Interplay between charge order and superconductivity in the kagome metal KV_3Sb_5
Feng Du, Shuaishuai Luo, Brenden R. Ortiz, Ye Chen, Weiyin Duan, Dongting Zhang, Xin Lu, Stephen D. Wilson, Yu Song, Huiqiu Yuan
aa r X i v : . [ c ond - m a t . s up r- c on ] F e b Pressure-tuned interplay between charge order and superconductivity in the kagomemetal KV Sb Feng Du,
1, 2, ∗ Shuaishuai Luo,
1, 2, ∗ Brenden R. Ortiz, Ye Chen,
1, 2
Weiyin Duan,
1, 2
Dongting Zhang,
1, 2
Xin Lu,
1, 2
Stephen D. Wilson, Yu Song,
1, 2, † and Huiqiu Yuan
1, 2, 4, ‡ Center for Correlated Matter and Department of Physics, Zhejiang University, Hangzhou 310058, China Zhejiang Province Key Laboratory of Quantum Technology and Device,Department of Physics, Zhejiang University, Hangzhou 310058, China Materials Department and California Nanosystems Institute,University of California Santa Barbara, Santa Barbara, CA, 93106, United States State Key Laboratory of Silicon Materials, Zhejiang University, Hangzhou 310058, China
The kagome metal KV Sb hosts charge order, topologically nontrivial Dirac band crossings, anda superconducting ground state with unconventional characteristics. Here we study the evolution ofcharge order and superconductivity in KV Sb under hydrostatic pressure using electrical resistivitymeasurements. With the application of pressure, the ambient pressure superconducting transitiontemperature T c ≈ . ≈ . . T ∗ decreases from 78 K to 50 K. Upon further increasing pressure, charge order disappears in afirst-order-like fashion at a pressure p just above 0.4 GPa, and T c undergoes a small reduction from3.1 K for 0.4 GPa to 2.6 K for 2.25 GPa. Thus, relative to its ambient pressure value of ≈ . T c is enhanced over a broad pressure range beyond p . These results suggest that the increase of T c with the suppression of charge order results from a competition between the two orders. Inaddition, the upper critical field µ H c2 ( T = 0) is significantly enhanced near the critical pressure p , but µ H c2 ( T ) at various pressures can be well scaled. PACS numbers: 74.25.Ha, 74.70.-b, 78.70.Nx
The kagome lattice provides a rich setting for realizingexotic states of matter, including quantum spin liquids[1–3] and topologically nontrivial electronic states [4–6].Recently, discovery of the two-dimensional kagome metalseries A V Sb ( A = K, Rb, Cs) sparked immense interest[7]. These materials exhibit topological band structures,bulk superconductivity and charge order [8–10], makingthem ideal for investigating the interplay between differ-ent electronic states on the kagome lattice [11, 12].In the A V Sb series, V atoms, which are coordinatedby Sb atoms, form a two dimensional kagome lattice.The alkaline metal A atoms form buffer layers betweenthe V Sb slabs, and allow for the exfoliation and A -deintercalation of these materials [9]. In all three vari-ants, an electronic order with salient features in resistiv-ity, magnetization, and specific heat measurements ap-pears below T ∗ , and superconductivity emerges in itspresence below T c . While a giant anomalous Hall effectwas observed in KV Sb [13], neutron scattering did notdetect magnetic order [7], and neither magnetic suscep-tibility [8] nor muon spin spectroscopy [14] detected thepresence of local moments in KV Sb , ruling out a mag-netic origin for the T ∗ anomaly. Instead, the T ∗ anomalyis associated with charge ordering [8], which exhibits chi-ral character and is proposed to be responsible for thegiant anomalous Hall effect [15].Given superconductivity in A V Sb under ambientpressure always appears in the presence of charge order[9], it is important to investigate whether the charge or-der is a prerequisite for the superconducting state, andhow it behaves once charge order is suppressed. These considerations motivate a detailed study of the interplaybetween charge order and superconductivity in A V Sb .Furthermore, the interplay between charge order and su-perconductivity is in itself a topic of general interest, es-pecially given both orders in KV Sb exhibit unconven-tional characteristics [8, 15]. While a dome of unconven-tional superconductivity typically emerges as magneticorder is suppressed towards a putative quantum criticalpoint [16–18], whether a similar picture holds for the in-terplay between charge order and superconductivity re-mains unsettled. Although a dome of superconductivityanchors around a charge order quantum critical point inLu(Pt − x Pd x ) In [19], in many other systems with coex-isting superconductivity and charge order, the interplaywas found to follow expectations of the Bardeen-Cooper-Schrieffer (BCS) theory [20–22].In this work, we study the temperature-pressure phasediagram of KV Sb single crystals through electricaltransport measurements. For p ≤ . T ∗ tobe gradually suppressed from T ∗ ≈
78 K (ambient pres-sure) to 50 K (0.4 GPa), and vanishes in a first-order-likefashion beyond a critical pressure p that is just above0.4 GPa. Concomitantly, the superconducting transitiontemperature T c increases for p < p , from ≈ . ≈ . p , T c decreases slightly with increasing pressure, reaching2.6 K at 2.25 GPa. Such a temperature-pressure phasediagram is consistent with charge order competing withsuperconductivity, and the robustness of superconductiv-ity beyond p differs from the typical behavior of super-conductivity anchored around a quantum critical point. ( µ Ω c m ) T (K) T * ~78K (c)(b) ( µ Ω c m ) (a) C e / T ( m J m o l - K - ) T (K) Figure 1: (a) In-plane resistivity ρ ( T ) of KV Sb under ambi-ent pressure, from 300 K down to 0.5 K. Zoomed-in (b) ρ ( T )and (c) electronic contribution to the specific heat C e / T bothevidence a bulk superconducting transition with T c ≈ . This combined with the absence of signatures of quantumcriticality in the normal state transport, suggests quan-tum fluctuations likely play a minor role in the interplaybetween charge order and superconductivity.Single crystals of KV Sb were grown using a self-fluxmethod, with physical properties under ambient pres-sure reported previously [9]. While K-deficiencies maybe utilized to achieve unusual transport behaviors [23],they also significantly increase residual resistivity andsuppress superconductivity [7]. Therefore, detailed char-acterization was performed to ensure that our samplesexhibit minimal K-deficiencies [9]. Electrical resistivitymeasurements were carried out using the standard four-probe method with current in the ab -plane, and pres-sure up to 2.25 GPa was applied using a piston-cylinder-type pressure cell, with Daphne 7373 as the pressure-transmitting medium to ensure hydrostaticity. Values ofthe applied pressure were determined through the shiftof T c for a high-quality Pb single crystal. Specific heatunder ambient pressure was measured using a QuantumDesign Physical Property Measurement System (PPMS)with a He insert, using a standard pulse relaxationmethod.We first studied the behavior of KV Sb under ambi-ent pressure, with results summarized in Fig. 1. Temper-ature dependence of the in-plane resistivity ρ ( T ) is shownin Fig. 1(a), with a clear kink at T ∗ ≈
78 K, which corre-sponds to the appearance of charge order. The residualresistivity ratio (RRR) is around 70, evidencing the highquality of the crystals and verifying minimal K-vacancieswithin the lattice. The presence of superconductivitybelow T c ≈ . ( µ Ω c m ) T(K) p (GPa)0.10 0.540.21 0.980.28 1.260.40 2.25 (b) d / d T ( a r bun i t ) T(K) (a) ( µ Ω c m ) T(K) p (GPa)0.100.210.280.400.540.981.752.25 Figure 2: (a) Temperature dependence of the in-plane resis-tivity ρ ( T ) in KV Sb , measured upon cooling under variouspressures. The inset shows the derivatives d ρ ( T )/d T , withthe corresponding charge ordering temperature T ∗ markedby arrows. (b) Low-temperature resistivity of KV Sb undervarious pressures, highlighting evolution of the superconduct-ing transition temperature T c with pressure. C p / T = γ n + βT , where γ is the Sommerfeld coeffi-cient and β represents the lattice contribution, yielding γ = 20.16 mJ mol − K − and β = 4.92 mJ mol − K − .A Debye temperature Θ D = 152 . D = (12 π nR /5 β ) / , where n = 9 is the number ofatoms per formula unit and R is the molar gas constant.By subtracting the phonon contribution, we obtain theelectronic contribution to the specific heat C e / T , shownin Fig. 1(c), which reveals a sharp bulk superconduct-ing transition. The specific heat jump at T c is deter-mined to be ∆ C/γT c = 1 .
02, which is slightly smallerthan the BCS value of 1.43, possibly due to multi-gapsuperconductivity or gap anisotropy. Overall, the ambi-ent pressure results are in good agreement with previousreports [7, 9], and confirms that minimal K-deficienciesare present in our samples.Measurements of ρ ( T ) with pressures up to 2.25 GPaare shown in Fig. 2(a), with the corresponding d ρ /d T curves shown in the inset. A clear anomaly associatedwith T ∗ can be seen for p = 0 . p = 0 .
54 GPa.These results imply that charge order associated with T ∗ disappears in a first-order-like fashion upon pressuretuning, at a critical pressure p between 0.4 GPa and0.54 GPa, without the presence of a quantum criticalpoint. In addition, it should be noted that the resis-tivity anomaly associated with T ∗ is weaker in KV Sb compared to CsV Sb , and it further weakens upon theapplication of pressure. As the strength of the resistiv-ity anomaly reflects the size of the underlying electronicorder parameter, this suggests that in addition to thesuppression of T ∗ , the magnitude of the charge order isalso reduced under pressure in KV Sb .Fig. 2(b) shows ρ ( T ) for T ≤ ! ( µ Ω c m ) T (K) B(T)1.8 0.451.2 0.31 0.20.8 0.10.6 0 ( µ Ω c m ) T (K) B (T)0.9 0.0650.2 0.040.15 0.020.1 0 (a) 2.25GPa ( µ Ω c m ) T (K) B(T)0.9 0.10.38 0.060.3 0.030.22 00.16 H C / [ T c (- d H C / d T ) T = T c ] T/T c WHH fitting
Figure 3: Low-temperature resistivity ρ ( T ) under various ab -plane magnetic fields for (a) 0.1 GPa, (b) 0.7 GPa, and (c)2.25 GPa. (d) The upper critical field of KV Sb as a functionof T / T c under various pressures, normalized by the productof T c and the slope of µ H c2 ( T ) near T c . Fits to the WHHmodel are shown as a dashed line. evolution of superconductivity upon pressure-tuning. Ascan be seen, T c increases with increasing pressure up to0 . p > p up to 2.25 GPa.This suggests the absence of a superconducting domeanchored around a quantum critical point in KV Sb ,different from typical unconventional superconductorsin proximity to magnetic quantum critical points [16–18]. Furthermore, the normal state transport evolvessmoothly across p without signatures of quantum criti-cality such as non-Fermi-liquid behavior [24], consistentwith the absence of a quantum critical point and corre-sponding critical fluctuations. The slow variation of T c for p > p is also reflected in the sharper superconductingtransitions, relative to those for p < p . This in turn sug-gests that internal stress may play a role in determiningthe temperature width of the superconducting transitionin KV Sb , especially under ambient and low pressures.To further probe the superconducting state as a func-tion of pressure, we measured resistivity under an ap-plied magnetic field in the ab -plane, for p = 0 . . .
25 GPa, corresponding to superconductingstates with and without charge order, with results shownin Figs. 3(a)-(c). The upper critical fields µ H c2 ( T )are determined from these curves as when ρ ( T ) dropsto half of its value just before the onset of supercon-ductivity. µ H c2 ( T ) could be fit with the Werthamer-Helfand-Hohenberg (WHH) model [25] , with fit valuesof µ H c2 ( T = 0) being 0.25 T for 0.1 GPa, 1.17 T for0.7 GPa, and 0.37 T for 2.25 GPa. For 0.7 GPa, whichis just above p , the value of µ H c2 ( T = 0) is signifi-cantly larger than that of both p < p (0.1 GPa) and p ≫ p (2.25 GPa), even though its T c = 3 . T c = 2 . µ H c2 ( T ) under 0.1, 0.7 and 2.25 GPa, plotted as a function of T / T c , and normalized by the productof T c and the derivative of H c2 ( T ) near T c . As can beseen, data almost overlap for different applied pressures,and are well-described by fits to the WHH model (dashedline). This suggests that superconductivity in KV Sb tobe orbital-limited, for the pressure range probed in ourmeasurements.The phase diagram obtained from electrical resistiv-ity measurements under pressure is shown in Fig. 4(a),with T c determined from when ρ ( T ) in Fig. 2(b) dropsto zero, and T ∗ determined from the dip of d ρ ( T )/d T in the inset of Fig. 2(a). The phase diagram reveals abroad pressure range above p over which T c is enhancedrelative to its ambient pressure value. This is differentfrom a scenario involving quantum critical fluctuations,where T c usually exhibits clear drops on both sides ofthe putative quantum critical point. Instead, a simpleinterpretation of the suppression of T c in the presenceof charge order is that it competes with superconductiv-ity. Such a competition may arise as charge order gapsout parts of Fermi surface, leading to a reduced densityof states ( g ( E F )), which leads to a reduction of T c inthe BCS theory. Although such a reduction of g ( E F ) isevidenced through the reduced Pauli paramagnetism be-low T ∗ [9], little or no effects are observed in resistivity,suggesting the reduction to be subtle. Thus, a changein g ( E F ) alone may not be sufficient to account for thecompetition between superconductivity and charge or-der, and additional mechanisms may also be at play. Theresidual resistivity ρ exhibits a plateau around p , andthen decreases continuously for p & . ρ is strongly af-fected by the presence of K-deficiencies [7], our measuredvalues of ρ < . µ Ω · cm are consistent with minimalK-deficiencies in our samples.Our study of KV Sb under hydrostatic pressure in-dicates an enhancement of superconductivity with thegradual suppression of charge order, which then remainsenhanced relative to its ambient pressure value over alarge pressure range with charge order being fully sup-pressed. Combined with the absence of signatures ofquantum criticality in the normal state transport across p , our results implies a minor role of quantum criticalfluctuations associated with charge order in enhancing T c . Instead, the enhanced superconductivity that we ob-serve in KV Sb results from the suppression of chargerorder, which competes with superconductivity. WithinBCS theory, such a competition may arise from chargeorder reducing g ( E F ), and the fact that T c changes lit-tle beyond p can then be naturally understood– g ( E F )varies slowly with pressure, once charge order is fullysuppressed. Given the commonality of charge order inthe A V Sb series, the effect shown in our work shouldalso be present across the A V Sb series, at least for theenhancement of T c in the regime p < p . Interestingly,recently studies of CsV Sb under pressure indicated the (b) T c T ( K ) KV Sb CDW SC T * ( µ Ω c m ) P (GPa) (a) Figure 4: (a) Temperature-pressure phase diagram ofKV Sb . T ∗ is determined from position of the dip in thederivative d ρ ( T )/d T . T c is determined as when ρ ( T ) dropsto zero (within the noise level of our measurements). For p > p , the small scatter of T c (less than 0.1 K) likely re-sults from slight differences between the samples used in ourstudy. (b) Pressure dependence of the residual resistivity ρ ,obtained from ρ ( T ) just above the onset of superconductivity. presence of either a single [11] or double [12] supercon-ducting domes. The discrepancy between these reportson CsV Sb , as well as with our results on KV Sb , war-rants further studies. As the A V Sb series is prone to A -deintercalation (the degree of which can be gaugedthrough the residual resistivity) [7], the effects of A -sitedeficiencies on charger order, superconductivity, as wellas their interplay, deserves to be thoroughly investigated.While our findings can be interpreted through a com-petition between charge order and superconductivity,there is a notable difference compared to systems suchas LaAuSb [22]. In the latter case, charge order is alsosuppressed with increasing pressure and disappears ina first-order-like fashion at a characteristic pressure p ;however, there is a sudden jump in T c and a significantdrop in the residual resistivity ρ across p , which is notseen in KV Sb . One possible cause of such a differencelies in the strength of charge order just before it is sup-pressed under pressure. If the charge order of the mate-rial is already substantially weakened, its full suppressionwith applied pressure would only lead a marginal suddenincrease in g ( E F ). The corresponding jump in T c and thedrop in ρ would be small, and may not be discerniblein experiments. Alternatively, additional effects may beinvolved, as suggested by the threefold increase in T c at p (relative to ambient pressure) and the enhanced H c2 for 0.7 GPa [Fig. 3(b)], which is slightly above p .In conclusion, we have studied the temperature-pressure phase diagram of the kagome metal KV Sb un-der hydrostatic pressure, and found that superconductiv- ity is gradually enhanced as charge order is suppressedfor pressure up to ≈ . T c , and instead sug-gests that the enhancement observed below ≈ . Sb should be relevant across the A V Sb series, andconstrains models that capture both orders.This work was supported by the National KeyR&D Program of China (No. 2017YFA0303100, No.2016YFA0300202),the Key R&D Program of ZhejiangProvince, China (2021C01002), the National NaturalScience Foundation of China (No. 11974306 and No.12034017) and the Science Challenge Project of China(No. TZ2016004). S.D.W. and B.R.O. gratefully ac-knowledge support via the UC Santa Barbara NSF Quan-tum Foundry funded via the Q-AMASE-i program underaward DMR-1906325. B.R.O. also acknowledges supportfrom the California NanoSystems Institute through theElings fellowship program. ∗ These authors contributed equally to this work. † Electronic address: yusong˙[email protected] ‡ Electronic address: [email protected][1] I. Syozi, Progress of Theoretical Physics , 306 (1951),URL https://doi.org/10.1143/ptp/6.3.306 .[2] T.-H. Han, J. S. Helton, S. Chu, D. G. No-cera, J. A. Rodriguez-Rivera, C. Broholm,and Y. S. Lee, Nature , 406 (2012), URL https://doi.org/10.1038/nature11659 .[3] C. Broholm, R. J. Cava, S. A. Kivel-son, D. G. Nocera, M. R. Norman, andT. Senthil, Science , eaay0668 (2020), URL https://doi.org/10.1126/science.aay0668 .[4] L. Ye, M. Kang, J. Liu, F. von Cube, C. R. Wicker,T. Suzuki, C. Jozwiak, A. Bostwick, E. Rotenberg,D. C. Bell, et al., Nature , 638 (2018), URL https://doi.org/10.1038/nature25987 .[5] E. Liu, Y. Sun, N. Kumar, L. Muechler, A. Sun,L. Jiao, S.-Y. Yang, D. Liu, A. Liang, Q. Xu,et al., Nature Physics , 1125 (2018), URL https://doi.org/10.1038/s41567-018-0234-5 .[6] M. Kang, L. Ye, S. Fang, J.-S. You, A. Levitan,M. Han, J. I. Facio, C. Jozwiak, A. Bostwick, E. Roten-berg, et al., Nature Materials , 163 (2019), URL https://doi.org/10.1038/s41563-019-0531-0 .[7] B. R. Ortiz, L. C. Gomes, J. R. Morey, M. Winiarski, M. Bordelon, J. S. Mangum, I. W. H. Oswald,J. A. Rodriguez-Rivera, J. R. Neilson, S. D. Wil-son, et al., Physical Review Materials (2019), URL https://doi.org/10.1103/physrevmaterials.3.094407 .[8] B. R. Ortiz, S. M. Teicher, Y. Hu, J. L. Zuo,P. M. Sarte, E. C. Schueller, A. M. Abeykoon,M. J. Krogstad, S. Rosenkranz, R. Osborn,et al., Physical Review Letters (2020), URL https://doi.org/10.1103/physrevlett.125.247002 .[9] B. R. Ortiz, E. Kenney, P. M. Sarte, S. M. L. Te-icher, R. Seshadri, M. J. Graf, and S. D. Wilson (2020),arXiv:2012.09097.[10] Q. Yin, Z. Tu, C. Gong, Y. Fu, S. Yan, and H. Lei (2021),arXiv:2101.10193.[11] C. C. Zhao, L. S. Wang, W. Xia, Q. W. Yin, J. M. Ni,Y. Y. Huang, C. P. Tu, Z. C. Tao, Z. J. Tu, C. S. Gong,et al. (2021), arXiv:2102.08356.[12] K. Y. Chen, N. N. Wang, Q. W. Yin, Z. J. Tu, C. S.Gong, J. P. Sun, H. C. Lei, Y. Uwatoko, and J. G. Cheng(2021), arXiv:2102.09328.[13] S.-Y. Yang, Y. Wang, B. R. Ortiz, D. Liu,J. Gayles, E. Derunova, R. Gonzalez-Hernandez,L. ˇSmejkal, Y. Chen, S. S. P. Parkin, et al.,Science Advances , eabb6003 (2020), URL https://doi.org/10.1126/sciadv.abb6003 .[14] E. M. Kenney, B. R. Ortiz, C. Wang, S. D. Wilson, andM. J. Graf (2020), arXiv:2012.04737.[15] Y.-X. Jiang, J.-X. Yin, M. M. Denner, N. Shumiya, B. R.Ortiz, J. He, X. Liu, S. S. Zhang, G. Chang, I. Belopolski,et al. (2020), arXiv:2012.15709.[16] N. D. Mathur, F. M. Grosche, S. R. Julian, I. R.Walker, D. M. Freye, R. K. W. Haselwimmer, and G. G. Lonzarich, Nature , 39 (1998), URL https://doi.org/10.1038/27838 .[17] H. Q. Yuan, Science , 2104 (2003), URL https://doi.org/10.1126/science.1091648 .[18] D. J. Scalapino, Reviews of Mod-ern Physics , 1383 (2012), URL https://doi.org/10.1103/revmodphys.84.1383 .[19] T. Gruner, D. Jang, Z. Huesges, R. Cardoso-Gil, G. H.Fecher, M. M. Koza, O. Stockert, A. P. Mackenzie,M. Brando, and C. Geibel, Nature Physics , 967(2017), URL https://doi.org/10.1038/nphys4191 .[20] A. Gabovich, A. Voitenko, and M. Aus-loos, Physics Reports , 583 (2002), URL https://doi.org/10.1016/s0370-1573(02)00029-7 .[21] B. Shen, F. Du, R. Li, A. Thamizhavel, M. Smid-man, Z. Y. Nie, S. S. Luo, T. Le, Z. Hossain, andH. Q. Yuan, Physical Review B (2020), URL https://doi.org/10.1103/physrevb.101.144501 .[22] F. Du, H. Su, S. S. Luo, B. Shen, Z. Y. Nie,L. C. Yin, Y. Chen, R. Li, M. Smidman, andH. Q. Yuan, Physical Review B (2020), URL https://doi.org/10.1103/physrevb.102.144510 .[23] Y. Wang, S. Yang, P. K. Sivakumar, B. R. Ortiz, S. M. L.Teicher, H. Wu, A. K. Srivastava, C. Garg, D. Liu, S. S. P.Parkin, et al. (2020), arXiv:2012.05898.[24] P. Gegenwart, Q. Si, and F. Steglich, Nature Physics ,186 (2008), URL https://doi.org/10.1038/nphys892 .[25] N. R. Werthamer, E. Helfand, and P. C. Ho-henberg, Phys. Rev. , 295 (1966), URL https://link.aps.org/doi/10.1103/PhysRev.147.295https://link.aps.org/doi/10.1103/PhysRev.147.295