Magnetic penetration depth and gap symmetry of the noncentrosymmetric superconductors CePt3Si and LaPt3Si
aa r X i v : . [ c ond - m a t . s up r- c on ] O c t . . Magnetic penetration depth and gap symmetry of the noncentrosymmetric superconductorsCePt Si and LaPt Si R. L. Ribeiro, I. Bonalde,
1, 2
Y. Haga, R. Settai, and Y. ¯Onuki
3, 4 Centro de F´ısica, Instituto Venezolano de Investigaciones Cient´ıficas, Apartado 20632, Caracas 1020-A, Venezuela Center for Quantum Science and Technology under Extreme Conditions andGraduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan Advanced Science Research Center, Japan Atomic Energy Research Institute, Tokai, Ibaragi 319-1195, Japan Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
PACS numbers:
The role of broken parity in the unconventional responsesof superconductors without inversion symmetry has been dif-ficult to pinpoint. The absence of inversion symmetry in acrystal structure causes the appearance of an antisymmetricspin-orbit coupling (ASOC) that a ff ects the electronic prop-erties. Some of these superconductors, like CePt Si and theseries CeTX (T = Rh, Ir, Co; X = Si, Ge), are also antiferro-magnetic heavy-fermions. A few models based on the lack ofparity [1, 2, 3] and the e ff ect of antiferromagnetic order [4, 5]have been introduced mainly to describe the unconventionalbehaviors of CePt Si. Among such behaviors are line nodesin the gap [6, 7, 8], an upper-critical field larger than the para-magnetic limiting field [9, 10] and a constant spin suscepti-bility across the transition [11]. The models are supposed toexplain all superconductors without inversion symmetry, butmost of the nonmagnetic noncentrosymmetric superconduc-tors with a strong ASOC display conventional s -wave super-conductivity. Thus, there is an uncertainty on what is reallycausing both types of behaviors. This doubt calls for furtherstudies addressing the origin of unconventional responses insuperconductors without inversion symmetry.Here, we aim to get further insight into the importanceof the lack of parity in the unusual responses of CePt Si bystudying the isostructural LaPt Si ( T c = .
64 K) without elec-tron correlations. LaPt Si and CePt Si have similar ASOCstrengths [1, 12]. Thus, LaPt Si constitutes a special systemto test the role of both electron correlations and broken par-ity in CePt Si. The superconducting phase of LaPt Si hasbeen hardly studied. Specific-heat data suggest that LaPt Siis a weak-coupling s -wave superconductor [8]. Experimentalresults in other superconducting properties are then requiredto confirm this. We report here on high-resolution magneticpenetration depth λ ( T ) measurements of a high-quality sin-gle crystal of LaPt Si down to 60 mK ( ∼ . T c ). We founda broad superconducting transition and evidence for conven-tional s -wave superconductivity.The single crystal of LaPt Si used in our experiment wasgrown by the Bridgman method [8] and has dimensionsaround 0 . × . × .
28 mm . The observation of deHaas-van Alphen oscillations and the mean-free path val-ues as large as 2400 Å in single crystals of the same batch[13] are strong indications of the high-quality of our crys- ( ∆λ ab )( ∆λ ab )CePt Si Al ∆ λ / ∆ λ T/T C LaPt Si FIG. 1: (Color online) Normalized ∆ λ ab ( T ) / ∆ λ of LaPt Si and sin-gle crystal B2 of CePt Si reported in ref. 14. For comparison thenormalized variation of the penetration depth of aluminum is alsodisplayed. tal. Penetration depth measurements were performed utiliz-ing a 13 MHz tunnel diode oscillator [6]. The magnitude ofthe ac probing field was estimated to be 3 mOe, and the dcfield at the sample was reduced to around 1 mOe. The de-viation of the penetration depth from the lowest measuredtemperature, ∆ λ ( T ) = λ ( T ) − λ (0.06 K), was obtained upto T ∼ . T c from the change in the measured resonancefrequency ∆ f ( T ) = G ∆ λ ( T ). No di ff erence is observed byusing ∆ f ( T ) = G ∆ χ ( T ), with the full sample susceptibility χ = [(2 λ/ a )tanh( a / λ ) −
1] for a slab [6]. Here G is a constantfactor that depends on the sample and coil geometries and thatincludes the demagnetizing factor of the sample, and a is therelevant dimension.Figure 1 shows the normalized variation ∆ λ ab ( T ) / ∆ λ as afunction of temperature in LaPt Si and single crystal B2 ofCePt Si reported in ref. 14. Here ∆ λ is the total penetrationdepth shift of the samples. For comparison, the figure alsodepicts the normalized variation in the penetration depth ofa 99.9995% Al polycrystalline sample. In LaPt Si the out-of-plane penetration depth λ c ( T ) is similar to λ ab ( T ), whichimplies isotropic superconductivity as in CePt Si. A notice-
LaPt Si T/T C ∆ λ ab / ∆ λ ∆ λ a b / ∆ λ T/T C CePt Si LaPt Si FIG. 2: (Color online) Low-temperature region of the variation inthe penetration depth of LaPt Si and CePt Si. The data of LaPt Sifollow a BCS s -wave behavior (see inset), whereas those of CePt Siresponse linearly as T →
0. The solid line in the inset is a fit to theBCS model for an isotropic pairing symmetry. able feature of the figure is that the superconducting transitionof LaPt Si is not sharp (transition width around 0.15 K), asexpected for a very clean high-quality single crystal. The tran-sition is also quite broad in CePt Si [14]. Interestingly, a lin-ear temperature response of the penetration depth of CePt Siand LaPt Si is clearly seen in the region just below T c . Thewide transition would lead to a strong suppression of the su-perfluid density near T c in LaPt Si, as observed in CePt Si[6, 15]. A broad superconducting transition in LaPt Si wasalso observed, even tough not discussed, in specific-heat [8]and resistivity [16] measurements. In LaPt Si and CePt Sithe wide transitions should not be associated with impuritiesor defects. The fact that the penetration depth data of LaPt Sido not show any kink or second drop suggests that there areno magnetic or second superconducting transitions below T c .The broad transition in LaPt Si can be evidently attributed toneither magnetic nor heavy-fermion e ff ects. It is unlikely thatthe wide transitions are a signature of broken parity, sinceother noncentrosymmetric superconductors show very sharptransitions. The superconducting transition in CePt Si hasbeen found to sharpen around the pressure at which the an-tiferromagnetic phase disappears [17].The main body of Fig. 2 displays the low-temperature re-gion of the penetration depth data of LaPt Si and CePt Sishown in Fig. 1. Whereas in CePt Si the penetration depthchanges linearly with temperature as T →
0, indicating linenodes in the gap [6, 14], in LaPt Si it flattens out below about0.2 T c (see inset to Fig. 2), as theoretically expected for a su-perconductor with an isotropic energy gap. At temperatures T < . T c the data of LaPt Si are fitted very well to the BCSmodel ∆ λ ( T ) ∝ r π ∆ k B T exp( − ∆ / k B T ) , (1)with ∆ = . k B T c . This value is quite similar to that of the weak-coupling BCS model 1 . k B T c . Overall the behaviorof the penetration depth of LaPt Si is in agreement with thatobserved in specific-heat measurements [8], although in thelatter case a lower value ∆ = . k B T c was obtained.The isostructural LaPt Si and CePt Si, apart from havingsimilar ASOC strengths, are thought to have similar Fermisurfaces and contributions of the bands to the density ofstates [13]. If parity mixing alone determines the behaviorsof the superconducting properties in these compounds, onewould expect such behaviors to be similar. However, LaPt Sipresents conventional s -wave responses, while CePt Si showsunconventional ones. Similar situation appears to take placein isostructural LaIrSi and CeIrSi , for which NMR measure-ments suggest an isotropic gap and a gap with line nodes, re-spectively [18]. Thus, it seems that in CePt Si and CeIrSi parity mixing does not lead -at least solely- to line nodes. Forthe case of CePt Si (applicable to CeIrSi ), it has been pointedout that line nodes are accidentally generated when the antifer-romagnetic order is taken into account and the p -wave com-ponent of the parity mixing is dominant [4, 5]. Morever, itis thought that the antiferromagnetic order favors the p -wavecomponent and that in the absence of such ordering the s -wavecomponent dominates. This will be consistent with the presentexperimental results. Within this theoretical scenario the non-magnetic Li Pt B with line nodes remains a puzzle, being theonly nonmagnetic superconductor with a strong ASOC thatdoes not display a BCS s -wave behavior. In a di ff erent schemeline nodes in noncentrosymmetric compounds can still be im-posed by symmetry [1, 2], as it occurs in some unconventionalsuperconductors with inversion symmetry.In summary, from measurements of the magnetic penetra-tion depth we found that the superconducting transition ofLaPt Si is broad, as is in CePt Si. We also observed a con-ventional s -wave behavior in LaPt Si, as opposed to the un-conventional response obtained in CePt Si. Since these com-pounds are isostructural and have the same ASOC strength,the present result would imply that the parity mixing alonedoes not lead to unconventional behaviors in CePt Si and thatthe antiferromagnetic order may need to be taken into account.
Acknowledgment
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