Articleshttps://doi.org/10.1038/s41563-020-0721-9

Evidence of higher-order topology in multilayer WTe2 from Josephson coupling through anisotropic hinge statesYong-Bin Choi1,10, Yingming Xie   2,10, Chui-Zhen Chen2,9, Jinho Park1, Su-Beom Song3, Jiho Yoon4, B. J. Kim1,5, Takashi Taniguchi6, Kenji Watanabe   6, Jonghwan Kim1,3, Kin Chung Fong   7 ✉, Mazhar N. Ali   4 ✉, Kam Tuen Law   2 ✉ and Gil-Ho Lee   1,8 ✉

1Department of Physics, Pohang University of Science and Technology, Pohang, Republic of Korea. 2Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China. 3Department of Materials Science and Engineering, Pohang University of Science and Technology, Pohang, Republic of Korea. 4Max Plank Institute for Microstructure Physics, Halle (Saale), Germany. 5Center for Artificial Low Dimensional Electronic Systems, Institute for Basic Science (IBS), Pohang, Republic of Korea. 6Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, Ibaraki, Japan. 7Raytheon BBN Technologies, Quantum Information Processing Group, Cambridge, MA, USA. 8Asia Pacific Center for Theoretical Physics, Pohang, Republic of Korea. 9Present address: Institute for Advanced Study and School of Physical Science and Technology, Soochow University, Suzhou, China. 10These authors contributed equally: Yong-Bin Choi, Yingming Xie. ✉e-mail: kc.fong@raytheon.com; maz@berkeley.edu; phlaw@ust.hk; lghman@postech.ac.kr

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Supplementary Information for

Evidence of Higher Order Topology in Multilayer WTe2 from Josephson

Coupling through Anisotropic Hinge States

Yong-Bin Choi1, Yingming Xie2, Chui-Zhen Chen2,†, Jinho Park1, Su-Beom Song3, Jiho

Yoon4, B. J. Kim1,5, Takashi Taniguchi6, Kenji Watanabe6, Jonghwan Kim1,3, Kin Chung

Fong7,*, Mazhar N. Ali4,*, Kam Tuen Law2,* and Gil-Ho Lee1,8,*

1Department of Physics, Pohang University of Science and Technology, Pohang, Republic of

Korea

2Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay,

Hong Kong, China

3Department of Materials Science and Engineering, Pohang University of Science and

Technology, Pohang, Republic of Korea

4Max Plank Institute for Microstructure Physics, Halle (Saale), Germany

5Center for Artificial Low Dimensional Electronic Systems, Institute for Basic Science (IBS),

Pohang, Republic of Korea

6Research Center for Functional Materials, National Institute for Materials Science, Tsukuba,

Ibaraki, Japan;

7Raytheon BBN Technologies, Quantum Information Processing Group, Cambridge, MA,

USA

8Asia Pacific Center for Theoretical Physics, Pohang, Republic of Korea

These authors contributed equally: Yong-Bin Choi, Yingming Xie.

†Current address: Institute for Advanced Study and School of Physical Science and Technology,

Soochow University, Suzhou 215006, China

*Correspondence and requests for materials should be addressed to K.C.F

(kc.fong@raytheon.com), M.N.A. (maz@berkeley.edu), K.T.L. (phlaw@ust.hk), or G.-H.L.

(lghman@postech.ac.kr).

S1. Magneto-transport on bulk and thin-flake WTe2

Magnetoresistance (MR) along the a-axis of up to 10,000 % was measured in bulk

WTe2 as shown in Supplementary Fig. 1a. Here, MR is defined as [𝑅xx(𝐵) − 𝑅0]/𝑅0, where

𝑅xx is the longitudinal resistance and 𝑅0 = 𝑅xx(𝐵 = 0) . Similar measurement of non-

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saturating MR1 demonstrated the nearly perfect compensation of electron (𝑛e) and hole (𝑛h)

carrier density, 𝑛e~𝑛h. This provides the evidence of high quality of our WTe2 crystal. Second

derivative of 𝑅xx with respect to B in Supplementary Fig. 1b shows Shubnikov de Haas (SdH)

oscillation of the bulk crystal. Supplementary Figure 1c show optical microscope image of

exfoliated WTe2 crystal of thickness of ~100 nm contacted with normal electrodes. Hall

resistance 𝑅xy(𝐵) shows nonlinear behaviour because both electron and hole carriers

contribute to the transport. To eliminate trivial contributions from the nonideal Hall bar

geometry and misalignment of Hall probes, we anti-symmetrized 𝑅xy(𝐵) to 𝑅𝑥𝑦𝑎𝑠𝑦𝑚(𝐵) =

[𝑅𝑥𝑦(B) − 𝑅𝑥𝑦(−𝐵)]/2 . Supplementary Figure 1d shows 𝑅𝑥𝑦𝑎𝑠𝑦𝑚

with two-band model

fitting2,3 up to |B| > 5.0 T with

𝑅𝑥𝑦𝑎𝑠𝑦𝑚 =

𝐵[(𝑛ℎ 𝜇ℎ2 − 𝑛𝑒 𝜇𝑒

2) + (𝑛ℎ − 𝑛𝑒) 𝜇ℎ 𝜇𝑒 𝐵2]

𝑒[(𝑛ℎ 𝜇ℎ + 𝑛𝑒 𝜇𝑒)2 + (𝑛ℎ − 𝑛𝑒)𝜇ℎ2 𝜇𝑒

2 𝐵2].

Here, the fitting parameters are 𝑛e = 3.872 × 1019 𝑐𝑚−3 , 𝑛h = 3.617 × 1019 𝑐𝑚−3 ,

electron mobility 𝜇𝑒 = 2,098 𝑐𝑚2/𝑉𝑠, and hole mobility μh = 2,182 𝑐𝑚2/𝑉𝑠.

Supplementary Figure 1 | Magneto transport measurements on bulk and thin-film WTe2.

a, Magnetoresistance (MR) with magnetic field 0 degree (blue), 45 degree (red), and 90 degree

(yellow) to the c-axis of crystal. b, Shubnikov de Haas (SdH) oscillation as a function of inverse

magnetic field. c, Optical micrograph of WTe2 device in a Hall bar geometry. d, Anti-

symmetrized Hall resistance 𝑅𝑥𝑦𝑎𝑠𝑦𝑚

(red) with the best fitting of two-band model (blue).

S2. Crystal axis identification from polarisation-resolved Raman spectrum

Polarisation-resolved Raman spectroscopy is utilized as an accurate and non-invasive

characterization tool to determine the anisotropic crystal orientation. The polarisations of

incident and scattered light are set in the parallel configuration while the crystal orientation of

WTe2 flakes relative the polarisation is rotated by a half waveplate as described in methods

section of the main text. The crystal axis can be determined from polarisation-angle dependence

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of the Raman intensity following the previous works6,21,22. Supplementary Figures 2a, d, and g

(Supplementary Figs. 3a, and b) shows micrograph of a WTe2 flake of Dev. A1, Dev. A2, and

Dev. A3 (Dev. B1, and Dev. B2), respectively. The polarisation direction (𝜃, red arrow) is varied

from 0 to 360 degree with respect to the vertical direction (black solid line) of the micrograph.

The Colour-coded plot of Raman intensity are shown in Supplementary Figs. 2b, e, and h

(Supplementary Figs. 3c, and d). The Raman signals originate from the A1 modes of Td-WTe2

crystals which all show polarisation-angle dependence. For example, the Raman modes around

at 165 cm-1 and 213 cm-1 show characteristic two-fold patterns (Supplementary Figs. 2c, f, and

i), (Supplementary Figs. 3e, and f) in their polarisation angle dependence. Intensity maximum

of ~ 165 cm-1 and 213 cm-1 Raman modes appear when the polarisation aligns respectively with

the a-axis and b-axis, which is previously established based on high-resolution atomic force

microscopy and Raman tensor analysis6,21,22.

Supplementary Figure 2 | Polarized Raman spectroscopy for determining crystal axis for

Dev. A1, A2, and A3. a, d, g Optical micrograph of WTe2 devices for Dev. A1 (a), Dev. A2 (d),

and Dev. A3 (g), respectively. b, e, h, Colour-coded plot of Raman intensity as a function of

relative crystal angle and relative Raman shift for Dev. A1 (b), Dev. A2 (e), and Dev. A3 (h),

θ

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respectively. c, f, i Polar plots of Raman intensity with a function of the polarisation angle.

Raman modes at ~ 165 (blue circles and line) and 213 cm-1 (red circles and line) show

characteristic two-fold patterns where intensity maximums align to a-axis and b-axis of WTe2

crystals for Dev. A1 (c), Dev. A2 (f), and Dev. A3 (i), respectively.

Supplementary Figure 3 | Polarized Raman spectroscopy for determining crystal axis for

Dev. B1 and B2. a, b Optical micrograph of WTe2 devices for Dev. B1 (a), and Dev. B2 (b),

respectively. c, d, Colour-coded plot of Raman intensity as a function of relative crystal angle

and relative Raman shift for Dev. B1 (c), and Dev. B2 (d), respectively. e, f, Polar plots of

Raman intensity with a function of the polarisation angle. Raman modes at ~ 165 (blue circles

and line) and 213 cm-1 (red circles and line) show characteristic two-fold patterns where

intensity maximums align to a-axis and b-axis of WTe2 crystals for Dev. B1 (e), and Dev. B2

(f), respectively.

S3. Summary of WTe2 Josephson junction series of Dev. A, and Dev. B

We summarized measured WTe2 Josephson junction devices in Supplementary Table

1. Here, Dev. A1 and Dev. B1 corresponds to Dev. A and Dev. B in the main text, respectively.

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Supplementary Table 1 | Summary of devices

S4. Hinge modes from the effective Hamiltonian

The effective Hamiltonian used to describe Td-WTe2 can be written as4:

𝐻(𝐤) = (𝑚1 + ∑𝑗=𝑎,𝑏,𝑐 𝑣𝑗cos𝑘𝑗 + 𝑚2𝜇𝑥 + 𝑚3𝜇𝑧)𝜏𝑧 + 𝜆𝑏sin𝑘𝑏𝜇 𝑦𝜏𝑦 + 𝜆𝑐sin𝑘𝑐𝜏𝑥 +

𝛾𝑥𝜇𝑥 + 𝛾𝑧𝜇𝑧 + 𝛽𝑎sin𝑘𝑎𝜇𝑧𝜏𝑦𝜎𝑧 (1)

Here 𝜎 operates on the spin space, the Pauli matrices 𝜏 and 𝜇 operate on the orbital space

(s1, s2, 𝑖p1, 𝑖p2) with s denotes an s orbital, p denotes an p orbital and 𝑖 is the complex number.

More explicitly, 𝜏 operates on (s, p) orbital space, 𝜇 operates on (s1, s2), (𝑖p1, 𝑖p2) orbital

space. The s orbitals have even parity and transform as 1 under C2a, while the p orbitals have

odd parity and acquire a minus sign under C2a. Then, it can be found that the Hamiltonian

exhibits time reversal symmetry 𝑇 = 𝑖𝜏𝑧𝜎𝑦𝐾 , parity symmetry 𝑃 = 𝜏𝑧 , two fold rotation

𝐶2𝑎 = 𝑖𝜏𝑧𝜎𝑦 along the a-axis and a mirror symmetry 𝑀𝑎 = 𝑃𝐶2𝑎 = 𝑖𝜎𝑦, where the mirror

plane is perpendicular to the C2 rotational axis. Therefore, the Hamiltonian possesses the C2h

point group symmetry which is the same symmetry as the point group symmetry of 1T’-WTe2

with nonsymmorphic space group P21/m. Moreover, 𝑘𝑎, 𝑘𝑏 and 𝑘𝑐 describe the momentum

in the a-, b- and c-axis directions respectively where the c-axis is perpendicular to the crystal

plane. It is important to note that even though Td-WTe2 has C2v point group which is

noncentrosymmetric, it has the same topological properties as the 1T’-WTe2 given that the

Weyl points are annihilated by lattice distortions. Therefore, the effective Hamiltonian can

faithly describe the higher order topological properties of Td-WTe2 4.

With the above Hamiltonian in momentum space, we construct a real space tight-

binding Hamiltonian to study the hinge states of the system. For a thin film of 100 sites wide,

3 site thick and periodic boundary condition along the a-axis direction, the energy spectrum in

the topological regime with hinge states is shown in Supplementary Fig. 4a. To show the

wavefunction of the hinge state, we constructed a three dimension lattice with 100×100×3

sites. The hinge state wavefunction at a chemical potential inside the bulk gap is shown in

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Supplementary Fig. 4b. The hinge state wavefunction at a chemical potential with bulk

conducting states is shown in Supplementary Fig. 4c. The parameters in the tight-binding

Hamiltonina are set to be 𝑚1 = −3𝑡, 𝑚2 = 0.3𝑡, 𝑚3 = 0.2𝑡, 𝑣𝑎 = 2𝑡, 𝑣𝑏 = 1.6𝑡, 𝑣𝑐 = 𝑡,

𝜆𝑏 = 0.1𝑡, 𝜆𝑐 = 𝑡, 𝛾𝑥 = 0.4𝑡, 𝛾𝑧 = −0.4𝑡, 𝛽𝑎 = 1.5𝑡. 𝑡 = 1 is a unit of energy.

It is clear from Supplementary Fig. 4b that we have well localized hinge states along

the a-axis direction. On the other hand, the hinge states along the b-direction are distributed

more uniformly on the side surfaces and we call it edge states instead. When the chemical

potential is located inside the valence band with bulk conducting states, the edge states along

the b-direction merges into the bulk, however, the hinge states along the a-axis direction is still

well localized. In the experiments, we expect that there are both bulk conducting states and

hinge states in the samples. As a result, we expect to see edge transport along the a-axis

direction but only bulk transport behaviors in the b-axis direction.

Supplementary Figure 4 | a, band structure of the effective Hamiltonian with periodic

boundary conditions along the a-axis direction. The two horizontal dashed lines indicate the

chemical potential in b and c respectively. b. The wavefunction of a hinge state with chemical

potential inside the energy gap. c. The wavefunction of the hinge state with chemical potential

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inside the valence band.

S5. Graphite Josephson junction

As a control experiment, we fabricated graphite-based Josephson junction, which is

expected not to have topological surface states or hinge states, with exactly same fabrication

process we have used for WTe2 Josephson junction. Here, we investigated two junctions, GJJ-

JJ1 of (L,W,t)=(250 nm, 7.1 m, 5.8 nm) and GJJ-JJ2 of (L,W,t)=(200 nm, 7.1 m, 5.8 nm) as

shown in Supplementary Fig. 5a. Supplementary Figures 5b and d shows magnetic field

interference pattern of critical current for GJJ-JJ1 and GJJ-JJ2, respectively. The critical current

at the field center is 3.5 A for GJJ-JJ1 and 3.3 A for GJJ-JJ2, and the IcRN product is 35 V

for GJJ-JJ1 and 31 V for GJJ-JJ2, which are in the same order of magnitude of those of Dev.

A and Dev. B discussed in the main text. The oscillation period of B=4.5 G for GJJ-JJ1 and

5.3 G for GJJ-JJ2 gives 𝐿′~200 for GJJ-JJ1 and 175 nm for GJJ-JJ12, both of which correspond

to the nearly half width of Nb electrodes. Josephson current density J (Supplementary Figs. 5c

and e) reconstructed via inverse Fourier transform of interference pattern shows uniform J

within the level of fluctuation. This implies that the observed edge-enhanced J for WTe2

Josephson junctions are not due to trivial artefacts introduced during the fabrication process.

Supplementary Figure 5 | Graphite Josephson junction for the control experiment. a,

Optical micrograph of graphite Josephson junctions. b, d, Colour-coded plot of differential

resistance dV/dI as a function of bias current I and perpendicular external magnetic field B for

GJJ-JJ1 (b) and GJJ-JJ2 (d). Red solid lines represent extracted Josephson critical current. c, e,

Extracted spatial distribution of Josephson current density J(x) for GJJ-JJ1 (c) and GJJ-JJ2 (e).

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S6. More WTe2 Josephson junction devices along a-axis

Supplementary Figure 6 show more Nb-WTe2-Nb Josephson junction device of Dev.

A2 (Supplementary Figs. 6a, b, and c), Dev. A3 (Supplementary Figs. 6d, e, and f), and Dev.

A4 (Supplementary Figs. 6g, h, and i). Detailed information of devices is summarized in

Supplementary Table 1. The fabrication process is completely same as described for Dev. A in

main text except that aluminium (Al) was used instead of niobium as a superconductor for Dev.

A2. For Dev. A2, the lobes of critical current decays over ~70 G because of the small critical

magnetic field (~100 G) of Al (Supplementary Fig. 6b). The oscillation period of B=7.0 G

gives 𝐿′~195 nm, which corresponds to the nearly half width of Al electrodes. For Dev. A3

and Dev. A4, the oscillation period of B=14.7 G, and 8.85 G gives 𝐿′~170 nm, and 210 nm,

respectively, which correspond to the nearly half width of Nb electrode.

Josephson current density in real space was reconstructed by using inverse Fourier

transform as shown in Supplementary Figs. 6c, f, i. Red dotted lines represent Gaussian fitting

for each left(right) edge enhancement. Supplementary Table 2 summarizes full-width-half-

maximum (FWHM) of edge enhancement of J, total Josephson current enhancement (Ic,edge,L(R),

the shaded areas in Supplementary Figs. 6c, f, i) and corresponding errors (Ic,edge,L(R))

estimated from the fluctuation of J in the bulk (Jbulk). Here, ‘L’ and ‘R’ stands for left and right,

respectively.

By considering a short ballistic junction limit (eIJ,h,Nb(Al)RN,h = Nb(Al)) the maximum

theoretical value of IJ,h,Nb(Al) = 140(22) nA for a single hinge state, where RN,h = h/e2 is the

normal resistance for a single hinge state and Nb(Al) = 1.763kBTc,Nb(Al) is the BCS

superconducting gap of the Nb(Al) electrode with Tc,Nb(Al) = 7.5(1.2) K. Total Josephson

current enhancements for all the devices are consistently smaller than or comparable to the

theoretical maximum value as shown in Supplementary Table 2.

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Supplementary Figure 6 | More devices of Dev. A2, A3 and A4. a, d, g, Scanning electron

micrograph of Dev. A2, A3 and A4 with measurement configuration, respectively. b, e, h,

Colour-coded plot of differential resistance dV/dI as a function of bias current I and

perpendicular external magnetic field B for Dev. A2 (b), Dev. A3 (e) and Dev. A4 (h). Red solid

lines represent extracted Josephson critical current. c, f, i, Extracted spatial distribution of

Josephson current density J for Dev. A2 (c), Dev. A3 (f) and Dev. A4 (i). Dotted line represents

Gaussian fitting for each edge enhancement.

Supplementary Table 2 | Summary of enhanced total Josephson current near edges and

corresponding errors. WFWHM,L(R) is full-width-half-maximum of enhanced current profile at

the left(right) edge, Jbulk is the standard deviation of current density profile J in the bulk area,

Ic,edge,L(R) is the enhanced Josephson current at the left(right) edge, and

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Ic,edge,L(R)=Jbulk×WFWHM,L(R) is the error of Ic,edge,L(R) at the left(right) edge.

S7. More WTe2 Josephson junction devices along b-axis

Supplementary Figure 7 shows more Nb-WTe2-Nb Josephson junction device of Dev.

B2 (Supplementary Figs. 7a and b), Dev. B3 (Supplementary Figs. 7c and d), and Dev. B4

(Supplementary Figs. 7e and f). Detailed information of devices is summarized in

Supplementary Table 1. The fabrication process is completely same as described for Dev. A in

main text. Supplementary Figures 7b, d, and f show measured Fraunhofer pattern for Dev. B2,

B3, and B4, respectively. The behaviour is similar to standard single slit Fraunhofer

interference. Red line is calculated standard single slit Fraunhofer interference.

Supplementary Figure 7 | More devices of Dev. B2, B3 and B4. a, c, e, Scanning electron

micrograph of Dev. B2, B3 and B4 with measurement configuration, respectively. b, d, f,

Colour-coded plot of differential resistance dV/dI as a function of bias current I and

perpendicular external magnetic field B for Dev. B2 (b), Dev. B3 (d) and Dev. B4 (f). Red line

represents calculated Fraunhofer patten.

S8. Fermi arcs states in a Weyl semimetal.

It is important to note that Fermi arc states can also conduct edge currents on the side

surfaces. In this section, we would like to point out two important difference between the Fermi

arc states and the hinge states. The two differences are:

1. The Fermi arc states are more uniformly distributed on the side surfaces. In

Supplementary Fig. 8, the wavefunction of the Fermi arc states of a Weyl semimetal is depicted.

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To illustrate the properties of the Fermi arc states of a Weyl semimetal, we constructed a tight-

binding model similar to the one in the work by Chen et al.5. To allow a better comparison with

the effective Hamiltonian model for HOTI, we set the hopping strength in the a-axis direction

to be stronger than that of the b-axis. As a result, the Fermi arc states in the b-direction are

merged into the bulk. As expected, the wavefunction is uniformly distributed among all the

layers of the sample, unlike the hinge state localized on the crystal hinge (the top or bottom of

the side surface) depicted in Supplementary Fig. 4c. Therefore, we expect the Type II device

shown in Fig. 4 of the main text can be used to distinguish between the Fermi arc states and

the hinge states.

2. In general, there are many branches of conducting modes if there are Fermi arc states

on the side surfaces. In our simple model of Weyl semimetal as described below, we see that

there are 4 branches of helical modes on each side surface. Therefore, we expect that the critical

supercurrent carried by the Fermi arc states is larger than the Josephson current carried by a

single branch of hinge mode. In our experiment, the Josephson current carried by the edge

modes was smaller than or comparable with the maximum Josephson current carried by a single

helical mode. Therefore, our measurement of the edge-localized Josephson current using the

Fraunhofer pattern supports the hinge mode interpretation, even though the Josephson current

measurement itself cannot rule out the Fermi arc picture.

Supplementary Figure 8 | a. The wavefunction of a Fermi arc state. The wavefunction is

uniformly distributed among all the layers. b. The band structure of the Weyl semimetal

showing that there are four branches of Fermi arc states. For thicker samples, the number of

branches of edge modes will increase in the Fermi arc scenario.

S9. Fabrication process for the control device Dev. AT

We fabricated control device Dev. AT shown in Fig. 4 of the main text such that the

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bottom of the side surfaces of WTe2 crystal are covered by insulating aluminium oxide (Al2O3).

Supplementary Figure 9 shows the schematics of the fabrication process in each step. WTe2

single crystals of thickness about 100 nm were mechanically exfoliated onto SiO2 substrate.

For etching WTe2 crystal, we used AR-P e-beam resist that has a strong endurance against

Argon (Ar) ion etching (Supplementary Figs. 9a and b). Ar etching of side parts of WTe2 flake

is immediately followed by deposition of insulating aluminium oxide (Al2O3) without

removing AR-P e-beam resist. Here, AR-P resist structure used for the etching mask in

Supplementary Fig. 9c is also used for the lift-off resist for Al2O3 layer in Supplementary Figs.

9d and e. This self-alignment of etching window and Al2O3 layer enables partial insulating of

the side surfaces of WTe2 crystal without covering the top hinges of crystal. After side surface

insulation, niobium (Nb) superconducting electrodes are deposited and finally makes contact

to the top surface and top part of side surfaces of WTe2 crystal (Supplementary Fig. 9f).

Supplementary Figure 9 | Schematics of fabrication process for Dev. AT. Lower panel in

each step shows the schematic of the side-view cut along the white dotted line of the top-view

schematic in upper panel. a, WTe2 single crystal (grey) is exfoliated on SiO2 substrate(black)

and coated with AR-P e-beam resist (orange). b, Etching window for Argon (Ar) ion etching is

formed by partially developing AR-P e-beam resist. c, Side parts of WTe2 and parts of SiO2

(marked by oblique dashed lines) are etched by Ar ions (downward green arrows). d, Insulating

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aluminium oxide Al2O3 (yellow) is deposited. e, AR-P e-beam resist is dissolved in solvent and

Al2O3 is lifted off. Side surfaces of WTe2 crystal are now partially covered by Al2O3. f, Niobium

(Nb) superconducting electrodes (green) are deposited and makes contact to the top surface

and top part of side surfaces of WTe2 crystal.

S10. Fitting of measured interference pattern to the standard Fraunhofer

pattern

Supplementary Figure 10 shows the fitting of measured interference patterns for

different devices to the standard Fraunhofer pattern. Fitting function is in the inset of

Supplementary Fig. 10a, and the fitting parameters are represented in the inset of each graph.

R-squared value (0~1) quantifies the goodness of fitting. Dev. A shows rather small R-squared

value (0.749), which means the measured interference pattern does not resemble to the standard

Fraunhofer pattern. Whereas, Dev. B (R-squared value: 0.969) and Dev. AT (R-squared value:

0.919) shows interference pattern similar to the standard Fraunhofer pattern.

Here, we note that the inverse Fourier transform (IFT) is an inappropriate tool to

examine the single-side enhancement in Josephson current density J(x). This is because the

asymmetry part in J(x) only can come from the small Ic at the nodes of interference pattern,

which cannot be measured properly in our experimental condition with the finite temperature

and the large dissipation in Josephson junction due to a small shunting resistance from the basal

part of WTe2 flake.

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Supplementary Figure 10 | Fitting to the standard Fraunhofer pattern. Measured

interference pattern for Dev. A (a), Dev. B (b), and Dev. AT (c) are fitted to the standard

Fraunhofer pattern. Insets of each graph shows corresponding fitting parameters.

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