the anisotropic factor can be estimated asλ= ξc/ξab (=1.72 at 1.8 K), indicating a weak anisotropy. Mean-while, the thickness of the sample is comparable to the diameterof a vortex of 2ξab. Once B//ab-plane, R2ωxx is enhanced due to thesize effect and/or possible anisotropic pinning potential9. Conse-quently, we conclude that the asymmetric property of pinningpotential is three-dimensional.Moreover, several specific series of peaks are observed otherthan one main peak predicted by the theory of vortex dynamics9.Particularly, four series can be identified when B//ab-plane andmuch more series exist in B//c-axis case. The locations of eachseries of peaks are weakly temperature-dependent. In otherwords, the nonreciprocity is strong when some number of vorticesexist in the device, indicating that the many-body interaction ofvortices may also play a role53. We select three major series ofpeaks in Fig. 3a to estimate the γ value as γ ¼ 2V2ωVωBI, and plottemperature dependence of γ in Fig. 4b. While the magnitude ofthese three peaks is comparable in the order of several mΩ at2.8 K, the coefficient γ varied from about 5 T−1 A−1 to near8000 T−1 A−1 for high-H peaks and low-H peaks, respectively. It isreasonable that the magnetic field weakens the pinning potential.The temperature plays a similar role as all these coefficientsdrastically decrease with increasing temperature. To compare withother systems, the values of 2V2ωVω j , where j is the current density, arealso estimated as up to about 10−11 m2 A−1. We then concludethat the ratchet effect is remarkable in CsV3Sb5, comparable tothe noncentrosymmetric 2D materials such as MoS2 and NbSe2.Current dependent nonreciprocityWe then focus on the current dependence of the nonrecipro-city, which should follow the relation of R2ωxx � γBI. The phasediagrams of the first and the second harmonic signals areplotted in Fig. 5a, b, respectively. The effect of current on R2ωxx issimilar to the effect of temperature as it suppresses thesuperconductivity and reduces the region of R2ωxx . Meanwhile,Fig. 3 The magnetic field and temperature dependence of R2ωxx of the 45-nm-thick sample. a and b are the second harmonicmagnetoresistance with the magnetic field applied along the ab-plane and the c-axis at different temperatures. Scale bar: 2.5 mΩ. c and d arethe color mapping plot of a and b, respectively. The dashed lines are the contours of first harmonic resistance Rω of zero resistance, half of thenormal state resistance (0.5RN), 0.75RN, and onset of transition.Y. Wu et al.4npj Quantum Materials (2022)   105 Published in partnership with Nanjing Universityseveral series of peaks and the corresponding sign reversals areobserved as well. The maximum of the second harmonicresistance is extracted as a function of current as given inFig. 5c, where the linear relation at current lower than 0.2 mA isverified for both B//ab-plane and B//c-axis cases. When applyinga larger current, the signal starts to reduce because of thesuppression of the rectification effect of vortex motion bythe relative weakening of the pinning potentials6,13,54–56. Thecurrent dependence of coefficient γ of these maximum peaksbehaves differently as shown in Fig. 5d, which drops exponen-tially as increasing the current when B//ab-plane, while no suchtendency can be observed clearly for B//c-axis, possibly owingto the maximum peaks belonging to different series of peaks. Itis worth noting that the nonreciprocity can be modified bycurrent as well as B and T, providing promising applicationssuch as superconducting diodes12.DiscussionFor the mechanism of the nonreciprocity phenomenon insuperconductors, several explanations have been proposed forsuperconducting SrTiO313, PbTaSe257, Bi2Te3/FeTe interface15,and NbN thin films58, which can be basically attributed to theintrinsic symmetry breaking through the vortex dynamics suchas viscous vortex flow, ratchet effect, or specific mechanisms ofsuperconductivity under spontaneous symmetry-breaking con-ditions. Under the vortex motion regime, one possibility is thatthe vortex liquid state and thermally activated vortex state maycontribute to the response with opposite signs6. The viscousvortex flow is also possible to the nonreciprocal signal, whichpredicts a monotonic enhancement of γ as decreasing tempera-ture. Nevertheless, one can only observe an individual non-reciprocity peak for each mechanism instead of multi-peaks inour present results. Another mechanism is the effect of period-ical pinning potential when the vortices match the latticeconstant or artificially structured pinning sites, resulting inthe modulation of condensing energy14,59–61. After breaking theinversion symmetry of the pinning potential, a well-controlledmany-body interaction can realize sign reversal in artificialstructures53. For single crystals, however, the symmetry ofpinning potential should reflect the intrinsic symmetry of thecrystal as well studied on MoS211 and PbTaSe257, where theanisotropy of nonreciprocity follows that of crystal. Therefore,the appearance of series of nonreciprocity peaks in our presentresults suggests an intrinsic symmetry breaking as well.One possible spontaneous symmetry breaking can be fromthe electronic structure, which is mainly dominated by thenature of the crystal structure and quantum phases. Hoshinoetal. proposed a possible mechanism9 in noncentrosymmetriccrystal structures and interfaces such as Rashba superconductor,and topological surface state with superconducting proximityeffect. For the intrinsic asymmetry like spin-orbital effects andtime-reversal symmetry breaking, an asymmetric energy disper-sion relation can be induced as E s; kð Þ≠ E s;�kð Þ andE s; kð Þ≠ E �s;�kð Þ, which is the key to the nonreciprocity. Inbulk CsV3Sb5, the Rashba spin-orbital interaction seems unlikelyto exist, because the crystal structure is centrosymmetric.Alternatively, a recent study of Raman spectrum in CsV3Sb5thin films revealed an intrinsic instability of crystalline struc-ture62, and STM measurement also shows an inhomogeneousCs-surface63. Such degradation may reduce the symmetry andmodify its electronic structure64, providing a possibility toinduce nonreciprocity. Nevertheless, these effects ought to beweak since our crystals is relatively thick, and particularly,the samples are single-crystalline and well protected by BN, thedegradation of crystalline can be basically avoided.In addition, the charge orders can also modulate therotational, translation, and time reversal symmetry. In CsV3Sb5,the nematicity63 reveals a C2 rotational symmetry, and theunidirectional 4a0 CDW also breaks rotational symmetry65. Theamplitudes of three q vectors within the in-plane 2a0 × 2a0 CDWare chiral, which can break the time-reversal symmetry aswell28,47. However, the CDW-induced lattice distortion CsV3Sb5was found to be centrosymmetric37, and no any evidencesuggests that one of these charge orders can break the inversionsymmetry up to now.Another possible origin of the spontaneously symmetricbreaking is the unconventional superconducting state. Among avariety of possible pairing states, superconducting states ontopological bands should keep a nontrivial nature and the pairpotential demonstrates anisotropic, for instance a spinlessp-wave superconductor66. Previously, the nonreciprocal trans-port has been comprehensively studied on the interfacialsystems of Bi2Te3/FeTe15, which were attributed to inversionsymmetry breaking of the topological superconductivity in theinterface. The effect of other unconventional states, forexample, chiral superconductors67, still needs further theoreticalanalysis and experimental evidence. Although the supercon-ductivity symmetry of AV3Sb5 family is still an open question asdiscussed in the introduction part, the ARPES and first principlescalculations16,17,27,46 indicate the existence of topological bandsFig. 4 Coherence lengths and nonlinear coefficient. a Critical fieldand coherence length are extracted for B//ab-plane and B//c-axiscases. Black dotted line shows the thickness of the sample. b Thenonlinear coefficient γ ¼ 2V2ωVωBI is calculated from several series of peaks.Y. Wu et al.5Published in partnership with Nanjing University npj Quantum Materials (2022)   105 and surface states, and a recent work reported an observation oftwo-fold symmetry on the c-axis resistivity under in-planerotation of magnetic field26. Therefore, our nonreciprocaltransport phenomenon should be a promising probe to reflectthe anisotropic nature of the unconventional superconductivitystate in CsV3Sb5.In conclusion, we have carefully investigated the nonrecipro-city under the dissipative state of CsV3Sb5 superconductors.With the reduction of thickness, we found that the super-conductivity is firstly enhanced and then suppressed due to thecompetition with CDW. Strong nonreciprocal signals can bedetected when superconductivity occurs, whose strength iscomparable to the artificially structured or noncentrosymmetricsuperconductors. The second harmonic resistance can beobserved as the magnetic field both in the ab-plane and alongthe c-axis, which can be basically attributed to the vortex ratchetmotion. The nonreciprocal signal with respect to magnetic fieldssplits into several series of peaks that are asymmetric withmagnetic fields. We suggest the intrinsic symmetry breaking insuperconducting states may induce the magnetochirality in theCsV3Sb5 superconductor.METHODSCrystal growthHigh-quality single crystal were synthesized by Sb flux methodand described in previous work45.Device fabricationThe thin crystals of CsV3Sb5 were prepared by mechanicalexfoliation from bulk crystal and transferred on pre-patternedSiO2(300 nm)/Si substrate using polydimethylsiloxane (PDMS)stamps in a laboratory-made vacuum transfer system. The pre-patterned leads were fabricated by standard photolithographymethod using Photoresist (AZ5214) and subsequent deposition ofTi/Au (5 nm/20 nm) by magnetron sputtering. Some of thesamples were then covered by a h-BN capping layer for furtherdegradation. The thicknesses of the samples were confirmed byAFM after transport measurement.Transport measurementsThe transport measurement was carried out in PPMS. The four-terminal DC and AC signal was measured by set of Keithley 2400Fig. 5 Current dependence of nonreciprocity of the 45-nm-thick sample. a and b are color mapping of the R2ωxx as a function of magneticfield and current. The dashed lines are the contours of first harmonic resistance Rωxx of 0RN, 0.5RN, 0.75RN and onset of transition. c Currentdependence of the maximum second harmonic resistance for B//ab-plane and B//c-axis. Error bars are standard deviations of the resistances.d The corresponding coefficient γ as estimated by γ ¼ 2V2ωVωBI.Y. Wu et al.6npj Quantum Materials (2022)   105 Published in partnership with Nanjing Universityand 2182a and set of Keithley 6221 and OE1022 lock-in amplifier,respectively. The first and second harmonic resistance weredefined as Rω= Vω/I0 and R2ω= V2ω/I0, where I0 is the amplitude ofthe AC current applied and Vω and V2ω are the amplitude of firstand second harmonic voltage. The current frequency was set tobe 113 Hz to lower the noise and the phase of second harmonicsignal was set as π/2.DATA AVAILABILITYThe data supporting the findings of this study are available from the correspondingauthors upon reasonable request.Received: 5 May 2022; Accepted: 17 October 2022;REFERENCES1. Rikken, G. & Raupach, E. Observation of magneto-chiral dichroism. Nature 390,493–494 (1997).2. Zhou, X., Zeng, F., Jia, M., Chen, H. & Wu, Y. Sign reversal of unidirectionalmagnetoresistance in monocrystalline Fe/Pt bilayers. Phys. Rev. B 104, 184413(2021).3. Tokura, Y. & Nagaosa, N. Nonreciprocal responses from non-centrosymmetricquantum materials. Nat. Commun. 9, 3740 (2018).4. Villegas, J. E. et al. A superconducting reversible rectifier that controls the motionof magnetic flux quanta. Science 302, 1188–1191 (2003).5. Moshchalkov, V., Woerdenweber, R. & Lang, W. Nanoscience and engineering insuperconductivity (Springer Science & Business Media, 2010).6. Zhang, E. et al. 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Res. 4, 033167(2022).ACKNOWLEDGEMENTSThis research was supported in part by the National Natural Science Foundation ofChina (Grants No. 12004251, 12104302, 12104303, U1932217, and 11974246), theNatural Science Foundation of Shanghai (Grant No. 20ZR1436100, 19ZR1477300), theScience and Technology Commission of Shanghai Municipality, the Shanghai SailingProgram (Grant No. 21YF1429200), the start-up funding from ShanghaiTechUniversity, Beijing National Laboratory for Condensed Matter Physics, the Inter-disciplinary Program of Wuhan National High Magnetic Field Center (WHMFC202124),the Elemental Strategy Initiative conducted by the MEXT, Japan, Grant NumberJPMXP0112101001, JSPS KAKENHI Grant Number JP20H00354 and A3 Foresight byJSPS, and National Key R&D Program of China (Grant No. 2018YFA0704300).AUTHOR CONTRIBUTIONSY.W. and Q.W. contributed equally to this work. Y.W. and J.L. designed the research.Q.W. and Y.Q. grew the single crystals of CsV3Sb5. K.W. and T.T. grew the singlecrystals of h-BN. Y.W. fabricated the samples and performed the electrical transportmeasurements. Y.Z. performed the atomic force microscopy experiment. Y.Z., P.D.,J.H., Y.D., Y.L., B.T., C.Z., and H.Z. assisted the device fabrication. Y.W., X.Z., J.W., Q.Y.,and J.L. contributed to analyze the data. Y.W. and J.L. wrote the paper.COMPETING INTERESTSThe authors declare no competing interests.ADDITIONAL INFORMATIONSupplementary information The online version contains supplementary materialavailable at https://doi.org/10.1038/s41535-022-00516-9.Correspondence and requests for materials should be addressed to Yueshen Wu,Yanpeng Qi or Jun Li.Reprints and permission information is available at http://www.nature.com/reprintsPublisher’s note Springer Nature remains neutral with regard to jurisdictional claimsin published maps and institutional affiliations.Open Access This article is licensed under a Creative CommonsAttribution 4.0 International License, which permits use, sharing,adaptation, distribution and reproduction in anymedium or format, as long as you giveappropriate credit to the original author(s) and the source, provide a link to the CreativeCommons license, and indicate if changes were made. The images or other third partymaterial in this article are included in the article’s Creative Commons license, unlessindicated otherwise in a credit line to the material. If material is not included in thearticle’s Creative Commons license and your intended use is not permitted by statutoryregulation or exceeds the permitted use, you will need to obtain permission directlyfrom the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2022Y. Wu et al.8npj Quantum Materials (2022)   105 Published in partnership with Nanjing Universityhttps://doi.org/10.48550/arXiv.2201.05330https://doi.org/10.48550/arXiv.2201.05330https://doi.org/10.48550/arXiv.2202.08570https://doi.org/10.48550/arXiv.2202.08570https://doi.org/10.1038/s41535-022-00516-9http://www.nature.com/reprintshttp://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/ Nonreciprocal charge transport in topological kagome superconductor CsV3Sb5 Introduction Results Sample characterization Nonreciprocal magnetoresistance Current dependent nonreciprocity Discussion Methods Crystal growth Device fabrication Transport measurements DATA AVAILABILITY References Acknowledgements Author contributions Competing interests ADDITIONAL INFORMATION