Superconductivity in topologically nontrivial material Au2Pb(4)

Superconductivity in topologically nontrivial material Au 2Pb

Y Xing et al

6

npj Quantum Materials (2016)16005

Published in partnership with Nanjing University

unconventional superconducting properties in Au 2Pb crystals.Furthermore,the ?rst-principles calculations point to the nontrivial topology of the orbital texture near the dominant Fermi surfaces,which suggests the possibility of topological superconductivity.The results presented in this work indicate the Au 2Pb crystal could be a promising platform for the investigation of topological superconductivity.For full understanding of the superconductivity in Au 2Pb,further investigations like thermal transport and ARPES experiments are clearly necessary and interesting.

Note added

After the completion of this work,we notice a recent hydrostatic pressure study of bulk Au 2Pb,43where T c decreases with pressure.It is opposite to our observation.The major difference between two studies is that their pressure is hydrostatic but ours is nearly local uniaxial pressure on (111)crystal face.MATERIALS AND METHODS

Sample growth and characterisation

Starting materials of high-purity elemental Au and Pb were prepared to synthesise single-crystalline Au 2Pb,the initial ratio of Au/Pb was 40:60,the extra Pb were used as ?ux.The materials were sealed in evacuated quartz ampoules,heated to 600°C,held for 1day and then slowly cooled down to 300°C over a period of 30h.This was then followed by centrifugation to remove the ?ux.Before transport and diamagnetic measurements,the samples were etched in a hydrogen peroxide solution for several minutes to remove the residual Pb ?ux.16

The data of powder XRD and single crystal XRD were collected from a Rigaku MiniFlex 600diffractometer (Rigaku,Tokyo,Japan)and then re ?ned by a Rietica Rietveld programme (/index.html).Crystal purity,structure and lattice constant (a 1=a 2=a 3=7.9603Å)can be retrieved.It is worth to mention that high-quality single crystal of Au 2Pb samples are in trapezoid stipe shape.The current is added parallel to the bottom edges for transport measurements,which is in [110]direction for cubic Laves phase.

To obtain HRTEM images,the Au 2Pb single crystal was examined by a FEI Tecnai G2F20S-TWIN TEM (FEI,Hillsboro,OR,USA)operating at 200kV.

Resistivity and diamagnetic measurements

For the transport measurements,the contacts on the single crystals were made by applying the silver paint on the top surface (111)of Au 2Pb samples,with contact resistance o 1Ω.The resistance and magnetoresistance were measured in a commercial Physical Property Measurement System (Quantum Design,San Diego,CA,USA,PPMS-16,d.c.technique),with the Helium-3option for temperature down to 0.5K and dilution option down to 0.05K.The excitation current of 1mA was used for the measurements in low-temperature regime.Angular dependence of magnetoresistance was measured by rotating the sample ((111)surface plane)in a Rotator option based on PPMS,within the instrumental resolution of 0.1°.

For diamagnetic measurement,DC magnetisation was studied during the zero-?eld cooling and ?eld cooling at H =5Oe,in a Magnetic Property Measurement System (MPMS 7-XL SQUID)from Quantum Design Company,with a resolution of 10?8e.m.u.The magnetic ?eld is applied parallel to the (111)face.The χis estimated by DC magnetisation.

The PC measurements

Our PCS are obtained using a standard lock-in technique in quasi-four probe con ?guration.PC measurements are realized in the standard ‘needle –anvil ’con ?guration.Both W and gold tips are used to make PC on the (111)surface of Au 2Pb single crystals.The W tip is prepared by electrochemical etching method with a wire of 0.25mm diameter,and is hard enough to penetrate through the surface layer and to probe the superconductor underneath.The gold tip is mechanically sharpened from a 0.5mm wire and is relatively soft.

The ?rst-principles calculations

The ?rst-principles calculations were performed in the scheme of density-functional theory,as implemented by the VASP package.44The projector-augmented wave pseudopotentials 45were used with Perdew –Burke –Ernzerhof exchange-correlation functional.46The energy cutoff of the plane wave basis set was chosen to be 350eV.The Brillouin zone was sampled by a 13×19×9grid in the self-consistent calculation.During the relaxation procedure,we used a force threshold of 0.01eV Å?1.Spin-orbit coupling was included in the calculation of energy bands and Fermi surfaces,and not included in the calculation of orbital textures to avoid the twofold degeneracy of the bands to obtain a well-de ?ned phase difference.

ACKNOWLEDGEMENTS

This work was ?nancially supported by the National Basic Research Programme of China (Grant Nos.2013CB934600&2012CB921300&2012CB927400),the Research Fund for the Doctoral Programme of Higher Education (RFDP)of China,the Open Project Programme of the Pulsed High Magnetic Field Facility (Grant

No.

Figure 6.Energy difference of the lowest conduction band and the top valence band in the Brillouin zone slices of (a )k x =0.65π,(b )k y =0.65π,(c )k z =0.69π.The top panels show the positions of the corresponding slices within the 1/8Brillouin zone,[0,π]×[0,π]×[0,π].Note that the background of Supplementary Figure 8a is a small region in the 2o ’clock direction of c .There are prominent white curves in all these panels,on which the lowest conduction band and the top valence band are nearly degenerate;i.e.,these white curves indicate the existence of (quasi)nodal surfaces around the Fermi level.

Superconductivity in topologically nontrivial material Au 2Pb Y Xing et al

7

Published in partnership with Nanjing University

npj Quantum Materials (2016)16005

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