www.sciencemag.org/cgi/content/full/science.aaf8227/DC1

Supplementary Materials for Evidence for bulk superconductivity in pure bismuth single crystals at

ambient pressure Om Prakash, Anil Kumar, A. Thamizhavel, S. Ramakrishnan*

*Corresponding author. Email: ramky@tifr.res.in

Published 1 December 2016 on Science First Release

DOI: 10.1126/science.aaf8227

This PDF file includes:

Materials and Methods Figs. S1 to S7 Table S1 and S2 References

2

Materials and Methods

1. Crystal growth and characterization

Under ambient condition, Bi is commonly designated as a rhombohedral lattice

(space group R-3m, so-called arsenic or A7 structure), which is characterized by a pair of

atoms spaced non-equidistantly along the trigonal axis in a Peierls distortion of the

simple cubic structure [47,48]. Alternatively, the structure of Bi can be described as a

hexagonal lattice with six atoms per unit cell, or as a pseudo-cubic structure with one

atom per unit cell [49]. The schematic diagram of the rhombohedral unit cell and

hexagonal crystal structure are shown in Fig S1A.

The Bi single crystals were grown using the Bridgman crystal growth technique. Bi

has a low melting point of 271.4C and Bridgman technique is suitable for growing Bi

single crystals. Highly pure Bi ingots (99.998%) packed in glass tubes with inert argon

were used for crystal growth. Here, we have used quartz tubes with pointed bottom to

grow the crystals. Prior to sealing, to avoid oxidation and contamination, the quartz tubes

were etched in dilute HF- solution followed by cleaning with distilled water and baked in

dynamical vacuum of 510-6 mbar, at 1000C for 24 hours. The Bi ingots then were

transferred from the original sealed tubes to the quartz tubes and the quartz tubes are

vacuum (110-6 mbar) sealed. Two such sealed quartz tubes with 2 gm of Bi in each,

were kept in a programmable box furnace. Initially, the temperature of the furnace was

raised to 600C in 10 h and kept at 600C for 12 h in order to ensure complete melting of

Bi. The tubes were then cooled to 350C with the rate of 1C /h, followed by cooling to

200C at 0.5C /h. Slow cooling in the temperature range of the crystallization helps in

the getting a large single grain crystal. Subsequently, the furnace was cooled down to

30C in next five hours.

Large crystals of 3-4 mm diameter and 2-3 cm length were obtained. The crystals

were stored in a dynamical vacuum of 110-3

mbar in desiccators to avoid any

contamination. To check the single crystalline nature of the crystals, small portions were

cut from both ends to get plane surfaces and exposed to Laue diffraction. The diffraction

images obtained from the plane surfaces at both ends of the crystals show patterns

corresponding to the [001] crystallographic direction, indicating the present of single

grain across the whole length of the crystals as shown in Fig S1B. The crystals were cut

to a rectangular bar of 20.20.2 cm3 using a spark erosion cutting machine. After the

cutting all the surfaces were carefully polished and cleaned using ultrasonics to get rid of

any surface contamination. The powder x-ray diffraction shows all the diffraction peaks

corresponding to the rhombohedral A7 structure [49] and no extra peaks were observed

as shown in Fig S1C. We used cleaved Bi crystals surfaces for characterization using

Energy Dispersive x-ray Spectroscopy (EDX). The EDX spectroscopy shows no trace of

any impurity elements and secondary phases. The Scanning Electron Microscopy (SEM)

images for both s1 and s2 samples are shown in Fig S2 and Fig S3 respectively along

with the EDX spectra for s1 crystal.

3

2. Hall coefficient and Specific heat measurements

The Hall coefficent at different temperatures is measured as shown in Fig S4A.

The value of the at 2K and 300K are in agreement with the existing literature. The heat

capacity measurements also agree with the previous measuremnts. The Hall coefficient,

specific heat, and all transport (including quantum osscilation) measurements were done

in the Physical Property Measurement System (PPMS, Qunatum Design Inc., USA)

equipped with dilution refridgerator.

3. Impurity trace analysis using ICP-AES

The Inductively Coupled Plasma - Atomic Emission Spectrometry (ICP- AES)

technique is used to estimate the impurity traces in the Bi crystals used for the

measurements. The spectroscopy results are shown in Table S1. Elements not listed in the

Table S1 are either absent or have less than 0.01ppm concentration in Bi crystal. Alkali,

Alkaline, 3d, 4d, 5d transition elements, rare earths, and p-block elements were

particularly searched and not found/less than 0.01ppm during the experiment. These

measurements were carried out at the Sophisticated Analytical Instrument Facility

(SAIF), Indian Institute of Technology Bombay (IITB http://www.rsic.iitb.ac.in/icp-

aes.html). These results confirm the high purity of our crystals and not contaminated

during crystal growth. The large Meissner effect observed in Bi crystals precludes the

possibility that the SC is coming from the impurities detected.

4. Resistivity measurements

The resistivity of the grown crystals at room temperature (300K) = 129 ± 0.2μ

Ω-cm is consistent with the reported values for pure Bi. The resistivity of all the samples

at 4.2 K is (4.2K) 0.3μΩ-cm giving a residual resistivity ratio of RRR ≥ 430 indicating high quality of the crystals. The low temperature resistivity of Bi is known to

have size dependence and resistivity in thinner crystals is often determined by the

scattering of charge carriers from the physical boundary of the samples rather than

electron - electron or electron-phonon scattering, due to large electronic mean free path

[29]. Due avoid size affects the resistivity measurements were performed on thicker

crystals to estimate correct RRR. The resistivity of one of the sample is shown in Fig. S5.

5. Quantum oscillation measurements

The quantum oscillation measurements at 2 K on the Bi crystal for the magnetic

field, H || Binary axis, are shown in Fig S6. Clear oscillations in the transverse

magnetoresistance data are seen as shown in Fig S6B. The minima in the

magnetoresistance are tagged with the values of the resonant magnetic fields. The

oscillations observed for the H ∥ binary axis are in good agreement with the reported experimental (Hiruma et.al.) [50] and theoretical results (Smith et.al.)[18] as shown in

Table S2. These results suggest that our single crystals are free from doping, in

agreement with the AES- chemical analysis.

Bi has three degenerate electron pockets in the absence of magnetic field. When a

magnetic field is applied parallel to the binary axis, this degeneracy is lifted resulting in

two equivalent degenerate light electron pockets and a single heavy electron pocket. In

this situation, for small magnetic field, Bi consists of 2:1 concentration of lighter to heavy

electrons. For magnetic fields H>1.5 T, all the light electrons are pushed to their quantum

4

limit (j=0) hence no quantum oscillations are seen due to lighter electrons for higher

magnetic fields [51]. The oscillations shown in the Fig S6B and listed in Table S2 are

only due to heavy electrons (eh’s) and hole pockets. In Table S2, eh represents the

magnetic field at which the oscillations of the heavy electron pocket occur and h

represents the magnetic field corresponding to the oscillations of the hole pocket.

6. Meissner fraction of Pb and Bi crystals

The magnetization measurement setup was calibrated for estimating the Meissner

fraction. Fig S7A shows the jump in the SQUID output voltage at the superconducting to

normal phase transition of Pb sample for an excitation magnetic field of 0.4T. The

change in the output voltage is proportional to the change in the susceptibility of the

sample. The setup consisted of cryoperm magnetic shield as described in Fig 1A and Fig

1B. The size of the Pb sample was same as the Bi crystals used in the measurements. All

the other parameters, such as the gain in the SQUID electronics and number of turns in

the pickup coil, directly wound on the samples, were same for both the samples. Fig S7B

shows the voltage jump at the superconducting to normal state transition for Bi crystal.

The size of the voltage jumps in Fig S7A and Fig S7B are nearly same, indicating large

Meissner fraction and bulk nature of superconductivity in Bi.

5

Fig. S1. Crystal structure and characterization of Bi single crystal: (A) The

schematic diagram of hexagonal crystal structure of Bismuth. The rhombohedral unit cell

(black) is shown within the crystal structure. Bismuth has two bilayers within the

hexagonal structure. (B) A Laue diffraction pattern of Bismuth crystal for [001]

crystallographic direction. The circular spots confirm the single crystalline nature of the

grown crystals. (C) X-ray diffraction of Bismuth crystals. All the peaks observed in the

recorded pattern can be indexed for the A7 structure and prominent peaks in the xrd

pattern are marked.

6

Fig. S2. Sample s1 characterization using EDX: SEM image of s1-Bi cleaved surface.

The EDX spectra were acquired on the front and back surface of the sample. No trace of

any elements other than Bismuth was found.

7

Fig S3: Sample s2 characterization using EDX: SEM image of s2-Bi cleaved surface.

8

Fig S4: Hall coefficient and specific heat: (A) Hall coefficient of Bi crystal from 2-300

K. (B) Specific heat of Bi from 0.1-275 K.

9

Fig. S5. Resistivity of Bi single crystal: (A) The resistivity of Bi crystal from 4.2 − 300 K. (B) Low temperature resistivity of Bi crystal with RRR = 430.

10

Fig. S6. Quantum oscillation measurements: (A) The magnetoresistance data at 2 K for

0 ≤ H ≤ 14 T. (B) The derivative of the magnetoresistance, dR/dH at 2 K shows clear quantum oscillations.

11

Fig. S7 SQUID output for Pb and Bi crystals: (A) SQUID output voltage across the

superconducting transition of Pb showing Tc=7.2K. (B) SQUID output voltage across the

superconducting transition of Bi showing Tc=0.53 mK. The jump in the output voltage is

comparable indicating large Meissner fraction in Bi crystal below Tc.

12

Table S1. Atomic % and ppm level of impurity elements in Bi

Element Atomic % ppm level

Al

Cu

Ni

Zn

Ag

0.00024

0.00024

0.00069

0.00012

0.00076

2.4

2.4

6.9

1.2

7.6

Bi 99.9980 ----

13

Table S2. Shubnikov-de Haas resonant magnetic field (in T) in Bi (H ∥ binary axis)

Landau level index Our experiment Hiruma et.al. (exp) Smith et.al. (theory)

eh(0+)

h(4±)

eh(1-)

eh(1+)

h(5±)

eh(2-)

eh(2+)

h(6±)

h(7±)

h(8±)

10.8

8.5

7.6

—

5.8

—

5.0

—

3.3

2.8

—

8.5

7.5

—

5.9

—

5.1

4.4

3.4

2.9

10.8

8.4

7.6

6.6

5.8

5.4

5.0

4.2

3.3

2.8

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aaf8227-Prakash-SM.ref-list.pdfReferences and Notes