Heat transport in Mo3Sb7 single crystal: Evidence for nodeless s-wave superconducting gap

Solid State Communications 195 (2014) 84–87

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Heat transport in Mo3Sb7 single crystal: Evidence for nodeless s-wave superconducting gap W.N. Dong, J. Pan, J. Zhang, X.C. Hong, L.P. He, S.Y. Zhou, J.K. Dong, S.Y. Li n State Key Laboratory of Surface Physics, Department of Physics, and Laboratory of Advanced Materials, Fudan University, Shanghai 200433, PR China

art ic l e i nf o

a b s t r a c t

Article history: Received 3 April 2014 Received in revised form 2 July 2014 Accepted 5 July 2014 by X.C. Shen Available online 18 July 2014

We investigate the superconducting gap structure of the intermetallic superconductor Mo3Sb7 single crystal by low-temperature thermal conductivity measurements. In zero field, the absence of a residual linear term κ 0 =T in the T-0 limit provides strong evidence for nodeless superconducting gap. The field dependence of κ 0 =T is very similar to that of InBi, a typical s-wave superconductor in the dirty limit. These results demonstrate that Mo3Sb7 has nodeless s-wave superconducting gap, despite the opening of a spin gap at 53 K and the possible interplay between superconductivity and magnetism. & 2014 Elsevier Ltd. All rights reserved.

Keywords: A. Intermetallic superconductor Mo3Sb7 C. S-wave gap E. Thermal conductivity

1. Introduction The interplay between superconductivity and magnetism is one of the main themes of superconductor research. In high-temperature cuprate superconductors, iron-based superconductors, as well as many heavy-fermion superconductors, superconductivity is believed to be unconventional, mediated by antiferromagnetic (AF) spin fluctuations [1]. In this context, other superconductors close to magnetic ordered state or associating with magnetic interaction have attracted considerable attentions, such as RNi2B2C (R¼Lu, Y, Tm, Er, Ho, and Dy), MgCNi3, CeRu2 and RuSr2YCu2O8 [2–5]. The intermetallic compound Mo3Sb7, with a cubic Ir3Ge7-type crystal structure, was found to be superconducting with T c  2:1 K more than ten years ago [6]. Interestingly, magnetic susceptibility, specific heat, and resistivity measurements on Mo3Sb7 polycrystals indicated the coexistence of superconductivity and spin fluctuations [7], and the opening of a spin gap below 50 K [8]. Further pressure studies on Mo3Sb7 polycrystals revealed that a spin density wave (SDW) exists under pressure, and the SDW is likely competing with superconductivity [9]. These results give the possibility of unconventional superconductivity in Mo3Sb7. Earlier point-contact Andreev-reflection experiments on single crystals found that the superconducting gap is strongly anisotropic, and suggested that Mo3Sb7 is not a trivial BCS (s-wave) superconductor but rather has (s þg)-wave or another unconventional pairing symmetry [10]. However, later specific heat and penetration depth

n

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http://dx.doi.org/10.1016/j.ssc.2014.07.005 0038-1098/& 2014 Elsevier Ltd. All rights reserved.

results all pointed to conventional s-wave superconducting gap [11–14]. While the penetration depth measurements on single crystals by Khasanov et al. suggested a single isotropic gap in Mo3Sb7 [12], specific heat and penetration depth measurements on polycrystalline samples by Tran et al. claimed that their results are consistent with two-gap s-wave model [13,14]. To clarify the superconducting gap structure of Mo3Sb7, more experiments on high-quality single crystals are needed. The low-temperature thermal conductivity measurement is a bulk technique to probe the gap structure of superconductors [15]. Whether there is a finite residual linear term κ 0 =T in zero field is a good judgment on the existence of gap nodes. The field dependence of κ 0 =T can further give information of nodal gap, gap anisotropy, or multiple gaps [16]. In this paper, we present the low-temperature thermal conductivity measurements of high-quality Mo3Sb7 single crystals down to 80 mK. The absence of residual linear term κ 0 =T in zero field confirms nodeless superconducting gap in Mo3Sb7. The field dependence of κ 0 =T is slow in low field, which does not show the behavior of anisotropic gap or multiple gaps with significantly different magnitudes. These results suggest a nodeless s-wave superconducting gap in Mo3Sb7.

2. Experimental details Single crystals of Mo3Sb7 were grown by the self-flux method, as described in Ref. [17]. The excessive Sb flux was removed by centrifuging. The typical size of the single crystals is 3  2  2 mm3. We chose a single crystal with a large flat surface identified as the (001) plane by

W.N. Dong et al. / Solid State Communications 195 (2014) 84–87

X-ray diffraction measurements. It was cut and polished to a barshaped sample of dimensions 4  0.75  0.12 mm3, with the edges of the largest surface along [100] and [010]. The dc magnetic susceptibility was measured at H¼10 Oe with magnetic field along the [001] direction, using a SQUID (MPMS, Quantum Design). Four silver wires were attached to the sample with silver paint, which was used for both thermal conductivity and resistivity measurements. The typical contact resistance is 50 m Ω at 2 K. Resistivity measurements from 300 to 1.5 K and from 4 K to 80 mK were performed in a 4He cryostat and a dilution refrigerator, respectively. Thermal conductivity was measured in a dilution refrigerator, using a standard four-wire steady-state method with two RuO2 chip thermometers, calibrated in situ against a reference RuO2 thermometer. Magnetic fields were applied along the [001] direction. To ensure a homogeneous field distribution in the sample, all fields were applied at temperatures above Tc for resistivity and thermal conductivity measurements.

3. Results and discussions Fig. 1(a) shows the temperature dependence of dc magnetic susceptibility of Mo3Sb7 single crystal with both zero-field-cooling

(ZFC) and field-cooling (FC) modes. The observed diamagnetic transition is very similar to the previously reported one [17]. The transition temperature T c  2:3 K is determined from the onset of the transition. Fig. 1(b) presents the temperature dependence of resistivity of the sample in zero field. The T c defined by ρ ¼0 is 2.35 K and the 10–90% resistive transition width is less than 0.05 K. The normal-state resistivity behaves nearly the same as in Ref. [17]. The data between 3 and 40 K can be well fitted to the formula ρðTÞ ¼ ρ0 þ cT þd expð  Δ=TÞ with ρ0 ¼ 77:6 μΩ cm, c ¼ 0:096 μΩ cm K  1 , d ¼ 115:9 μΩ cm, and Δ ¼ 90 K. This formula points to a gap feature [8,17]. The upper critical field H c2 of Mo3Sb7 single crystal is obtained from the resistivity measurements in different magnetic fields. Fig. 2(a) shows the low-temperature resistivity of the sample in magnetic fields up to 2 T. A positive magnetoresistance is observed and the residual resistivity in H¼ 1.8 T is ρ0 (1.8 T) ¼85.5 μΩ cm. The temperature dependence of H c2 , defined by ρ ¼0, is plotted in Fig. 2(b). The H c2 ð0Þ  1:85 T is roughly estimated. Choosing a slightly different H c2 ð0Þ does not affect our discussion on the field dependence of κ 0 =T below. Fig. 3 shows the temperature dependence of thermal conductivity in magnetic fields up to 1.8 T, plotted as κ/T vs T. The measured

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Fig. 1. (Color online) (a) Temperature dependence of dc magnetic susceptibility of Mo3Sb7 single crystals, measured in H¼ 10 Oe along the c-axis with both zero-fieldcooling (ZFC) and field-cooling (FC) modes. (b) Resistivity of Mo3Sb7 single crystal in zero field. The solid line in the inset is a fit of the data between 3 and 40 K to ρðTÞ ¼ ρ0 þ cT þ d expð  Δ=TÞ.

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Fig. 2. (Color online) (a) Low-temperature resistivity of Mo3Sb7 single crystal in magnetic fields up to 2 T. (b) Temperature dependence of the upper critical field Hc2 ðTÞ, defined by ρ ¼ 0. The dashed line is a guide to the eye, which points to Hc2 ð0Þ  1:85 T.

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crystal strongly suggests that the superconducting gap is nodeless. This result is consistent with the conclusion based on the specific heat and penetration depth measurements [11,12]. The magnetic field dependence of κ 0 =T gives complementary information on the gap structure. Fig. 3(b) plots the thermal conductivity of Mo3Sb7 single crystal in different fields. κ 0 =T gradually increases with the increasing field. In H c2 ¼ 1:8 T, κ 0 =T ¼ 0:273 7 0:13 mW K  2 cm  1 was obtained from the fitting. This value roughly meets the Wiedemann-Franz law expectation L0 =ρ0 ð1:8 TÞ ¼ 0:285 mW K  2 cm  1 , with L0 the Lorenz number 2.45  10  8 WΩ K  2 and ρ0(1.8 T) ¼85.5 μΩ cm. The verification of the Wiedemann-Franz law in the normal state confirms the reliability of our thermal conductivity measurements. The normalized κ 0 ðHÞ=T is plotted as a function of H=H c2 in Fig. 4. For comparison, similar data of the clean s-wave superconductor Nb [22], dirty s-wave superconductor InBi [23], multi-band s-wave superconductor NbSe2 [24] and d-wave superconductor Tl-2201 [20] are also plotted. For a clean type II s-wave superconductor with a single gap, κ should grow exponentially with field, as observed in Nb [22]. While for s-wave superconductors in the dirty limit such as InBi, the curve is exponential at low fields and crosses over a roughly linear behavior closer to Hc 2 [23]. The normalized κ 0 ðHÞ=T plot of Mo3Sb7 single crystal in Fig. 4 mimics that of the dirty s-wave superconductor InBi and does not show any multi-gap behavior like NbSe2 [24]. This result further suggests that the superconducting gap of Mo3Sb7 is single and s-wave like. Therefore our current work does not support the interpretation of highly anisotropic gap in Ref. [10] or multiple gaps in Ref. [14], but agrees with the single s-wave gap in Ref. [12]. The field dependence of normalized κ 0 ðHÞ=T also suggests that our Mo3Sb7 single crystal, like InBi, is in the dirty limit with l 5 ξ0 . To check this, we need to estimate the coherent length ξ0 and 2 mean free path l. Using the relation H c2 ð0Þ ¼ ϕ0 =ð2πξ0 Þ, the coherence length ξ0 ¼ 12:5 nm is obtained. Since the normalstate thermal conductivity κ N ¼ 13CvF l, we have l ¼ 3ðκ N =TÞ=γ vF . With κ N =T ¼ L0 =ρ0 ð1:8 TÞ ¼ 0:285 mW K  2 cm  1 and γ ¼33.5 mJ mol  1 K  2 [11], we obtained l E9 Å, one order of magnitude smaller than ξ0. This confirms that Mo3Sb7 is indeed in the dirty limit.

Fig. 3. (Color online) Low-temperature thermal conductivity of Mo3Sb7 single α1 crystal. (a) In zero field, the fit to κ=T ¼ a þ bT below 0.5 K gives a negligible residual linear term κ 0 =T ¼ 4 μW K  2 cm  1 . (b) The dashed line is the normal-state Wiedemann–Franz law expectation L0/ρ0(1.8 T), with L0 the Lorenz number 2.45  10  8 W Ω K  2 and ρ0(1.8 T) ¼85.5 μΩ cm. In H¼1.8 T, the Wiedemann–Franz law κ0 =T ¼ L0 =ρ0 is roughly satisfied.

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thermal conductivity is the sum of contributions from electrons and phonons. The residual linear term κ 0 =T contributed by electrons is obtained by extrapolating κ/T to T¼ 0. This process can be done by α1 fitting the data to κ/T¼a þ bT at low temperature, with the two α terms aT and bT representing the contribution from electrons and phonons, respectively [18,19]. The power of the phonon term α is typically between 2 and 3, due to the specular reflections of phonons at the sample boundary [18,19]. The zero field κ/T curve in Fig. 3 α1 (a) was well fitted by κ/T¼ κ 0 =T þ bT , which gives α ¼ 2.67 and 2 1 κ 0 =T ¼ 4 7 10 μW K cm . Considering that our experimental error bar is about 5 μW K  2 cm  1, the residual κ 0 =T could not be clearly resolved. In stark contrast, for unconventional superconductors with nodes in the superconducting gap, the nodal quasiparticles will contribute to a finite κ 0 =T in zero field, as in the case of d-wave cuprate superconductor Tl2Ba2CuO6 þ δ (Tl-2201) [20]. Nevertheless, all electrons are condensed into Cooper pairs as T-0 in nodeless superconductors and there are no thermally excited fermionic quasiparticles available to carry heat, thus the linear term of thermal conductivity goes to zero, as in the conventional s-wave superconductor V3Si [21]. The observed negligible κ 0 =T in Mo3Sb7 single

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4. Summary In summary, we have measured the thermal conductivity of high-quality single crystal Mo3Sb7 down to 80 mK to investigate its superconducting gap structure. The absence of κ 0 =T in zero field provides strong evidence for a gap without node. The field dependence of κ 0 =T is consistent with what is expected for a single nodeless s-wave gap. In this sense, the superconductivity in Mo3Sb7 may not relate to spin fluctuations. Acknowledgments This work is supported by the Natural Science Foundation of China, the Ministry of Science and Technology of China (National Basic Research Programs no. 2012CB821402), Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning. References [1] M.R. Norman, Science 332 (2011) 196. [2] T. Siegrist, H.W. Zandbergen, R.J. Cava, J.J. Krajewski, W.F. Peck Jr., Nature 367 (1994) 254. [3] T. He, Q. Huang, A.P. Ramirez, Y. Wang, K.A. Regan, N. Rogado, M.A. Hayward, M.K. Haas, J.S. Slusky, K. Inumara, H.W. Zandbergen, N.P. Ong, R.J. Cava, Nature 411 (2001) 54. [4] A.D. Huxley, C. Paulsen, O. Laborde, J.L. Tholence, D. Sanchez, A. Junod, R. Calemczuk, J. Phys.: Condens. Matter 5 (1993) 7709.

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