Superconductivity in topologically nontrivial material Au2Pb(2)

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Figure 1.Sample characterisation.(a )X-ray diffraction patterns at room temperature for the Au 2Pb samples.The major diffraction peaks can be indexed with a cubic Laves phase of Au 2Pb.A few tiny diffraction peaks are from the impurity phases of a small amount of Pb residue.Inset:the X-ray diffraction pattern from the basal plane crystal surface of Au 2Pb only shows (111)n re ?ections,which indicates the measured crystal plane of the crystal is (111)plane.(b )High-resolution transmission electron microscopy image of Au 2Pb crystal.(c )Selected area electron diffraction image looking down from the [112]zone axis showing the reciprocal lattice of Au 2Pb.

Superconductivity in topologically nontrivial material Au 2Pb

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npj Quantum Materials (2016)16005

Published in partnership with Nanjing University

model to be applicable over entire ?eld range.It is noticed that

this longitudinal linear MR (H //I )due to its balanced hole and

electron populations,was ever observed in type II Weyl semimetal

candidate WTe 2.22,29The linearity here may originate from the

multiband nature of Au 2Pb.

T c

onset and H c2enhancements in PC measurement with a W tip PC Andreev re ?ection spectroscopy is a powerful tool to probe

the order parameters of superconductor.30The temperature

dependence of zero-bias differential resistance of PC between a

gold tip and Au 2Pb single crystal is shown in Figure 3a.The presence of a signi ?cant resistance drop at the onset temperature T c onset =1.13K at zero magnetic ?eld and the absence of this drop at 0.03T applied perpendicular to the (111)surface indicate a superconducting transition,which is similar to that in the bulk measured by standard four-electrode method (see Figure 2).However,when measured with a W tip as shown in Figure 3b,the onset temperature increases to 2.1K,higher than the bulk value.And the perpendicular ?eld (H ?)used to fully suppress the superconductivity transition is 0.755T,also much higher than the bulk value.The PC spectra (PCS)at different temperatures with

a Figure 2.Transport measurements of Au 2Pb.(a )ρ(T )curves of Au 2P

b single crystal.Inset:close-up of the same data from 30to 60K.(b )Temperature dependence of χ,shows the Meissner effect:sharp diamagneti

c drops at 1.15K.The inset presents low-?el

d M (H )curves at various temperatures from 0.5to 1.1K.(c )ρ(T )characteristics at various H ⊥up to 0.05T.Th

e ρ(T )obtained in zero ?eld shows T c onset =1.3K,T c zero =1.18K.(d )Magnetoresistance o

f Au 2Pb crystal at various temperatures under H ⊥.Inset:normalised upper critical ?eld h *=H c2/T c (d H c2/d T |T =T c )as a function of normalised temperature t =T /T c ,with the red dashed line indicatin

g the expectation for a polar p -wave state.19The black dashed line indicates the WHH theory for s-wave superconductor.18(e )MR at temperatures 1,5,10,20,30,50,80,100,120,150and 200K measured in H ⊥.(f )Parallel magnetic ?eld H //-dependent resistivity at T =2.5K wit

h H //varying from the 0°to 90°.Inset:MR(H )curves at 2.5K for H //I plotted on a logarithmic scale.The linear ?tting gives the slope ～1.09±0.02.

Superconductivity in topologically nontrivial material Au 2Pb

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Published in partnership with Nanjing University npj Quantum Materials (2016)16005

gold tip and a W tip are shown in Figure 3c,d,respectively.For the PC with a gold tip,DCPs are observed at 0.5K and gradually get smeared with increasing temperature.The resulted broad conductance peak totally diminishes at 1.1K,consistent with the transition temperature in d V /d I (T )as shown in Figure 3a.For the PC with a W tip,similar DCPs feature is clearly shown at lower temperatures,and the broad conductance enhancement totally diminishes at T =2.1K,consistent with T c

onset in Figure 3b.We note that besides the DCPs feature,there are also conductance dips outside the conductance enhancement regime as shown in Figure 3d for temperatures 41K,which evolve to broad valleys o 1K (around bulk T c shown in Figure 2b).These conductance dips might be related to the critical current effect.31Alternatively,conductance dips at around the gap energy with a broad ZBCP could be a result of the helical p -wave order parameter.32Another unusual feature of the PCS is a small splitting of the conductance peaks at 0.3K,which can be ?tted by the modi ?ed Blonder –Tinkham –Klapwijk (BTK)model 33,34for two gaps,while

the double conductance dips and broad conductance valleys cannot be ?tted by conventional s-wave pairing symmetry considerations (Supplementary Figure S5).

The magnetic ?eld dependence of PCS at 0.5K is shown in Figure 3e,f for PC with a gold tip and a W tip,respectively.All the PCS show gradual suppression of the superconducting features with increasing magnetic ?eld.The H c2for PC with a gold tip is about 0.02T at 0.5K,which is close to the bulk value (~0.05T)obtained by standard four-electrode measurements,while the H c2value of PC with a W tip is about 0.60T,which is 410times larger than the bulk value.

Analysis of PC results

For PC with a W tip (harder than gold tip),both T c

onset and H c2are larger than bulk values (Supplementary Figure S6).The T c enhancement seems related to the pressure applied by the hard W tips,which may cause changes of the band structure

or

Figure 3.PC results with the gold tip and the W tip.(a ,b )The zero-bias PC resistance as a function of temperature for the gold tip and the W tip,respectively;(c ,d )the PCS at different T ;(e and f )the PCS under different H ⊥at 0.5K;curves shifted in c –f for clarity.

Superconductivity in topologically nontrivial material Au 2Pb

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npj Quantum Materials (2016)16005

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