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18 of 5-mmol AgNO3 and 1-mmol Pb(NO3)2 . All the mea- (a) Ag5Pb2O6, HDC = 0 Oe 4 3 surements reported here were performed with a He- He 5 dilution refrigerator (Cryoconcept, Model DR-JT-S-100- 4 10), covering the measurement temperatures as low as 3 16 mK. The resistivity was measured using a conven- 2 1 tional four-probe method with an AC current of 10.4 µA 0 rms at 163 Hz with a hexagonal-stick single crystal which units) (arb. -1 3 AC

fits in 0.14 0.21 1.15 mm . We used pure gallium to ' -2 attach electrical× wires× of copper to the sample crystals. χ -3 We note here that one must keep the temperature of the 20 30 40 50 60 electrodes well below the melting point of gallium (29◦C) T (mK) all the time after soldering in order to avoid the electrical contacts getting worse. We avoided using gold wires (b) Ag5Pb2O6 HDC // c because gallium easily dissolves gold. The AC susceptibility was measured by a mutual inductance method. We 53 mK fabricated a very small and highly-sensitive cell by wind- ing a 50-µm-diameter copper wire on a 0.5-mm-diameter 50 mK polyimide tube (The Furukawa Electric Co., Ltd., PIT- S). The excitation field HAC was 8.7 mOe rms at 887 Hz, which is much lower than the Hc of Ag5Pb2O6. To re- 47 mK duce the influences of remnant magnetic fields such as the earth’s field and the residual field in the equipment, these measurements were performed in a magnetic shield. units) (arb. 45 mK AC We used a cylinder of permalloy (Hamamatsu Photonics ' χ K.K., E989-28), which has an extremely high permeabil- 30 mK ity. Inside the permalloy tube, we also placed a lead cylinder with a closed bottom, to expel the remaining magnetic flux. The DC magnetic field for the measure- 16 mK ments was applied with a small solenoidal coil of Nb-Ti superconducting wire placed inside the shield. The mag- -2 -1 0 1 2 nitude of the DC field H is numerically calculated by DC HDC (Oe) taking into account the shielding current on lead shield’s surface19,20. FIG. 2: (color online) AC susceptibility of Ag5Pb2O6. (a) Re- The observed zero-resistivity transition is shown in sult of a temperature sweep with a sweep rate of 0.2 mK/min. Fig. 1. A clear zero resistivity is seen, which marks defini- The residual field Hres has been compensated in this sweep, tive evidence of superconductivity of Ag5Pb2O6. We yielding Tc0 = 52.4 mK. (b) Results of field sweeps at several note here that the result in Fig. 1 was obtained without temperatures with a sweep rate of 24-47 mOe/min. From the the magnetic shield. A hysteresis at the superconducting slight asymmetry of the data, the residual field is estimated as Hres = 0.040 Oe. transition and a lower Tc than that in the AC susceptibility measurement are attributable to the influence of the uncanceled residual field. We confirmed that the hysteresis indeed disappears in the measurement with the mag- ing transition under magnetic fields while no supercooling netic shield. We next show in Fig. 2 the real part of the ′ is seen in zero field. This means that the superconduct- AC susceptibility χAC of a mono-crystal with the mag- ing transition becomes first order only when an external netic shield described below. It is worth noting that we field is applied. Such behavior is only seen in type-I su- used the identical crystal for the measurements for Figs. 1 perconductors. The other is the very large positive peaks and 2 (see the left inset of Fig. 1). We also note here that ′ of χAC just before the superconducting to normal tran- the diamagnetic signal shown in Fig. 2 is as large as that sitions. These peaks are ascribable to the “differential of pure Al with a similar size and shape. Such results of paramagnetic effect” (DPE)21, which represents that the the low-frequency susceptibility add a strong support for field derivative of the magnetization ∂M/∂H is positive the bulk nature of the superconductivity in Ag5Pb2O6. near the transition and also the magnetic process in this The measurements were performed under the condition region is reversible. In a type-I superconductor with a fi- HDC HAC c. The critical temperature Tc to some k k nite size, the intermediate state takes place and the DPE extent depends on samples; the highest Tc obtained is should be observed. On the other hand, type-II supercon- 52.4 mK, as shown in Fig. 2. ductors should show no or rather small DPE because of In Fig. 2, there are two strong pieces of evidence that the irreversibity of magnetic process due to flux pinning. Ag5Pb2O6 is a type-I superconductor. One is the fact Thus the large DPE is a hallmark of type-I superconduc- that a large supercooling is observed at the superconduct- tivity. 3

Ag5Pb2O6, H // c The Ginzburg-Landau (GL) coherence length, ξ0 = 2.5 ~ ~ ∗ → (0.18 vF)/(kBTc) = 11 µm, where vF = kF/m is Hc (S N) the Fermi velocity, is comparable to that of tungsten24 Hsc (N → S) 2 (ξ0 = 32 µm,Tc = 15.4 mK). The mean free path l is given by l = vFτ, where τ is the scattering time of electrons and has a relation τ −1 = ne2ρ/m∗ for the Drude 1.5 model. If we use ρ = 1.5 µΩ cm, the residual resistivity (Oe) Normal State 18

c in the ab plane , we obtain l = 240 nm.

H 1 One of the important consequences of the above evaluation is that Ag5Pb2O6 is a dirty-limit (ξ0 l) su- 0.5 Superconducting perconductor. This is rather inevitable, since≫ it seems State practically impossible to make l longer than ξ0. Ina 0 dirty-limit superconductor, the GL parameter κ is given 0 10 20 30 40 50 60 by κ =0.75λL(0)/l (Ref. 27), and is 0.26 in our case. This T (mK) is indeed smaller than 1/√2, the border between type-I and -II superconductors, and is consistent with the type- FIG. 3: Phase diagram of the superconducting phase of I behavior of Ag5Pb2O6. The dirty-limit conclusion also Ag5Pb2O6, determined from the field-sweep data of ac sus- implies that the pairing symmetry of the superconductiv- ceptibility. The residual field has been subtracted in the ity is not anisotropic, because anisotropic superconduc- shield Hres = 0.040 Oe from the raw data. The filled squares tivity should be easily suppressed even by non-magnetic are superconducting to normal transition field and should impurities. be equal to Hc (see text). The crosses are the supercool- According to the GL theory, analysis of supercooling ing field Hsc corresponding to the normal to superconduct- gives the upper limit of κ. When one decreases the ex- ing transitions. The broken line is the result of fitting with α ternal field of a supercooled superconductor at constant Hc(T )= Hc0[1 (T/Tc0) ]. − temperature, the sample turns into the superconducting state before the field reaches the ideal supercooling field Hsc,ideal. If the sample is in vacuum, Hsc,ideal is equal to 25 Figure 3 is the phase diagram based on the AC sus- the surface nucleation field Hc3 , which has a relation ceptibility of the crystal with the highest Tc. Here we Hc3 = 1.695Hc2 = 1.695√2κHc. The observed super- identify the transition fields of the superconducting to cooling field Hsc satisfies an inequality: normal transition as critical fields Hc. This should be valid despite the possibility of superheating, because the Hsc Hsc ideal =1.695√2κHc. (1) ≥ , observed DPE shows that Ag5Pb2O6 is in the intermediate state, in which superconducting and normal states Thus κ must be smaller than κsc Hsc/(1.695√2Hc). coexist, and there should be no superheating at the An approach based on this has been≡ used to determine “transition” from the intermediate state to the normal κ of several pure metals and alloys by observing ideal state. We also define the normal to superconducting supercooling. For example, Feder and McLachlan26 real- transition fields as supercooling fields Hsc. This tran- ized ideal supercooling of indium and tin with precise ex- sition should be from the normal to the full Meissner periments and obtained κIn =0.0620 and κSn =0.0926. states since we observed no DPE. We can fit a relation We calculated κsc of Ag5Pb2O6 at each tempera- α Hc(T ) = Hc0[1 (T/Tc0) ] to all the Hc data down − ture as shown in Fig. 4. The steep increase of κsc to 16 mK using Hc0 and α as fitting parameters, while close to Tc is attributed to the size effect, which oc- Tc0 = 52.4 mK is determined from the temperature sweep curs when the temperature-dependent coherence length 1/2 data in zero field. As a result, we obtained Hc0 =2.19 Oe ξ(T ) [Tc/(Tc T )] ξ becomes comparable to the and α = 1.56. The data can also be fitted by a conven- size of∝ a sample.− In fact, the coherence length, being ∗ 2 tional relation with α = 2: Hc(T ) = H [1 (T/Tc0) ]. 1/2 27 c0 − ξ (ξ0l) in a dirty-limit superconductor , becomes However, the fitting is successful only down to T/Tc =0.7 ∼ ∗ 1.4 µm. This is large enough to cause the size effect near and the resulting parameter is Hc0 =1.80 Oe. Tc in a sample of 100-200 µm ( 100ξ). Indeed, in the ∼ 26 Now we can evaluate some of the superconducting pa- experiments of Feder and McLachlan a sphere of clean rameters from these results. First, the London penetra- indium (ξ ξ0 =0.20 µm) with a radius 16 µm ( 80ξ) ∗ 2 2 1/2 ∼ ∼ tion depth is obtained as λL(0) = (m c /4πne ) = showed the size effect near Tc. 22 3 83 nm. Here n = 1.0/VM = 0.51 10 electrons/cm Feder and McLachlan determined κ by extrapolating × 3 is the electron carrier density, where VM =0.195 nm is κ(T ) to T = Tc, because the influence of nucleation 22 ∗ ~2 2 the volume of a unit cell , and m = (3 γe)/(kBkF)= centers becomes negligible near Tc due to divergence of 1.2me is the effective mass. We used here the ξ(T ). Following their procedure we extrapolated κsc(T ) 18 measured electronic specific heat coefficient γe = in 35 mK

T (mK) superconductivity is rare in compounds, although there is 0 10 20 30 40 50 no fundamental reason to prohibit it. The present discov- ) c ery indeed demonstrates that even an oxide can be an ex- H 0.4 Ag5Pb2O6 treme type-I superconductor. Superconducting parame- 2

√ ters indicate that Ag5Pb2O6 is a dirty-limit type-I super- 0.3 conductor and thus the pairing symmetry of Ag5Pb2O6 should be isotropic. The discovery of this novel class of 0.2 superconductor, silver oxide superconductor with a lay- / (1.695 ered structure, should motivate searches for more super- sc 0.1

H conductors among similar silver oxides. A salient next target is to adjust the doping to realize the electronic = 0

sc states with strong electron correlations, closely analogous κ 0 0.2 0.4 0.6 0.8 1 to that of the high-Tc cuprates, in order to seek for un- T / Tc conventional superconductivity.

FIG. 4: The ratio κsc Hsc/(1.695√2Hc) of Ag5Pb2O6, ≡ which gives the upper limit of the GL parameter. The up- Acknowledgments turn of the graph near Tc is attributable to the size effect. The broken line is the result of linear fitting between T = 35 and 47 mK, where the size effect is not significant. We would like to acknowledge K. Ishida, S. Nakatsuji, H. Yaguchi, K. Deguchi and K. Kitagawa for their support, K. Yamada, R. Ikeda and S. Fujimoto for helpful upper limit is smaller than the calculated value but the discussions, and Y. Sasaki for his advise on experimen- difference should be within a consistency. In the case of tal techniques. We also appreciate Furukawa Electric indium or tin26, there are also differences of a few factors Co., Ltd. for providing us with polyimide tubes. This among values of κ obtained by different procedures. work has been supported by a Grant-in-Aid for the 21st In conclusion, we succeeded in observing zero resistiv- Century COE “Center for Diversity and Universality in ity transition of a silver oxide Ag5Pb2O6, giving defini- Physics” from Ministry of Education, Culture, Sports, tive evidence of the long-awaited layered silver oxide Science and Technology (MEXT) of Japan. It has also superconductor since the discovery of high-Tc cuprates. been supported by Grants-in-Aids for Scientific Research The AC susceptibility reveals that Ag5Pb2O6 is an oxide from MEXT and from Japan Society for the Promotion type-I superconductor. It is widely considered that type-I of Science (JSPS).

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