Tip-induced Superconductivity Coexisting with Preserved

Topological Properties in Line-nodal Semimetal ZrSiS

Leena Aggarwal1, Chandan K. Singh2, Mohammad Aslam1, Ratnadwip Singha3, Arnab

Pariari3, Sirshendu Gayen1, Mukul Kabir2, Prabhat Mandal3,∗ and Goutam Sheet1†

1Department of Physical Sciences, Indian Institute of

Science Education and Research Mohali, Sector 81,

S. A. S. Nagar, Manauli, PO: 140306, India

2 Department of Physics and Centre for Energy Science,

Indian Institute of Science Education and Research, Pune 411008, India and

3Experimental Condensed Matter Physics Division,

Saha Institute of Nuclear Physics, HBNI,

1/AF Bidhannagar, Kolkata 700064, India

(Dated: February 23, 2018)

Abstract

ZrSiS was recently shown to be a new material with topologically non-trivial band

structure which exhibits multiple Dirac nodes and a robust linear band dispersion

up to an unusually high energy of 2 eV. Such a robust linear dispersion makes the

topological properties of ZrSiS insensitive to perturbations like carrier doping or lat-

tice distortion. Here we show that a novel superconducting phase with a remarkably

high Tc of 7.5 K can be induced in single crystals of ZrSiS by a non-superconducting

metallic tip of Ag. From first-principles calculations we show that the observed super-

conducting phase might originate from dramatic enhancement of density of states due

to the presence of a metallic tip on ZrSiS. Our calculations also show that the emerg-

ing tip-induced superconducting phase co-exists with the well preserved topological

properties of ZrSiS.

∗Electronic address: prabhat.mandal@saha.ac.in†Electronic address: goutam@iisermohali.ac.in

1

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2018

It is widely believed that inducing superconductivity in topologically non-trivial materi-

als might eventually lead to the discovery of topological superconductors where the elusive

particles called Majorana fermions can, in principle, be realized in the vortex state.1–4 Mo-

tivated by this idea, efforts have been made to induce superconductivity through a number

of methods including chemical doping5–8 and applying pressure9–12 on topological materials.

As a result, superconductivity was observed in a number of topological systems upon chem-

ical doping (e.g., Cu-intercalated Bi2Se3)5 and applying pressure (e.g.,Bi2Te3)12. However,

such methods worked only on a very limited number of systems. Recently, it was shown

that a novel mesoscopic superconducting phase can also be induced in a non-superconducting

topological system simply by making a point contact with sharp needle made of a simple

elemental normal metal.13,14 The observed supercondcuting phase originating only under a

point of contact is known as tip-induced superconductivity (TISC). This discovery expanded

the landscape over which the possibility of a topological superconductor can be explored.

In this paper, we report the discovery of TISC in a novel topological material ZrSiS.15,16

The TISC on ZrSiS shows a critical temperature (Tc) of ∼ 7.5 K and a superconducting

energy gap ∆(T=0) ∼ 1 meV. Such discovery is particularly important because ZrSiS is known

to show a linear band dispersion over a large energy range ∼ 2 eV17 whereas the linear

extent for most of the other topological materials is limited up to few hundred meV from

respective Dirac points.18,19 This makes the topological properties of ZrSiS extremely robust

against carrier doping, variation of stochiometry and other external perturbative effects

thereby implying that when a superconducting phase is realized on ZrSiS point contacts,

the topological properties of ZrSiS are not expected to be destroyed merely by the presence

of a metallic tip forming the point contacts. Therefore, the superconducting phase realized

on ZrSiS does not emerge at the expense of the topological nature of ZrSiS. This makes

ZrSiS the most promising candidate for a topological superconductor and the idea is also

supported by our first-principles calculations.

The ZrSiS single crystals were grown in standard iodine vapor transport method. The

polycrystalline powder was prepared in two steps. At first, elemental Si (Strem Chem.

99.999%) and S (Alfa Aesar 99.9995%) were mixed in stoichiometric ratio (1:1) and heated

at 1000oC under vacuum. The resultant powder was mixed with elemental Zr (Alfa Aesar

99.9%) and again heated at 1100oC. This polycrystalline ZrSiS along with iodine (5mg/cm3)

were sealed in a quartz tube under vacuum and kept in a gradient furnace for 72 h. During

2

this period, a temperature gradient of 100oC was maintained along the quartz tube with

hotter end at 1100oC. Shinny rectangular plate like crystals were obtained at the cooler

end. The single crystals have been characterized by high-resolution transmission electron

microscopy (HRTEM) and energy-dispersive X-ray (EDX) spectroscopy in a FEI, TECNAI

G2 F30, S-TWIN microscope operating at 300 kV. The details of characterization techniques

are described elsewhere.20

0 3 6 9 12 15

0.25

0.30

0.35

0.40

0.45

0 kG

1 kG

2 kG

3 kG

4 kG

5 kG

6 kG

7 kG

8 kG

9 kG

10 kG

12 kG

R (

)

T (K)

-4 -2 0 2 4

0.8

1.0

1.2

1.4

1.6

1.8

(dI/d

V)

N

V (mV)

(a) Nb/Ag

V

Sample

Tip

(b)

(c) (d)Nb/Ag Nb/Ag

0 3 6 9

0

1

2

3

T (K)

H (k

G)

Figure 1: Point-contact spectroscopy on a conventional superconductor, Nb using Ag tip. (a) A

schematic of a point-contact spectroscopy experiment. (b) A normalized diffrential conductance

((dI/dV )N ) vs applied bias (V ) point contact spectrum in thermal regime of transport for a

conventional superconductor, Nb using Ag tip at 1.8 K. (c) Resistance versus temperautue (R−T )

curves obtained for Nb/Ag point-contact showing systematic drop of the superconducting transition

temperature with varying the applied magnetic field. (d) The H−T phase diagram extracted from

Figure 1(c) in blue dashed line is empirically expected and red dots are experimental data.

Figure 1 (a) depicts a schematic of the point contacts. The point contacts were made

by bringing sharp metallic tips of silver (Ag) on the surface of single crystals of ZrSiS (Also

3

see Figure S1 in the supplementary materials). The experiments were performed on two

independently grown single crystals in order to confirm the reproducibility of the results

(see Figure S3, S4, S5 in supplementary materials). A lock-in based modulation technique

was used to measure the differential conductance, dI/dV of the point-conatcts as a function

of an applied dc bias, V (see Figure S2 in supplementary materials).

Usually, for mesoscopic point contacts, the resistance RPC is given by Wexler’s formula1:

RPC = 2h/e2

(akF )2+ Γ(l/a)ρ(T )

2a, where h is Planck’s constant, e is the charge of a single electron,

a is the contact diameter, kF is a Fermi momentum, Γ(l/a) is a slowly varying function of

the order of unity, ρ is the bulk resistivity of the material and T is the effective temperature

at the point-contact. The first term is known as ballistic or Sharvin’s resistance (RS)22 that

depends on the fundamental constants h, e and the number of conducting channels in the

point contacts. The second term in Wexler’s formula is called the Maxwell’s resistance (RM)

which is qualitatively similar to the bulk resistance and depends directly on the resistivity of

the materials forming the point contact. The Wexler’s formula also suggests that when the

contact diameter is small compared to electronic mean free path i.e., when the contact is

in the so-called ballistic regime, RS dominates and in the other extreme called the thermal

regime, RM contributes most to RPC . Therefore resistive transitions lead to non-linearities

in the I − V characteristics corresponding to RM of point-contacts.23 For superconducting

point contacts in the thermal regime, as the current through a point contact goes down

below the critical current (Ic) associated with the point contact, the resistivity (ρ) of the

superconducting component of the point contact will be zero leading to a sharp change in

RM .23,24 This change introduces a large non-linearity in the I−V characteristic of a thermal

regime point contact, resulting in two sharp dips in the differential conductance (dI/dV ) vs

dc bias (V ) spectra. Such dips are seen to be symmetric about V = 0 and the position of

the dips normalized by the normal state resistance of the point contacts provides a direct

estimate of the magnitude of Ic.

In order to highlight the points discussed above directly, in Figure 1(b), we show a

(dI/dV )N vs V spectrum acquired in the thermal regime point contact between a known

conventional superconductor niobium (Nb) and a sharp metallic tip of silver (Ag). The

conductance dips symmetric about V = 0 are clearly visible. Furthermore, as shown in

Figure 1(c), the resistance (R) vs. temperature (T ) of a superconducting (thermal regime)

point contact on Nb shows a sharp change corresponding to the superconducting transition

4

-6 -3 0 3 6

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

0 kG

2 kG

4 kG

6 kG

8 kG

10 kG

12 kG

14 kG

16 kG

18 kG

20 kG

V (

mV

)

I (mA)

-8 -4 0 4 8

-1.0

-0.5

0.0

0.5

1.0 0 kG

0.6 kG

2 kG

3 kG

4 kG

5 kG

6 kG

7 kG

8 kG

9 kG

10 kG

11 kG

13 kG

14 kG

19 kG

20 kG

V (m

V)

I (mA)

-4 -2 0 2 4

0.9

1.2

1.5

0 kG

0.6 kG

2 kG

3 kG

4 kG

5 kG

6 kG

7 kG

8 kG

9 kG

10 kG

11 kG

13 kG

14 kG

19 kG

20 kG

(dI/

dV)

N

V (mV)

-4 -2 0 2 4

0.6

0.8

1.0

1.2

1.4

1.6

1.8 0 kG

2 kG

4 kG

6 kG

8 kG

10 kG

12 kG

14 kG

16 kG

18 kG

20 kG

(dI/

dV)

N

V (mV)

2 4 6 8 10

3.2

3.6

4.0

4.4

4.8

0 kG

1 kG

2 kG

3 kG

4 kG

8 kG

10 kG

12 kG

T (K)

R

0 2 4 6 8

0

5

10

15

20

T (K)

H (k

G)

(a) (b)

(c) (d)

ZrSiS/Ag

ZrSiS/Ag ZrSiS/Ag

Nb/Ag

I-V curve from

Maxwell’s contribution

(e) (f)

I-V curve from

Maxwell’s contribution

Nb/AgZrSiS/Ag

Figure 2: A comparision of (dI/dV )N vs V spectra on ZrSiS/Ag point-contact with Nb/Ag point-

contact spectra in thermal regime of transport by showing magnetic field dependent data. Mag-

netic field dependent point-contact spectra at 1.8 K in thermal regime of transport (a) on ZrSiS/Ag

point-contact, (b) on Nb/Ag point-contact. (c) Magnetic field dependent R−T curves showing dis-

apearance of superconducting transition temperature with increasing magnetic field for ZrSiS/Ag

point-contact. (d) The H − T phase diagram extracted from Figure 2(c) in blue dashed line is

empirically expected and red dots are experimental data. Magnetic field dependence of I − V

curves at 1.8 K calculated by BTK theory containing Maxwell’s contribution only (e) for ZrSiS/Ag

point-contact, (f) for Nb/Ag point-contact.

of Nb at 9.2 K. The R− T evolves systematically involving a monotonic decrease in Tc with

increasing magnetic field (H).

In the R−T data obtained from Nb point contacts, it is clear that the resistance does not

5

become zero down to 1.4 K. This shows that for a superconducting point-contact, the contact

resistance does not become zero. This is primarily due to several reasons including (i) the

existence of a non-superconducting component of the point-contact, (ii) a small contribution

from Sharvin’s resistance that might be present even when the contacts are far from the

ballistic regime and (iii) possible mismatch of the Fermi-velocities in the two materials

forming the point-contact.25 Hence the measurement of “zero-resistance” is not a hallmark

signature of superconductivity in a superconducting point contact. However, despite the

absence of a zero-resistance in the measurement, from other hallmarks of supercondcutivity

like, the field dependent critical current, combined with the field dependent R − T data, a

mesoscopic tip-induced superconducting (TISC) phase emerging only under a point contact

can be detected and verified. Figure 1(d) shows the H−T phase diagram (red dots) extracted

from magnetic field dependence R − T data as shown in Figure 1(c). The blue dashed line

in the same Figure is expected H − T phase diagram for a conventional superconductor as

known empirically.

Now we focus on the data obtained on high quality single crystals of ZrSiS. In Figure

2(a) we present the magnetic field dependence of a spectrum obtained on ZrSiS/Ag point

contacts. The striking similarity of the zero field data with that obtained on Nb point

contacts must be noted. The conductance dips appearing in the spectrum originate from

the critical current of the point contact. All the spectral features show monotonic evolution

with increasing magnetic field until all the features smoothly disappear at 20 kG. In order

to highlight the superconducting nature of ZrSiS/Ag point contacts, in Figure 2(b) we

provide the systematic magnetic field dependent data obtained on supercondcuting Nb/Ag

point contacts. The qualitative similarity in the magnetic field dependence of ZrSiS point

contacts and Nb point contacts is clear.

In Figure 2(c) we present the magneto-transport data on ZrSiS/Ag point contacts. The

superconducting transition temperature (TC) is seen to be 7.5 K. This value is remarkably

high and comparable to the TC of the celebrated elemental superconductors like Pb and Nb.

The critical temperature decreases monotonically with increasing magnetic field. Again, the

zero resistance state cannot be directly measured for reasons discussed before. The H − Tphase diagram extracted from these data has been shown in Figure 2(d). The blue dashed

line in Figure 2(d) shows the expected dependence for a conventional superconductor as

known empirically. The projected upper critical field of the supercondcuting phase could

6

-6 -3 0 3 6

-1.6

-0.8

0.0

0.8

1.6

1.8 K

2 K

4 K

5 K

6 K

7 K

7.5 K

8 K

8.5 K

9 K

V (m

V)

I (mA)

-8 -4 0 4 8

-1.0

-0.5

0.0

0.5

1.0

1.7 K

2 K

4 K

5 K

6 K

7 K

7.5 K

V (m

V)

I (mA)

-4 -2 0 2 4

0.6

0.8

1.0

1.2

1.4

1.6

1.8 1.8 K

2K

4 K

5 K

6 K

7 K

7.5 K

8 K

8.5 K

9 K

(dI/d

V)

N

V (mV)

-3.6 -1.8 0.0 1.8 3.6

0.8

1.0

1.2

1.4

1.6

1.7 K

2 K

4 K

5 K

6 K

7 K

7.5 K

V (mV)

(dI/

dV)

N

ZrSiS/Ag

Nb/Ag

(a) (b)

(d)(c)

Nb/Ag

ZrSiS/Ag

I-V curve from

Maxwell’s contribution

I-V curve from

Maxwell’s contribution

Figure 3: A comparision of (dI/dV )N vs V spectra on ZrSiS/Ag point-contact with Nb/Ag point-

contact spectra in thermal regime of transport by showing temperature dependent data. (a)

Temperature dependence of thermal limit spectra on ZrSis/Ag point-contact. (b) Temperature

dependence of I − V curves calculated by BTK theory containing Maxwell’s contribution only

for ZrSiS/Ag point-contact. (c) Temperature dependence of the thermal limit spectra on Nb/Ag

point-contact (d) Temperature dependence of I − V curves calculated by BTK theory containing

Maxwell’s contribution only for Nb/Ag point-contact.

be as high as 17 kG and our experimental data points (red dots) deviate slighty from the

empirical expectation. This might be an indication of the existence of an unconventional

component in the supercodncuting phase realized on the topologically non-trivial system

ZrSiS.

In order to illustrate the role of critical current on the point contact spectra obtained on

ZrSiS, we have used BTK theory2 to calculate an approximate I−V characteristic associated

with the ballistic component (RS) of the point contact resistance and then subtracted the

same from the I−V associated with the total point contact resistance (RPC). The resultant

7

I−V thus obtained is associated with the Maxwell’s contribution (RM) alone. The resultant

I−V characteristic and the magnetic field dependence of the same has been shown in Figure

2(e). This I − V directly reflects the non-linearities associated with the critical current

of the superconducting point contact. The smooth decrease of the range over which the

voltage remains zero with increasing magnetic field is fully consistent with the magnetic field

dependence of a critical current dominated I − V for a superconducting point contact. For

comparison, in Figure 2(f) we have also provided similar data extracted from the magnetic

field dependent point contact spectra obtained on superconducting Nb (Figure 2(b)).

To provide further support for the superconducting origin of the spectra presented here,

we have performed detailed temperature dependence of the spectra. In Figure 3(a) we show

the temperature dependence. The spectral features disappear at the critical temperature.

We have also extracted the temperature evolution of the critical current dominated I − Vfollowing the same protocol discussed above (Figure 3(b)). For comparison, we have also

included the temperature dependent data on superconducting Nb point contacts (Figure

3(c, d)).

Even when a point contact is in the thermal regime of transport, as per Wexler’s formula1,

a small but finite ballistic component exists. From a visual inspection it is clear that between

-0.8 meV and +0.8 meV, the zero field spectrum on ZrSiS remains flat. This could be a

signature of Andreev reflection when the barrier potential at the interface is extremely

small making the barriers almost transparent. Such an attribution is consistent with the

prediction from the theory of Blonder, Tinkham and Klapwijk (BTK)2 for superconducting

point contacts. Going by the arguments provided by BTK, there is a strong indication that

the superconducting energy gap (∆) of the superconducting phase realized on ZrSiS is 0.8

meV.

In order to understand the mechanism through which superconductivity might be induced

in the system, we have carried out first-principles calculations and investigated the change

in Fermi surface properties of ZrSiS due to the presence of a metallic tip. Our first-principles

calculations are based on density functional theory, within the projector augmented wave

formalism.27–29 The wave functions were expanded in the plane wave basis with 400 eV

cutoff. The structures were fully optimized using 31×31×19 Monkhorst-Pack k-grid to

sample the Brillouin zone. The Perdew-Burke-Ernzerhof functional form of generalized

gradient approximation was used to describe the exchange-correlation energy.30 Calculated

8

-2.0

-1.0

0.0

1.0

2.0

Γ X M Γ Z R A Z 1 2 3 4 5

TDOSZrSiS

-2.0

-1.0

0.0

1.0

2.0

Γ X M ΓZ R A Z 1 2 3 4 5

Ag tip

c

c

(a) (b)

(c)

(d)

Zr

S

Si

Ag

DOS(States/eV·u.c.)

Ene

rgy

E−

EF

(eV

)

DOS(States/eV·u.c.)

Ene

rgy

E−

EF

(eV

)

Figure 4: The crystal lattice and band structure of ZrSiS without and with Ag-tip. (a) ZrSiS

crystallizes in tetragonal P4/nmm structure. The Zr and S layers are sandwiched between the

Si square nets in a fashion that the two neighbouring S layers are between the Zr layers. Calcu-

lated lattice parameters are in excellent agreement with experimental data.17 (b) Calculated band

structure of ZrSiS without spin-orbit coupling showing Dirac cones along ΓX, MΓ and AZ lines

of the Brillouin zone. The corresponding DOS indicate Zr-d character around the Fermi level.

(c) The 1×1×3 [ZrSiS]4Ag4 superlattice to investigate the effect of Ag-tip. (d) The superlattice

band structure, showing Dirac cones along the MΓ and AZ lines. Resulting DOS at the EF show

substantial increase.

lattice parameters for bulk P4/nmm ZrSiS (Figure 4(a), a = 3.55 and c = 8.14 A) are in

excellent agreement with the experimental results.17 The electronic structure of bulk ZrSiS

hosts several Dirac cones along ΓX, MΓ and AZ lines (Figure 4(b)). However, due to the

C2v symmetry lines, the Dirac cones at the Fermi level open up small gap ∼ 35 meV,

while spin-orbit coupling is considered (see Figure S6 in supplementray materials). The

density of states (DOS) is found to be 0.86 states/eV·unit-cell at EF , which is dominated

9

by Zr-d character. To investigate the effects of metallic Ag point contacts on the electronic

structure of ZrSiS, we have considered 1×1×3 [ZrSiS]4Ag4 (shown in Figure 4(c)) and 3×1×1

[ZrSiS]4Ag6 superlattice (presented in Figure S7 in the supplementray report). The Ag-tip

substantially perturbs the band structure of ZrSiS and for both cases, we observe enormous

increase in DOS at the EF , 2.77 and 3.73 states/eV·unit-cell, respectively. In both cases, the

contribution of Ag in terms of density of states at and around the Fermi level is considerably

small. Thus, it can be surmised that substantial increase in the carrier density around the EF

has explicit role in observed tip-induced superconductivity in ZrSiS. It is important to note

that while the Dirac cone along the ΓX disappears due to Ag-tip insertion for [ZrSiS]4Ag4

superstructure, the Dirac cones along the MΓ and AZ lines are found to be protected along

with the appearance of extra nesting feature (Figure 4(d)). This observation hints to the co-

existience of topological character of ZrSiS along with tip-induced superconductivity thereby

opening a strong possibility of topological superconductivity at ZrSiS/Ag point contact

interfaces.

It is true that in point contact spectroscopy, some amount of pressure is applied under-

neath the tips. Hence, it is also important to look at the possibility of a pressure induced

superconducting phase in ZrSiS. However, first of all, a high pressure superconducting phase

of ZrSiS is not known to exist. In the high-pressure transport measurements on ZrSiS in

our lab we did not find any signature of superconductivity in the system up to 8 GPa.

Furthermore, by including the effect of strain in our calculations, did not find any signif-

icant change in the fermi surface density of states. Therefore, it is most likely that the

exotic superconducting phase emerging under the point contacts on ZrSiS do not arise from

pressure.

In the light of our experimental and theoretical investigations it might be rational to sur-

mise that pristine ZrSiS might be on the verge of a superconducting ground state, but some

intrinsic processes like order parameter fluctuations due to the fragility of phase coherence

destabilize such a ground state. In the past, it was shown that a non-superconducting system

possesing a phase-fluctuating supercodnucting order parameter might be stabilized into a su-

percondcuting ground state simply by increasing the stiffness of the fluctuating phase of the

complex superconducting order parameter through an enhancement of superfluid density.31

Such an idea is consistent with our observation of tip-induced superconductivity in ZrSiS,

where the sole role of the tip is to increase the local density of states leading to an increase

10

in local superfluid density.

In conclusion, we have shown that superconductivity can be induced in the topological

semimetal ZrSiS using a metallic tip. The transition temperature of such a phase is very high

(7.5 K). Our first principles calculations hint to the possibility of coexistence of topological

properties and superconductivity under ZrSiS point contacts thereby making the tip-induced

supercondcuting phase a strong candidate for topological supercondcutivity.

Acknowledgement: G.S. would like to acknowledge partial financial support from a

research grant from DST-Nanomission under the grant number SR/NM/NS-1249/2013 and

from SERB under the grant number EMR/2015/001650. Calculations were done using the

supercomputing facilities at the Centre for Development of Advanced Computing, Pune;

Inter University Accelerator Centre, Delhi. M.K. acknowledges the funding from the De-

partment of Science and Technology, Government of India, under Ramanujan Fellowship

and Nano Mission project SR/NM/TP-13/2016.

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[22] Datta, S. Electronic Transport in Mesoscopic Systems. Cambridge University Press, 1995.

[23] Sheet, G., Mukhopadhyay, S. & Raychaudhuri, P. Role of critical current on the point-contact

12

Andreev reflection spectra between a normal metal and a superconductor. Phys. Rev. B 69,

134507 (2004).

[24] Naidyuk, Y. G. & Yanson, I. K. Point-contact Spectroscopy. Springer Newyork, 2004.

[25] Goutam, S. Point-contact Andreev Reflection Spectroscopy on Superconductors and Ferro-

magnets. TIFR (2006).

[26] Blonder, G. E., Tinkham, M. & Klapwijk, T. M. Transition from metallic to tunneling regimes

in superconducting microconstrictions: excess current, charge imbalance, and supercurrent

conversion. Phys. Rev. B 25, 4515 (1982).

[27] Kresse, G. & Hafner, J. Ab Initio Molecular Dynamics for Liquid Metals. Phys. Rev. B 47,

558 (1993).

[28] Kresse, G. & Furthmller, J. Efficient Iterative Schemes for Ab Initio Total-energy Calculations

Using a Plane-wave Basis Set. Phys. Rev. B 54, 11169 (1996).

[29] Blochl, P. E. Projector Augmented-wave Method. Phys. Rev. B 50, 17953 (1994).

[30] Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized Gradient Approximation Made Simple.

Phys. Rev. Lett. 77, 3865 (1996).

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multi-band origin in the ferromagnetic superconductor Sr0.5Ce0.5FBiS2. J. Phys.: Condens.

Matter 28, 195701 (2016).

13

Supplementary materials

Point-contact Spectroscopy

Point-contact spectroscopy experiments were performed using a home-built low-

temperature probe. The probe consists of a long stainless steel tube at the end of which

the probe-head is mounted. The probe head is equipped with a 100 threads per inch (t.p.i.)

differential screw that is rotated by a shaft running to the top of the cryostat. The screw

drives a tip-holder up and down with respect to the sample. The sample-holder is a circular

copper disc of diameter 1”. A cernox thermometer was mounted on the copper disc for

the measurement of the temperature. The temperature of the disc was varied by a heater

mounted on the same copper disc (as shown in Figure S1).

Tip

Sample

Sensor

Heater

Point-contact probe

Figure 5: The real image of the point-contact probe: A close view of the bottom part of

point-contact probe showing tip-sample assembly.

The tips were fabricated by cutting the metal wire (diameter 250µm) at an angle. The tip

was mounted on the tip holder and two gold contact leads were made on the tip with silver

epoxy. The samples were mounted on the sample holder and two silver-epoxy contact leads

were mounted on the sample as well. These four leads were used to measure the differential

resistance (dV/dI) across the point-contacts.

The point-contact spectra were captured by ac-modulation technique using a lock-in-

amplifier (Model: SR830 DSP). A voltage to current converter was fabricated to which a

dc input coupled with a very small ac input was fed. The output current had a dc and a

14

small ac component. This current passed through the point-contact. The dc output voltage

across the point-contact, V was measured by a digital multimeter (model: Keithley 2000)

and the ac output voltage was measured by a lock-in amplifier working at 721 Hz. The

first harmonic response of the lock-in could be taken to be proportional to the differential

change in the voltage dV/dI. Properly normalized dI/dV is plotted against V to generate

the point-contact spectrum. The software for data acquisition was developed in house using

lab-view.

Figure 6: Experimental arrangement of point-contact spectroscopy measurements: The

schematic diagram of electrical connections for point-contact measurements. It describes a lock-in

based modulation technique which is used to record the diffential resistance (dV/dI) (using a lock-

in amplifier, SR 830) with respect to the dc voltage drop across the junction (measured by a digital

multimeter, Kiethley 2000). The data is normalized to obtain the PC spectrum i.e. (dI/dV )N vs

V .

How did we determine the critical temperature (Tc)?

For all the point-contacts reported here we have measured the temperature (T ) depen-

dence of the point-contact resistance (R) with V = 0. The R - T data show a broad transition

to the superconducting state. We have drawn the slope of the R - T curves above and below

15

the onset of transitions. The temperature at which the two slopes for a given R - T curve

meet has been taken as the Tc for the corresponding point-contacts. It is important to note

that for the ballistic point-contacts we cannot measure the Tc as for such point-contacts

the contact-resistance depends only on fundamental constants and remain temperature in-

dependent. However, from the thermal limit point-contacts we learn that the Tc does not

have a strong dependence on contact size for a given sample.

Determination of the I − V characteristics corresponding to RM

For a point-contact between two different materials, the resistance is given by Wexler’s

formula1 that has contribution from both ballistic or Sharvin’s resistance (RS = 2h/e2

(akF )2)

and thermal or Maxwell’s resistance (RM = ρ(T )2a

). RS is always finite and depends only

on fundamental constants namely the Planck’s constant (h) and the charge of a single

electron (e). RM is directly dependent on the resistance of the materials forming the point-

contact and therefore becomes zero in the superconducting state. The measured data on

the point-contacts have contribution of both RM and RS. As per Wexler’s formula, the

total point-contact resistance is R = RS +RM . In order to extract the I − V corresponding

to the RM component alone we have subtracted the ballistic component (RS) from the

total resistance (R). The ballistic I − V for superconducting point-contacts is dominated

by Andreev reflection. The Andreev reflection dominated ballistic I − V was calculated

as discussed below using standard BTK theory2 for superconducting point-contacts and

the data before and after subtraction are presented in Figure 2 (e,f) and 3 (b,d) of the

manuscript.

As per BTK theory, the I − V characteristics of a superconducting point-contact can be

generated by using the expression of the current through a ballistic interface given by

Iballistic= C∫ +∞−∞ [f(E − eV )− f(E)][1 + A(E)−B(E)]dE

where, A(E) is the Andreev reflection probability and B(E) is the normal reflection

probability.

A(E) and B(E) were calculated using the following formula:

Since the superconducting phase is found to be unconventional, in order to make the

analysis more general, for our simulation we have used the modified BTK formula that also

accounts for finite quasiparticle lifetime (Γ) at the interface as described by Plecenik et.al.3:

A(E) = aa∗ and B(E) = bb∗, where the coefficients a and b are given by

16

a = u0v0/γ, b = −(u20 − v2

0)(Z2 + ιZ)/γ, where u20 and v2

0 are the probabilities of an

electronic state being occupied and unoccupied respectively:

u20 = 1

2[1 +

√(E+ιΓ )−∆2

E+ιΓ], v2

0 = 1− u20γ

2 = γγ∗, γ = u20 + (u2

0 − v20)Z2

Z is the dimensionless parameter used in BTK theory and it is directly proportional to

the strength of the potential barrier at the point-contact interface. For all our simulation

the value of Γ remained zero. The constant C has been determined by matching the scales

of the experimental data and the theoretical curves.

Additional experimental data

-1 0 -8 -6 -4 -2 0 2 4 6 8 1 0

0 .9

1 .0

1 .1

1 .2

1 .3

1 .4

0 k G

1 k G

2 k G

4 k G

6 k G

1 0 k G

1 6 k G

(dI/d

V)

N

V (m V )

-1 0 -5 0 5 1 0

0 .9 5

1 .0 0

1 .0 5

1 .1 0

1 .1 5

1 .2 0

1 .2 5

1 .3 0

1 .3 5

1 .8 K

3 K

4 K

6 K

7 K

8 K

(dI

/dV

)N

V (m V )

(a) (b)

Sample-I: ZrSiS/Ag

Figure 7: (dI/dV )N vs. V spectra on ZrSiS/Ag at different point of contact on the

same Sample-I as discussed in the main manuscript : (a) Magnetic field dependent point-

contact spectra at 1.8 K in thermal regime of transport on ZrSiS/Ag point-contact (b) Temperature

dependent point-contact spectra at 1.8 K in thermal regime of transport on ZrSiS/Ag point-contact.

This spectrum was obtained far away from the ballistic regime and consequently the flat region at

low bias is absent.

17

-3 -2 -1 0 1 2 3

1 .0 0

1 .0 5

1 .1 0

1 .1 5

1 .2 0

1 .2 5

(dI/

dV

) N

V (m V )

-3 -2 -1 0 1 2 3

1 .0

1 .1

1 .2

1 .3

(dI/

dV

)N

V (m V )

-3 -2 -1 0 1 2 3

1 .0

1 .1

1 .2

V (m V )

(dI/

dV

)N

-5 0 5

1 .0 0

1 .0 5

1 .1 0

1 .1 5

1 .2 0

(dI/

dV

) N

V (m V )

-4 -2 0 2 4

1 .0

1 .2

1 .4

1 .6

(dI/

dV

)N

V (m V )

-4 -2 0 2 4

1 .0 0

1 .0 5

1 .1 0

(dI/

dV

)N

V (m V )

-6 -4 -2 0 2 4 6

1 .0 0

1 .0 2

1 .0 4

1 .0 6

1 .0 8

(dI/

dV

) N

V (m V )

-3 -2 -1 0 1 2 3

1 .0

1 .2

1 .4

1 .6

(dI/

dV

)N

V (m V )

-2 -1 0 1 2

0 .9

1 .0

1 .1

1 .2

1 .3

1 .4

1 .5

(dI/

dV

)N

V (m V )

Sample-II: ZrSiS/Ag

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

Figure 8: (dI/dV )N vs. V spectra at different points of contact on another sample of ZrSiS named

as “Sample-II” using Ag tip.

-2 -1 0 1 2

0 .9 5

1 .0 0

1 .0 5

1 .1 0

1 .1 5

1 .2 0

(dI/

dV

) N

V (m V )

V (m V )

-6 -4 -2 0 2 4 6

0 .8

0 .9

1 .0

1 .1

1 .2

(dI/

dV

)N

V (m V )

-2 -1 0 1 2

1 .0 0

1 .0 5

1 .1 0

1 .1 5

(dI/

dV

) N

V (m V )

-2 -1 0 1 2

0 .9 8

1 .0 5

1 .1 2

(dI/

dV

) N

V (m V )

-2 -1 0 1 2

1 .0 0

1 .0 5

1 .1 0

1 .1 5

(dI/

dV

) N

V (m V )

-1 .5 -1 .0 -0 .5 0 .0 0 .5 1 .0 1 .5

1 .0

1 .1

1 .2

(dI/

dV

)N

V (m V )

-2 -1 0 1 2

0 .9 8

1 .0 5

1 .1 2

(dI/

dV

) N

V (m V )

-1 .0 -0 .5 0 .0 0 .5 1 .0

0 .9 5

1 .0 0

1 .0 5

1 .1 0

1 .1 5

1 .2 0

(dI/

dV

) N

V (m V )

(a)

Sample-II: ZrSiS/W

-1 .5 -1 .0 -0 .5 0 .0 0 .5 1 .0 1 .5

0 .9 8

1 .0 5

1 .1 2

(dI/

dV

)N

V (m V )

(e)

(b)

(h)(g)

(f)(e)(d)

(c)

Figure 9: (dI/dV )N vs. V spectra at different points of contact on another sample of ZrSiS named

as “Sample-II” using tungsten (W) tip.

18

Additional theoretical data

-2.0

-1.0

0.0

1.0

2.0

Γ X M Γ Z R A Z

Ene

rgy

E−

EF

(eV

)

Figure 10: Calculated bandstructure of ZrSiS including spin-orbit coupling, which opens up small

gap of ∼ 35meV for the Dirac cones near the Fermi surface.

-2.0

-1.0

0.0

1.0

2.0

Γ X M Γ Z R A Z 1 2 3 4 5

TDOSZrSiS

Ag tip

DOS(States/eV·u.c.)

Ener

gyE

−E

F(e

V)

Figure 11: Calculated bandstructure for the 3×1×1 [ZrSiS]4Ag6 superlattice indicating destruction

of all the Dirac points.

19

[1] Wexler, A. The size effect and the non-local Boltzmann transport equation in orifice and disk

geometry. Proc. Phys. Soc. 89, 927 (1966).

[2] Blonder, G. E., Tinkham, M. & Klapwijk, T. M. Transition from metallic to tunneling regimes

in superconducting microconstrictions: excess current, charge imbalance, and supercurrent

conversion. Phys. Rev. B 25, 4515 (1982).

[3] Plecenik, A., Grajkar, M. Benacka, S., Seidel, P. & Pfuch, A. Finite-quasiparticle-lifetime

effects in the differential conductance of Bi2Sr2CaCu2Oy/Au junctions.Phys. Rev. B 49, 10016

(1994).

20