Quick suppression of superconductivity of NbSe2 by Rb intercalation

Solid State Communications 297 (2019) 6–10

Contents lists available at ScienceDirect

Solid State Communications journal homepage: www.elsevier.com/locate/ssc

Communication

Quick suppression of superconductivity of NbSe2 by Rb intercalation Xiao Fan

a,b

, Hongxiang Chen

a,b

, Linlin Zhao

a,b

a,c

T

a,d,∗

, Shifeng Jin , Gang Wang

a

Research and Development Center for Functional Crystals, Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinses Academy of Sciences, Beijing, 100190, China b University of Chinese Academy of Sciences, Beijing, 100049, China c School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 101408, China d Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China

A R T I C LE I N FO

A B S T R A C T

Communicated by Alessandra Lanzara

2H-NbSe2, a typical layered transition metal dichalcogenide (TMD), has attracted tremendous research interest for its higher superconducting transition temperature (Tc = 7.2 K) than Tc of other TMDs (2–4 K) and hosting of charge density wave (CDW). The van der Waals (vdW) bonding between NbSe2 layers makes it a good platform for tuning the crystal structure, CDW, and superconducting gap by intercalation. Here we report the crystal structure and superconductivity of Rb-intercalated NbSe2 prepared by solid-state reaction. For Rb intercalation with 0 ≤ x ≤ 0.025, there is only one phase with space group P63/mmc. With Rb intercalation, Tc of RbxNbSe2 decreases from 7.2 K for x = 0 to 4.2 K for x = 0.025 in an L-shaped way. The suppression rate of Tc is similar to the one with magnetic Fe doping, but much quicker than those with Li, Ga, and Cu doping. The superconducting phase diagram of RbxNbSe2 is established accordingly and is compared with those of LixNbSe2, CuxNbSe2, FexNbSe2, and GaxNbSe2. The suppression of superconductivity is discussed based on the ionic radius, valence, and magnetism of doping elements and the expansion between the NbSe2 layers.

Keywords: 2H-NbSe2 Superconductivity Metal intercalation Phase diagram

1. Introduction Layered transition metal dichalcogenides (TMDs) have attracted considerable attention because of the novel mechanical, electronic, optical, magnetic, and chemical properties mainly due to their low structural dimensionality [1–10]. TMDs are a series of compounds with the MX2 formula, where M and X represent transition metal (Ti, Zr, Hf, V, Nb, Ta, Mo, W, Re, etc.) and chalcogen (S, Se, and Te), respectively [11,12]. The MX2 slab is composed of one atomic layer of transition metal sandwiched between two atomic layers of chalcogen. The structures are made from stacking MX2 layers with van der Waals (vdW) bonding between each other and feature polymorphism, such as 1T, 2H, 3R, etc. The weak nature of vdW interaction makes TMDs a good platform to tune the crystal structure, charge density wave (CDW), and superconductivity by intercalation [13–18]. MoS2 and TiSe2 are both semiconductors and superconductivity can be induced by metal intercalation [13,19]. For intercalated MoS2, the superconducting transition temperature (Tc) (3–7 K) depends on the content of the intercalated alkali metals and alkali-earth metals [20,21]. The superconductivity of 2H-TaS2 can be strengthened through intercalation of Lewis bases due to the suppression of the CDW [22,23].

Among TMDs, 2H-NbSe2 is the most representative studied with Tc of ∼7.2 K, which is higher than Tc of other TMDs (2–4 K) and can be manipulated by doping charge carrier through intercalation [24]. Meanwhile, 2H-NbSe2 hosts a CDW with critical temperature (TCDW) of ∼33 K [3]. Thus it is very attractive to study the potential interplay between superconductivity and CDW [4,16,25,26]. For optimal superconductors, Tc typically decreases with increasing “impurity”, such as the alkali metals [27], 3d transition metals [28], and organic molecules [29]. However, different intercalants can lead to the suppression of superconductivity in varying rates and manners [24,27,28,30]. Given the larger radius of ionic Rb, unique suppression speed and shape could be expected compared with those of smaller alkali metal intercalated one, which may shade light on the understanding of the mechanism of superconductivity in NbSe2. Here, we investigated the crystal structure and superconductivity of RbxNbSe2 synthesized by solid-state reaction. We found that there is only one pure phase with space group P63/mmc for 0 ≤ x ≤ 0.025. The lattice parameters a and c both increase with increasing Rb content within this range. Up to x = 0.05, the side phase comes out. With Rb doping, the superconductivity of NbSe2 is suppressed with Tc decreasing from 7.2 K for x = 0 to 4.2 K for x = 0.025 in an L-like shape.

∗ Corresponding author. Research and Development Center for Functional Crystals, Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinses Academy of Sciences, Beijing, 100190, China. E-mail address: [email protected] (G. Wang).

https://doi.org/10.1016/j.ssc.2019.04.016 Received 12 November 2018; Accepted 30 April 2019 Available online 02 May 2019 0038-1098/ © 2019 Elsevier Ltd. All rights reserved.

Solid State Communications 297 (2019) 6–10

X. Fan, et al.

3. Results and Discussion

The superconducting phase diagram for AxNbSe2 (A = Rb, Li, Cu, Fe, and Ga) is constructed combining our results and those reported in the literature [24,27,28,30]. Larger ionic radius, higher valence, and magnetic moment bring the faster suppression of superconductivity in A-intercalated NbSe2.

3.1. Crystal structure for RbxNbSe2 Fig. 1(b) shows the PXRD patterns of RbxNbSe2 with x ranging from 0 to 0.05, which indicate that there is only one pure phase (2H) formed with a continuous variable Rb content for 0 ≤ x ≤ 0.025. Up to x = 0.05, a side phase comes out. As shown by the enlarged (008) diffraction peak (the right part of Fig. 1(b)), the peak position gradually shifts to lower angle with Rb doping, which means that the lattice parameter c enlarges and Rb comes into NbSe2. In fact, for RbxNbSe2 (0 ≤ x ≤ 0.025), both lattice parameters a and c increase with increasing Rb contents, as shown in Fig. 1(c). The lattice parameter a increases from 3.44513(3) Å (x = 0) to 3.44719(9) Å (x = 0.025), and c increases from 12.5498(2) Å (x = 0) to 12.5864(5) Å (x = 0.025). The Rb atoms are speculated to distribute randomly between NbSe2 slabs for the low Rb contents, as shown in Fig. 1(a), the slabs being not separated due to such a slight increase in c.

2. Methods A series of polycrystalline RbxNbSe2 (0 ≤ x ≤ 0.05) samples were synthesized by solid-state reaction. The Nb powder (Alfa Aesar, 99.99%) and Se shot (Alfa Aesar, 99.999%) in the stoichiometric ratio were reacted at 973 K for 5 h in Al2O3 crucibles sealed in evacuated quartz tubes to synthesize NbSe2. The Rb metal piece (Alfa Aesar, 99.75%) and as-prepared NbSe2 powder in a ratio of Rb: NbSe2 = x: 1 (x = 0, 0.001, 0.002, 0.003, 0.005, 0.015, 0.025, and 0.05) were reacted at 923 K for 60 h in Al2O3 crucibles sealed in evacuated quartz tubes. After that, the as-prepared RbxNbSe2 powders were well ground, pelletized, and sintered at 1023 K for 48 h. Powder X-ray diffraction (PXRD) patterns were measured using a Panalytical X'pert PRO diffractometer (Cu Kα radiation) with a graphite monochromator in the 2θ range from 10° to 70°. Indexing was performed using Dicvol06 [31]. Dc magnetizations were measured in a Quantum Design (QD) physical properties measurement system (PPMS) using finely grounded powders. Resistivity measurements were carried out on a QD PPMS using the standard four-probe configuration. The sintered samples for resistivity measurements were cut into bars, and four platinum wires were attached to the bar by silver paste. All the Rb content is nominal in the Results and Discussion section.

3.2. Superconductivity for RbxNbSe2 Fig. 2(a) shows the temperature dependence of dc magnetic susceptibility of RbxNbSe2 (0 ≤ x ≤ 0.025) from 3 K to 10 K under an applied magnetic field of 40 Oe in the zero-field-cooling (ZFC) protocol. With Rb intercalation, the superconductivity of NbSe2 is suppressed with Tc decreasing from 7.2 K for x = 0 to 4.2 K for x = 0.025. Meanwhile, the superconducting volume fraction (SVF) decreases from −1.1 for x = 0 to −0.01 for x = 0.025 at 3 K. The dependence of Tc on x for RbxNbSe2 determined from the magnetic susceptibility is summarized in Fig. 2(b). Tc quickly drops about 2 K with an increase in Rb content from 0 to 0.005 and then slower drops about 1 K with the increasing Rb content from 0.005 to 0.025. The x-dependent Tc shows an L-like shape in RbxNbSe2, which differs from the S-like shape in CuxNbSe2 [24] and

Fig. 1. The crystal structure for RbxNbSe2 with 0 ≤ x ≤ 0.025. (a) Schematic crystal structures for 2H-NbSe2 and RbxNbSe2 (0 < x ≤ 0.025). (b) The PXRD patterns for RbxNbSe2 (0 ≤ x ≤ 0.05). (c) The Rb-content-dependent lattice parameters for RbxNbSe2 (0 ≤ x ≤ 0.025). The dashed lines are given as guides to eyes. 7

Solid State Communications 297 (2019) 6–10

X. Fan, et al.

Fig. 2. The superconductivity for RbxNbSe2 with 0 ≤ x ≤ 0.025. (a) The magnetic susceptibility of RbxNbSe2 (0 ≤ x ≤ 0.025) at temperatures from 3 K to 10 K under an applied magnetic field of 40 Oe in the ZFC protocol. (b) The superconducting phase diagram for RbxNbSe2 (0 ≤ x ≤ 0.025). The solid curve is given as a guide to eyes.

bulk superconductivity in Rb0.002NbSe2. Fig. 3(b) shows the magnetic field dependence of magnetization for Rb0.002NbSe2 at 3 K and 10 K, respectively. A typical magnetic hysteresis curve at 3 K indicates that Rb0.002NbSe2 is a type-II superconductor, similar to NbSe2 [32]. The temperature dependence of ρ(T) at various magnetic fields for Rb0.002NbSe2 is shown in Fig. 3(c). A sharp drop emerges at 6.6 K (Tconset) and ΔTc = 0.9 K at zero field. With increasing field, Tconset gradually shifts to lower temperature and the transition width becomes

the monotonic decline in LixNbSe2 [27], FexNbSe2 [28], and GaxNbSe2 [30]. Fig. 3(a) shows the temperature dependence of dc magnetic susceptibility of Rb0.002NbSe2 under an applied magnetic field of 40 Oe in the ZFC and field-cooling (FC) protocols. The superconducting shielding emerges at about 5.6 K with a rather sharp drop, suggesting the Tconset reaches a value up to 5.6 K. Meanwhile, the SVF was estimated to be about 55% at 3 K from the ZFC magnetic susceptibility, indicating the

Fig. 3. (a) The temperature dependence of magnetic susceptibility 4πχ(T) for Rb0.002NbSe2 at low-temperature region with an applied magnetic field H = 40 Oe. (b) The magnetic field dependence of magnetization for Rb0.002NbSe2 at 3 K and 10 K, respectively. (c) The temperature dependence of ρ(T) at low-temperature region under various magnetic field for Rb0.002NbSe2. (d) The temperature dependence of resistive upper critical field μ0Hc2(T) corresponding to two criteria for Rb0.002NbSe2. (e) The magnetic field dependence of magnetization for Rb0.002NbSe2 at different temperatures. (f) The temperature dependence of resistive lower critical field μ0Hc1(T) for Rb0.002NbSe2.

8

Solid State Communications 297 (2019) 6–10

X. Fan, et al.

broader. The Tconset observed in resistance is almost 1 K higher than that in magnetic susceptibility, consistent with the result in CuxNbSe2 [24]. The upper critical field μ0Hc2(T) is determined from 50% and 10% ρn (the normal ρ upon Tconset) in Fig. 3(d). Clear linear dependence of μ0Hc2 on T is seen near Tcmiddle and Tczero, and the slopes of μ0Hc2(T) near Tcmiddle and Tczero are −1.22(2) and −1.13(2) T/K, respectively. Using the Werthamer-Helfand-Hohenberg (WHH) equation [32], μ0Hc2(0) = −0.693Tc(dHc2/dT)|Tc, the estimated μ0Hc2(0) is 5.58(9) and 5.19(9) T, when choosing the 50% and 10% ρn criteria, respectively, which are smaller than 9.96 T for NbSe2 [24]. According to the equation μ0Hc2 = Φ0/(2πξGL2), where Φ0 is the quantum of flux and μ0Hc2(0) being 5.58(9) T, the superconducting coherence length ξGL(0) can be estimated to be 7.7 nm for Rb0.002NbSe2, which is also smaller than 10.1 nm for NbSe2 [24]. Fig. 3(e) shows the magnetic field dependence of magnetization at various temperatures for Rb0.002NbSe2. Fig. 3(f) shows the lower critical field μ0Hc1 as a function of temperature. The μ0Hc1(T) is obtained using the demagnetization correction [24]. By fitting the μ0Hc1(T) data to the equation μ0Hc1(T) = μ0Hc1(0)[1 – (T/Tc)2], the estimated μ0Hc1(0) is 0.0073 T, which is smaller than 0.0158 T for NbSe2 [24]. From the relation μ0Hc1(0) = (Φ0/4πλGL2)ln (λGL/ξGL), the magnetic penetration depth (λGL) obtained increases from 191 nm for NbSe2 [24] to 285.3 nm for Rb0.002NbSe2, which reduces the SVF. The Ginzburg-Landau parameter kGL = λGL/ξGL ≈ 37, which further confirms the type-II superconductivity in RbxNbSe2. Meanwhile the thermodynamic critical field μ0Hc = (μ0Hc1*μ0Hc2/ lnk)1/2 decreases from 209 mT for NbSe2 [24] to 106.3 mT for Rb0.002NbSe2. 3.3. Phase diagram for AxNbSe2 (A = Rb, Li, Cu, Fe, and Ga) Combining the results presented above and those reported in the literature [24,27,28,30], the A-content dependence of lattice parameter c of AxNbSe2 (A = Rb, Li, Cu, Fe, and Ga) is summarized and shown in Fig. 4(a). By the Rb intercalation, the lattice parameter c of RbxNbSe2 increases more slowly than those of AxNbSe2 (A = Li, Cu, and Ga), especially compared with that of LixNbSe2. The Coulomb interaction between the intercalated cation and the charged NbSe2 layers is closely correlated to the lattice parameter c [33,34]. Relatively small lattice parameter c of RbxNbSe2 means a stronger Coulomb interaction between the interacted Rb+ and the negatively charged NbSe2 layers. As shown in Fig. 4(b), the superconducting phase diagram of AxNbSe2 synthesized by solid-state reaction is established. By the Rb intercalation, the superconductivity of NbSe2 is quickly suppressed, with Tc decreasing from 7.2 K for x = 0 to 4.2 K for x = 0.025. The L-like shape differs from the S-like shape in CuxNbSe2 and the monotonic decline in LixNbSe2, FexNbSe2, and GaxNbSe2. The suppression of Tc for Rb-intercalated NbSe2 is more rapid than those of Cu-, Ga-, and Li-intercalated and is similar to Fe-intercalated. The spin flip, an electron scatters off a magnetic impurity violates the time-reversal symmetry, makes that Fe works as the effective pair breaker [28,35,36], which results in the quick suppression of superconductivity in NbSe2. Nonmagnetic Rb works similar to the magnetic Fe. As is known, larger cation radius can make electron doping more effectively due to the more loosely bonding of the electrons in the outermost shell. The relationship among the ion radii is r(Rb+) > r(Li+) > r(Cu2+) > r (Ga3+). Electron transfer from the valence s orbital of Rb to the d orbital of Nb is more effective [37], which induces the stronger Coulomb interaction and the smaller lattice parameter c, consistent with a slower increase of lattice parameter c for RbxNbSe2. We speculate that this is the main reason for the observation of more rapid suppression of superconductivity in RbxNbSe2 than in CuxNbSe2, GaxNbSe2, and LixNbSe2. As for more rapid suppression of the superconductivity in CuxNbSe2 and GaxNbSe2 than that in LixNbSe2, higher-valence Cu2+ and Ga3+ are more effective in carrier doping than monovalent Li+. Larger ionic radius, higher valence, and magnetic moment bring a faster suppression of superconductivity in NbSe2. It has been demonstrated

Fig. 4. (a) The A-content-dependent lattice parameter c of AxNbSe2 (A = Rb, Li [27], Cu [24], Fe [28], and Ga [30]). (b) The superconducting phase diagram for AxNbSe2 (A = Rb, Li [27], Cu [24], Fe [28], and Ga [30]). Here all x is nominal. The solid lines are given as guides to eyes.

that superconductivity can be strengthened/weakened through hole/ electron doping by reversible modulation of the carrier density in bilayer NbSe2 using ionic gating [38]. So the alkali, 3d transition, or main group (post-transition) metal intercalations will always suppress the Tc of NbSe2 with electron doping. The speed and shape of the suppression of superconductivity are different for varying intercalation, which sheds light on the understanding of the superconductivity mechanism of TMDs. The bulk superconductivity with Tc higher than 7.2 K in NbSe2 may be realized if hole doping could succeed. 4. Conclusion The crystal structure and superconductivity of Rb-intercalated NbSe2 synthesized by solid-state reaction were carefully investigated. We found that there is only one pure phase with space group P63/mmc for Rb intercalation with 0 ≤ x ≤ 0.025. With increasing Rb content, the superconductivity of NbSe2 is suppressed with Tc decreasing from 7.2 K for x = 0 to 4.2 K for x = 0.025 in an L-like shape. The suppression of superconductivity for Rb-intercalated NbSe2 is more rapid than Cu-, Ga-, and Li-intercalated and is similar to the case in Fe-intercalated. Bulk Tc higher than 7.2 K may be realized in NbSe2 system if hole doping could succeed. Acknowledgements This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 51832010, 51572291, and 9

Solid State Communications 297 (2019) 6–10

X. Fan, et al.

51532010), the National Key Research and Development Program of China (Grant No. 2017YFA0302902), the Key Research Program of Frontier Sciences, Chinese Academy of Sciences (Grant No. QYZDJSSW-SLH013), and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB07000000).

G.W. Zheng, K.P. Loh, ACS Energy Lett 2 (2017) 1835–1840. [16] A.H. Castro Neto, Phys. Rev. Lett. 86 (2001) 4382–4385. [17] Z. Muhammad, K. Mu, H. Lv, C. Wu, Z. ur Rehman, M. Habib, Z. Sun, X. Wu, L. Song, Nano Res 11 (2018) 4914–4922. [18] M.H. Zhou, X.C. Li, C. Dong, Supercond. Sci. Technol. 31 (2018) 065001. [19] E. Morosan, H.W. Zandbergen, B.S. Dennis, J.W.G. Bos, Y. Onose, T. Klimczuk, A.P. Ramirez, N.P. Ong, R.J. Cava, Nat. Phys. 2 (2006) 544–550. [20] R.B. Somoano, V. Hadek, A. Rembaum, J. Chem. Phys. 58 (1973) 697–701. [21] R.B. Somoano, V. Hadek, A. Rembaum, S. Samson, J.A. Woollam, J. Chem. Phys. 62 (1975) 1068–1073. [22] F.J. Di Salvo, G.W. Hull, L.H. Schwartz, J.M. Voorhoeve, J.V. Waszczak, J. Chem. Phys. 59 (1973) 1922–1929. [23] R.A. Klemm, Physica C 514 (2015) 86–94. [24] H. Luo, J. Strychalska-Nowak, J. Li, J. Tao, T. Klimczuk, R.J. Cava, Chem. Mater. 29 (2017) 3704–3712. [25] X. Zhu, Y. Cao, J. Zhang, E.W. Plummer, J. Guo, Proc. Natl. Acad. Sci. U.S.A. 112 (2015) 2367–2371. [26] C.S. Lian, C. Si, W. Duan, Nano Lett. 18 (2018) 2924–2929. [27] C.S. Mcewen, D.J.S. Julien, P.P. Edwards, M.J. Sienko, Inorg. Chem. 24 (1983) 1656–1660. [28] J.J. Hauser, M. Robbins, F.J. DiSalvo, Phys. Rev. B 8 (1973) 1038–1042. [29] S.F. Meyer, R.E. Howard, G.R. Stewart, J.V. Acrivos, T.H. Geballe, J. Chem. Phys. 62 (1975) 4411–4419. [30] I. Naik, A.K. Rastogi, Physica B 405 (2010) 955–957. [31] A. Boultif, D. Louër, J. Appl. Crystallogr. 37 (2004) 724–731. [32] N.R. Werthamer, E. Helfand, P.C. Hohenberg, Phys. Rev. 147 (1966) 295–302. [33] C.-S. Lian, C. Si, J. Wu, W. Duan, Phys. Rev. B 96 (2017) 235426. [34] Y. Liu, G. Wang, T. Ying, X. Lai, S. Jin, N. Liu, J. Hu, X. Chen, Adv. Sci. 3 (2016) 1600098. [35] S. Parham, T.J. Reber, Y. Cao, J.A. Waugh, Z. Xu, J. Schneeloch, R.D. Zhong, G. Gu, G. Arnold, D.S. Dessau, Phys. Rev. B 87 (2013) 104501. [36] H. Kim, F. Gay, A. Del Maestro, B. Sacépé, A. Rogachev, Nat. Phys. 14 (2018) 912–917. [37] M. Chhowalla, H.S. Shin, G. Eda, L.J. Li, K.P. Loh, H. Zhang, Nat. Chem. 5 (2013) 263–275. [38] X. Xi, H. Berger, L. Forro, J. Shan, K.F. Mak, Phys. Rev. Lett. 117 (2016) 106801.

References [1] Q.H. Wang, K. Kalantar-Zadeh, A. Kis, J.N. Coleman, M.S. Strano, Nat. Nanotechnol. 7 (2012) 699–712. [2] J.A. Wilson, A.D. Yoffe, Adv. Phys. 18 (1969) 193–335. [3] C.J. Arguello, S.P. Chockalingam, E.P. Rosenthal, L. Zhao, C. Gutiérrez, J.H. Kang, W.C. Chung, R.M. Fernandes, S. Jia, A.J. Millis, R.J. Cava, A.N. Pasupathy, Phys. Rev. B 89 (2014) 235115. [4] A. Soumyanarayanan, M.M. Yee, Y. He, J. van Wezel, D.J. Rahn, K. Rossnagel, E.W. Hudson, M.R. Norman, J.E. Hoffman, Proc. Natl. Acad. Sci. U.S.A. 110 (2013) 1623–1627. [5] C. Wan, X. Gu, F. Dang, T. Itoh, Y. Wang, H. Sasaki, M. Kondo, K. Koga, K. Yabuki, G.J. Snyder, R. Yang, K. Koumoto, Nat. Mater. 14 (2015) 622–627. [6] M.N. Ali, J. Xiong, S. Flynn, J. Tao, Q.D. Gibson, L.M. Schoop, T. Liang, N. Haldolaarachchige, M. Hirschberger, N.P. Ong, R.J. Cava, Nature 514 (2014) 205–208. [7] J.T. Ye, Y.J. Zhang, R. Akashi, M.S. Bahramy, R. Arita, Y. Iwasa, Science 338 (2012) 1193. [8] H. Chen, Z. Li, X. Fan, L. Guo, X. Chen, Solid State Commun. 275 (2018) 16–20. [9] H. Chen, Z. Li, L. Guo, X. Chen, Europhys. Lett. 117 (2017) 27009. [10] B. Sipos, A.F. Kusmartseva, A. Akrap, H. Berger, L. Forro, E. Tutis, Nat. Mater. 7 (2008) 960–965. [11] B.T. Matthias, T.H. Geballe, V.B. Compton, Rev. Mod. Phys. 35 (1963) 1–22. [12] J.A. Wilson, F.J. Di Salvo, S. Mahajan, Adv. Phys. 24 (1975) 117–201. [13] R. Zhang, I.L. Tsai, J. Chapman, E. Khestanova, J. Waters, I.V. Grigorieva, Nano Lett. 16 (2016) 629–636. [14] Y. Liao, K.-S. Park, P. Xiao, G. Henkelman, W. Li, J.B. Goodenough, Chem. Mater. 25 (2013) 1699–1705. [15] B. Tian, W. Tang, K. Leng, Z. Chen, S.J.R. Tan, C. Peng, G.-H. Ning, W. Fu, C. Su,

10