# Single in situ Interface Characterization Composed of Niobium and a
Selectively Grown (Bi1-xSbx)2Te3 Topological Insulator Nanoribbon

Kevin Janßen  Peter Grünberg Insitute 9, Forschungszentrum Jülich GmbH, 52425
Jülich, Germany  Peter Grünberg Insitute 6, Forschungszentrum Jülich GmbH,
52425 Jülich, Germany  JARA-Fundamentals of Future Information Technology,
Jülich-Aachen Research Alliance, Forschungszentrum Jülich GmbH and RWTH Aachen
University, Germany  Philipp Rüßmann  Institute for Theoretical Physics and
Astrophysics, University of Würzburg, D-97074 Würzburg, Germany  Peter
Grünberg Institute 1 and Institute for Advanced Simulation 1,
Forschungszentrum Jülich and JARA, 52425 Jülich Germany  Sergej Liberda  Peter
Grünberg Insitute 9, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
JARA-Fundamentals of Future Information Technology, Jülich-Aachen Research
Alliance, Forschungszentrum Jülich GmbH and RWTH Aachen University, Germany
Michael Schleenvoigt  Peter Grünberg Insitute 9, Forschungszentrum Jülich
GmbH, 52425 Jülich, Germany  JARA-Fundamentals of Future Information
Technology, Jülich-Aachen Research Alliance, Forschungszentrum Jülich GmbH and
RWTH Aachen University, Germany  Xiao Hou  Peter Grünberg Insitute 6,
Forschungszentrum Jülich GmbH, 52425 Jülich, Germany  Abdur Rehman Jalil
Peter Grünberg Insitute 9, Forschungszentrum Jülich GmbH, 52425 Jülich,
Germany  JARA-Fundamentals of Future Information Technology, Jülich-Aachen
Research Alliance, Forschungszentrum Jülich GmbH and RWTH Aachen University,
Germany  Florian Lentz  Helmholtz Nano Facility, Forschungszentrum Jülich
GmbH, 52425 Jülich, Germany  Stefan Trellenkamp  Helmholtz Nano Facility,
Forschungszentrum Jülich GmbH, 52425 Jülich, Germany  Benjamin Bennemann
Peter Grünberg Insitute 9, Forschungszentrum Jülich GmbH, 52425 Jülich,
Germany  JARA-Fundamentals of Future Information Technology, Jülich-Aachen
Research Alliance, Forschungszentrum Jülich GmbH and RWTH Aachen University,
Germany  Erik Zimmermann  Peter Grünberg Insitute 9, Forschungszentrum Jülich
GmbH, 52425 Jülich, Germany  JARA-Fundamentals of Future Information
Technology, Jülich-Aachen Research Alliance, Forschungszentrum Jülich GmbH and
RWTH Aachen University, Germany  Gregor Mussler  Peter Grünberg Insitute 9,
Forschungszentrum Jülich GmbH, 52425 Jülich, Germany  JARA-Fundamentals of
Future Information Technology, Jülich-Aachen Research Alliance,
Forschungszentrum Jülich GmbH and RWTH Aachen University, Germany  Peter
Schüffelgen  Peter Grünberg Insitute 9, Forschungszentrum Jülich GmbH, 52425
Jülich, Germany  JARA-Fundamentals of Future Information Technology, Jülich-
Aachen Research Alliance, Forschungszentrum Jülich GmbH and RWTH Aachen
University, Germany  Claus-Michael Schneider  Peter Grünberg Insitute 6,
Forschungszentrum Jülich GmbH, 52425 Jülich, Germany  Stefan Blügel  Peter
Grünberg Institute 1 and Institute for Advanced Simulation 1,
Forschungszentrum Jülich and JARA, 52425 Jülich Germany  Detlev Grützmacher
Peter Grünberg Insitute 9, Forschungszentrum Jülich GmbH, 52425 Jülich,
Germany  JARA-Fundamentals of Future Information Technology, Jülich-Aachen
Research Alliance, Forschungszentrum Jülich GmbH and RWTH Aachen University,
Germany  Lukasz Plucinski  Peter Grünberg Insitute 6, Forschungszentrum Jülich
GmbH, 52425 Jülich, Germany  Thomas Schäpers  Peter Grünberg Insitute 9,
Forschungszentrum Jülich GmbH, 52425 Jülich, Germany  JARA-Fundamentals of
Future Information Technology, Jülich-Aachen Research Alliance,
Forschungszentrum Jülich GmbH and RWTH Aachen University, Germany
<EMAIL_ADDRESS>
###### Abstract

With increasing attention in Majorana physics for possible quantum bit
applications, a large interest has been developed to understand the properties
of the interface between a $s$-type superconductor and a topological
insulator. Up to this point the interface analysis was mainly focused on in
situ prepared Josephson junctions, which consist of two coupled single
interfaces or to ex-situ fabricated single interface devices. In our work we
utilize a novel fabrication process, combining selective area growth and
shadow evaporation which allows the characterization of a single in situ
fabricated Nb/$\mathrm{(Bi_{0.15}Sb_{0.85})_{2}Te_{3}}$ nano interface. The
resulting high interface transparency is apparent by a zero bias conductance
increase by a factor of 1.7. Furthermore, we present a comprehensive
differential conductance analysis of our single in situ interface for various
magnetic fields, temperatures and gate voltages. Additionally, density
functional theory calculations of the superconductor/topological insulator
interface are performed in order to explain the peak-like shape of our
differential conductance spectra and the origin of the observed smearing of
conductance features.

##  I Introduction

With the prediction of Majorana zero modes in $p$-wave superconducting
systems, a large interest has grown on the interface physics of three-
dimensional topological insulators (3D TIs) and $s$-wave superconductors [1,
2]. Recent studies tried to establish $p$-wave superconductivity by either
proximizing or doping a 3D TI with an $s$-wave superconductor [3, 4, 5, 6, 7,
8, 9, 10, 11, 12]. Due to the superconducting proximity effect, $p$-wave
superconductivity is expected to be established in the interface region and
give rise to Majorana zero modes. For the realization of Majorana zero modes,
a pristine interface between the two materials is of great importance, since
surface oxidation can lead to non-topological states [13, 14]. Currently, the
major platform for the analysis of these interfaces is the topological
Josephson junction, [15, 4, 5, 6, 7, 8] where 4$\pi$-contributions in the
Josephson current are predicted to be a proof of established $p$-wave
superconductivity [16].

Nevertheless, in a Josephson junctions, always two coupled
superconductor/topological insulator interfaces are investigated. Such a
coupled system gives rise to multiple Andreev reflections and leads to
additional effects like a change of the density of states in the junction
[17]. Furthermore, evidence for a topological proximity effect has been found
in angle-resolved photo-emission experiments [18, 19], which shows that a
comprehensive understanding of the interface physics between these two
material classes is not established, yet. Therefore, measurements on single
interfaces are needed to obtain an in-depth understanding of the interface
physics between superconductors and topological insulators. Up to now, such
single interfaces have been measured on a variety of systems, like exfoliated
flakes [20] or grown crystals [21, 22, 23], but were limited to two-point
configurations and ex-situ lift-off processes. However, ex-situ fabrication
can lead to degradation of the interface region due to oxidation or surface
roughening by Ar milling.

Here, we present a new fabrication process based on selective-area molecular
beam epitaxy growt in combination with shadow-mask evaporation. This process
enabled us to fabricate and analyze a clean in situ processed single
superconductor/topological insulator interface made out of Nb as a
superconductor and $\mathrm{(Bi_{0.15}Sb_{0.85})_{2}Te_{3}}$ (BST) as a
topological insulator. Furthermore, we investigated the response of the
differential conductance of the interface on varying temperature, magnetic
field and gate voltage. For the theoretical description of the transport,
density functional calculations of the superconductor/topological insulator
interface were performed, in order explain the origin of the measured
conductance features.

##  II Results and Discussion

###  II.1 Material Characterization

For the characterization of our $\mathrm{(Bi_{0.15}Sb_{0.85})_{2}Te_{3}}$
topological insulator layer, we conducted Hall measurements. Thereby, the
resistivity, two-dimensional carrier concentration, and charge carrier
mobility were determined to be $\rho=4.94\cdot 10^{-4}\,\mathrm{\Omega cm}$,
$n_{\mathrm{2D}}=4.44\cdot 10^{13}\mathrm{cm}^{-2}$, and
$\mu=285\,\mathrm{cm{{}^{2}}/Vs}$ (see Supplementary Information I).
Furthermore, the critical temperature and magnetic field of our Nb layer were
determined to be $T_{\mathrm{c}}=7.0\,$K and $B_{\mathrm{c}}=3.5\,$T,
respectively, and were associated with a superconducting band gap of
$\Delta_{\mathrm{Nb}}=1.06\,$meV, following BCS theory (see Supplementary
Information II).

In order to estimate the resistance contribution of the
$\mathrm{(Bi_{0.15}Sb_{0.85})_{2}Te_{3}}$ ribbon up to the normal contact, a
number of reference devices and their interfaces for several distances have
been measured. The $\mathrm{(Bi_{0.15}Sb_{0.85})_{2}Te_{3}}$ and the Nb film
of these reference devices were processed in the exact same run as the
presented device. Measurements at DC zero bias for different distances to the
superconducting interface lead to an interface resistance at zero bias voltage
of $R_{\mathrm{0}}=(200\,\pm\,200)\,\Omega$ and a resistance per length of the
100 nm $\mathrm{(Bi_{0.15}Sb_{0.85})_{2}Te_{3}}$ ribbon of
$R/l_{\mathrm{BST}}=(4.9\pm 0.3)\,\mathrm{k\Omega/\mu m}$ (see linear
regression in Supplementary Information III).

###  II.2 Differential Conductance Spectra

Next we analyze the transport across a single
$\mathrm{(Bi_{0.15}Sb_{0.85})_{2}Te_{3}}$/Nb interface in detail. The
corresponding device and the cross section of the interface are depicted in
Fig. 1 (a)-(c). Details on the sample fabrication can be found in the Methods
section.

Figure 1: (a) High-angle annular dark-field scanning transmission electron
microscopy image of the interface region. (b) Scanning electron micrograph of
the measured device with additional top-gate contact, corresponding to
(a)(iv). The Nb contacts are highlighted in light gray, the
$\mathrm{(Bi_{0.15}Sb_{0.85})_{2}Te_{3}}$ in green, the Ti normal contacts in
yellow and the top-gate in purple. (c) Scanning electron micrograph of the
device. The black line indicates the region shown in (b) while the orange
lines show the contacts where current is applied and voltage is measured.
Remaining Nb islands due to stencil mask process are not highlighted with any
color since they are not relevant for the transport measurements.

The normalized differential conductance $(dI/dV)/G_{N}$ as a function energy
shown in Fig. 2 for $T$=1.5 K and zero gate voltage. For this sample the
distance between the Nb electrode and the normal contact was 220 nm. In order
to gain detailed information on the interface properties itself, first the
resistance contribution $R_{\mathrm{BST}}$ of the
$\mathrm{(Bi_{0.15}Sb_{0.85})_{2}Te_{3}}$ ribbon up to the normal contact was
subtracted. Assuming an interface resistance of $R_{\mathrm{0}}=200\,\Omega$
at zero bias, as given above, we estimate this contribution to be
$R_{\mathrm{BST}}=1220\,\Omega$. The voltage drop at the interface itself was
determined by subtracting the according voltage drop in the nanoribbon segment
from the total voltage (for the raw data, see Supplementary Information IV).

Figure 2:  Normalized differential conductance data (blue) of the Nb/BST
interface $(dI/dV)/G_{N}$ for $R_{\mathrm{BST}}=1220\,\Omega$ and
$G_{\mathrm{N}}^{-1}=339.7\,\Omega$ at $T=1.5\,$K.

The normal state conductance $G_{\mathrm{N}}$ is determined by the mean
conductance at $\pm 6\,\Delta_{\mathrm{Nb}}$. The high interface quality from
our in situ process becomes apparent in the large conductance increase around
zero bias voltage, as expected for a high contribution of Andreev reflection.
This agrees well with the results of Schüffelgen et al. [24], who derived an
interface transparency of 0.95, on a Josephson junction device, fabricated
with the same in situ approach.

Concerning the Blonder-Tinkham-Klapwijk (BTK) model, such a conductance
increase is generally expected, but the sharp and peak-like form does not
agree with the model. For the original BTK model the increase is expected to
start close to $\Delta$ and not significantly before. A broadening could be
achieved with the consideration of inelastic scattering, as presented by
Pleceník et al. [25]. However, the overall peak-like shape can still not be
obtained. Furthermore, our temperature dependent data can exclude a critical
current based origin, since the peak height and shape is stable up to 4.5 K,
as discussed later. Additionally, the high $p$-doping of our ribbon results in
a low contribution of the topological surface states to the overall current.
Therefore, we do not expect that a modeling extension in this manner would be
reasonable. However, the BTK model neglects the superconducting proximity
effect, which is expected to be especially distinct in high quality
interfaces. Therefore, a density functional theory analysis of our interface
has been carried out in order to investigate the interface coupling between
the TI ribbon and the Nb (see Sec. II.6).
In order to estimate the error of the peak height, we additionally modelled
our data for an upper and a lower limiting case of the interface resistance.
The upper case was chosen by the error of the linear regression to be
$R^{\mathrm{up}}_{\mathrm{0}}=400\,\Omega$. In order to not exceed the maximal
value of $2G_{\mathrm{N}}$ for ideal Andreev reflection, the lower value was
limited to $R^{\mathrm{low}}_{\mathrm{0}}=146\,\Omega$. This procedure results
in a maximum peak height of 2 and a minimum peak height of 1.3. In any case a
significant zero bias conductance increase is justified.

###  II.3 Temperature Dependence

The temperature dependence of the interface properties has been measured for
temperatures up to 10 K. As done for the measurement shown in the previous
section, the additional resistance of $R_{\mathrm{BST}}=1220\,\Omega$ has been
subtracted (for the raw data, see Supplementary Information VI). The
differential conductance as a function of energy is shown in Fig. 3(a). A
prominent conductance peak is observed at zero energy with basically no change
up to 4.5 K. At a temperature of $6.5$ K the peak height is significantly
reduced, whereas at around 10 K, which is already above the superconducting
transition temperature of our Nb, no features are observed anymore. This
confirms that the zero bias conductance peak originates from the
superconducting Nb electrodes.

Figure 3: (a) Differential interface conductance for the Nb electrodes in the
superconducting state, i.e. temperatures up to 6.5 K and in the normal
conducting state at 9.9 K. The curves are offset by $5\,\mathrm{e^{2}/h}$. (b)
Differential conductance without subtraction of $R_{\mathrm{BST}}$ for
different gate voltages.

With the robustness of the peak height and width up to temperatures of 4.5 K,
which corresponds to half of the superconducting band gap of the Nb film, we
can exclude a spurious zero bias conductance, as discussed in [26]. Such a
spurious zero bias peak can arise when local currents exceed the critical
current and can also lead to a voltage dependent decrease of the differential
conductance.

###  II.4 Gate Dependence

The effect of the top gate on the differential resistance without subtraction
of $R_{\mathrm{BST}}$ is shown in Fig. 3(b). The gating behaviour of our
$\mathrm{(Bi_{0.15}Sb_{0.85})_{2}Te_{3}}$ ribbon reveals $p$-type conductance
of our composition, since the conductance at zero bias increases with more
negative gate voltage. This agrees well with the findings of Weyrich et al.
[27] who estimated the transition from $n$-type to $p$-type doping for
$\mathrm{(Bi_{1-x}Sb_{x})_{2}Te_{3}}$ in electron transport for $x=0.30-0.49$.
For the spectra no systematic behaviour with gate voltages up to $\pm 10$ V is
observed. Note, the increasing peak height with decreasing gate voltage
results from the general increase of conductance by the gate voltage. When
subtracting the influence of the gate voltage, no systematic behavior of the
peak with gate voltage is observed (see Supplementary Information V). Since,
the gate contact is directly above the
$\mathrm{(Bi_{0.15}Sb_{0.85})_{2}Te_{3}}$/Nb interface region, gating of the
interface region and the nanoribbon is assured. Due to the expected screening
of the superconducting Nb above the interface region, it is plausible that the
interface properties do not change with gate voltage. Since, a mismatch in
Fermi velocities between Nb and the TI material contributes to the effective
barrier strength, this also indicates that both Fermi velocities are not
changed significantly. In case of our $p$-doped
$\mathrm{(Bi_{0.15}Sb_{0.85})_{2}Te_{3}}$ ribbon this is reasonable, since the
Fermi level is expected to be located in the valence band which has a high
density of states.

###  II.5 Magnetic Field Dependence

The out-of-plane magnetic field dependence has been investigated for magnetic
fields up to 6 T. The differential conductance of the interface is shown in
Fig. 4(a). As before, a resistance of $1220\,\Omega$ has been attributed to
the BST ribbon segment up to the normal contacts and has been subtracted to
achieve the resistance of the interface itself. With increasing magnetic field
we find a suppression of the zero bias conductance peak. From 2.4 T to 3.2 T
we observe a region which is driven out of superconductivity for increasing
bias voltage. For magnetic fields above $3.6\,$T the superconductivity of our
Nb electrodes is completely suppressed, as expected ($B_{c}=3.5\,$T, see
Supplementary Information II) and no conductance increase for low bias
voltages is observed anymore. In contrast to that, a zero bias conductance dip
is now observed in our measurements at 4-6 T. We have strong indications that
this is an electron-electron interaction based phenomenon originating from the
$\mathrm{(Bi_{0.15}Sb_{0.85})_{2}Te_{3}}$ film, as previously reported by
Stehno et al. [21, 28]. Additional investigations reveal that the dip is also
present in a four terminal measurement only containing the
$\mathrm{(Bi_{0.15}Sb_{0.85})_{2}Te_{3}}$, see Supplementary Information VII.
This allows us to rule out the re-entrance effect as a possible explanation,
as reported for the data of Finck et al. [22]. The dip is stable with magnetic
field up to 6 T and vanishes with increasing temperature, since its not
present at 9.9 K, see Fig. 3(a). This behaviour agrees with the findings of
Stehno et al. [21], who attributed the dip to electron-electron interaction.

Figure 4: (a) Differential interface conductance for different magnetic
fields. (b) Waterfall plot of the differential interface conductance for
magnetic fields up to $2.2\,$T. The curves are offset by
$6\,\mathrm{e^{2}/h}$. (c) Position of the conductance dips, highlighted in
(b) by green dots, for different magnetic fields.

Figure 4(b) shows the differential conductance up to 2.2 T in a waterfall
plot. We observe conductance dips which are marked by green dots. From 0.5 T
the magnetic field response of the dip position can be described by a linear
relation, as shown in Fig. 4(c). The position is clearly outside the
superconducting band gap of our Nb layer and even a second set of dips with a
similar behaviour, starting at 9 meV for zero magnetic field can be observed.
Such dips have been observed before with different possible explanations [20,
29, 30]. Because of the response to magnetic field and the high voltage at
which the dips occur, we expect these features to originate from the bulk Nb
contact and to not be related to the interface region.

###  II.6 Superconducting density of states of the superconductor-TI interface
from density functional theory

In this section we will discuss the origin of the shape of our conductance
peak and the smearing in the conductance dips. To this end, we conducted
state-of-the-art DFT calculations of the density of states in the interface
region for various chemical potentials $\mu$. We employ the Kohn-Sham
Bogoliubov-de Gennes method taking into account all details of the electronic
structure to model superconductivity [31], which is described in Sec. IV.3.
Our DFT results for the superconductor-topological insulator (SC-TI) interface
are summarized in Fig. 5. With varying position of the chemical potential
$\mu$ in the TI, the density of states at the chemical potential $\rho(E=\mu)$
changes drastically when $\mu$ lies in the bulk valence band (VB) or
conduction band (CB) of the TI compared to the case when it resides inside the
bulk band gap (see also Supplementary Section IX). In the latter case, only
the topological surface state contributes to $\rho(E=\mu)$ and very few states
are available for hybridization with the electronic structure of the
superconductor. This is seen in the contribution to the normal state density
at $\mu$, integrated over the TI region, which is reported in Tab. 1. This
fact is illustrated in Fig. 5(a) where the charge density at the chemical
potential is visualized throughout the SC-TI heterostructure for a $p$-type
TI.

Figure 5(b) shows the corresponding superconducting density of states (DOS),
integrated over (i) the superconductor, (ii) the first, and (iii) the second
quintuple layer (QL) of the TI in the SC-TI heterostructure. When compared to
the coherence peak of a clean Nb surface [31], we find that the increased
hybridization with states of bulk-conducting TI leads to a distinct broadening
of the superconducting coherence peak by more than a factor two. We measure
this with the full width at half maximum (FWHM) of the coherence peak that is
given in Tab. 1. We stress that the coherence peak mainly originates from the
Nb layers in the simulation and is strongly suppressed in the local DOS within
the TI, where it decays with the distance from the surface. Thus, the
broadening of the coherence peak is a result of the inverse proximity effect
[32].

Additionally, stronger in-gap features are visible in the DOS which further
washes out the sharp coherence peaks coming from Nb. We attribute the in-gap
features to the reduced gap size in the TI which are only proximity-coupled
without any intrinsic superconductivity in the TI. A comparison of the first
to the second QL (QL1/2) reveals the decay of the proximity-induced gap in the
TI electronic structure [33] which is evident by the flattening-out of the DOS
with larger distance from the SC contact. We expect this flattening of the
DOS, which gets exceptionally clear in QL2, to be the origin for the sharp and
peak like shape of our differential conductance spectra. It is noteworthy that
we observe similar behavior for $\mu$ inside the VB and the CB where in both
cases the normal state charge density at $\mu$ in the TI is roughly a factor 2
larger than when $\mu$ lies in the TI gap (see Tab. 1).

Our DFT data for the SC/TI interface with $p$-type Bi2Te3 can be linked to the
transport data obtained for our samples. The transport measurements proved the
high quality of the interface with a robust zero-bias conductance peak. Our
DFT data qualitatively proves that a good electrical coupling, which is the
case in the in situ-grown samples of this work, leads to significant
hybridization and a proximity effect in the TI. This in turn results in a
broadening of the superconducting coherence peaks and a narrowing of the DOS
inside the superconducting band gap. According to the BTK model, the transport
features are closely connected to the shape of the superconducting DOS. The
broadening of the coherence peak thus can be connected to the largely feature-
less conductance data. Therefore, we conclude that our DFT data qualitatively
explains the origin of the sizable broadening in the zero bias conductance
peak.

Figure 5: (a) DFT-calculated contribution from the Fermi energy to the charge density in the superconductor/TI heterostructures for $p$-type Bi2Te3. (b) Superconducting density of states in the superconductor (Nb) and the first and second quintuple layers of the TI. The grey background shows the superconducting DOS for a clean Nb surface [31]. The black bars indicates the full width at half maximum (FWHM) of the Nb coherence peaks. Table 1: Average full width at half maximum $\langle\mathrm{FWHM}\rangle$ (in units of the intrinsic gap size of the superconductor $\Delta_{0}$) of the coherence peaks for different locations of the chemical potential ($\mu$) in the TI. The FWHM is averaged over the first 5 layers in the Nb superconductor and over the coherence peak at positive and negative energies. The third column shows the normal state DOS integrated in the TI in 1/eV.  $\mu$ of the TI | $\langle\mathrm{FWHM}\rangle$ | $\int_{V_{\mathrm{TI}}}\rho(\mathbf{r},E=\mu)d^{3}r$ | reference
---|---|---|---
in gap | 0.39 | 0.49 | this work
in VB | 0.49 | 1.32 | this work
in CB | 0.47 | 0.88 | this work
– | 0.22 | – | Ref. 31

##  III Conclusion

In summary, we presented a new in situ fabrication scheme for the fabrication
of pristine high quality superconductor/topological insulator single
interfaces. With the analysis of our differential conductance data we can
confirm the high interface quality with a resulting zero bias conductance
increase by a factor of almost 1.7. Furthermore, we deliver a comprehensive
analysis of the interface including studies of perpendicular magnetic field,
temperature and top gate dependence. The robustness of the zero bias
conductance peak to temperatures up to 4.5 K excludes a critical current
induced origin and confirms that the peak originates from Andreev reflection
at the interface. The gate dependent measurements showed that the interface
properties do not change significantly with gate voltage. Furthermore, we
could reveal signatures of electron-electron interaction in
$\mathrm{(Bi_{0.15}Sb_{0.85})_{2}Te_{3}}$ and confirm the interpretation of
Stehno et al. [21]. Since, our differential conductance spectra are not well
represented by the BTK modeling, a DFT-based analysis has been carried out.
Our DFT-based analysis provides further evidence for the strong electrical
coupling that influences the proximity effect in the SC/TI heterostructure.
This results in strong hybridization and a broadening of the superconducting
coherence peak at the interface, which is in line with our transport data.
Furthermore, a strong decrease of the DOS is observed inside the gap for the
first QLs. We expect this decrease to be the reason for the peak-like shape of
our differential conductance spectra and the deviation to the Blonder-Tinkham-
Klapwik model. With our investigations on a single in situ interface of
superconductor and topological insulator we deliver a solid foundation for
understanding the interface physics between these two material classes and
contribute to the research on topological quantum bits.

##  IV Methods

###  IV.1 Sample fabrication

For the fabrication of our devices we utilize a combination of selective-area
growth and shadow mask evaporation technique [24, 34, 35]. The fabrication
step sequence is illustrated in Fig. 6. In order to fabricate our substrates,
a 4” silicon (111) wafer ($\rho>2000\,\Omega\mathrm{cm}$) is first thermally
oxidized with 7 nm $\mathrm{SiO_{2}}$ and then a 30 nm $\mathrm{Si_{3}N_{4}}$
film is deposited via plasma-enhanced chemical vapor deposition at
$350^{\circ}$C. In the next step, the trenches for the selective-area growth
are etched in the $\mathrm{Si_{3}N_{4}}$ layer utilizing electron beam
lithography and $\mathrm{CHF_{3}}$/$\mathrm{O_{2}}$-based reactive ion etching
[36]. For the stencil mask 300 nm $\mathrm{SiO_{2}}$ and 100 nm
$\mathrm{Si_{3}N_{4}}$, are deposited. The stencil mask $\mathrm{Si_{3}N_{4}}$
layer is structured by an electron beam lithography process and
$\mathrm{CHF_{3}}$/$\mathrm{O_{2}}$ reactive ion etching, see Figs. 6(a) and
(b), respectively. A 12% buffered HF etch is utilized to under etch
$\mathrm{Si_{3}N_{4}}$ to define the stencil bridge structure. Simultaneously,
the the predefined trenches in the lower double layer are revealed as well, as
depicted in Fig. 6(c).

Figure 6: Schematic illustration of the fabrication step sequence, with
$\mathrm{Si_{3}N_{4}}$ in blue, $\mathrm{SiO_{2}}$ in yellow, Si in black,
resist in brown, topological insulator in green, Nb in grey, Ti normal
contacts in dark yellow and the Ti top gate in purple.

Prior to the crystal growth, the sample is etched with 1$\%$ hydrofluoric acid
to remove surface oxides. Immediately after,
$\mathrm{(Bi_{0.15}Sb_{0.85})_{2}Te_{3}}$ is selectively grown via molecular
beam epitaxy. The specific composition is chosen such that the Fermi level is
close to the Dirac point [27]. In our selective-area growth scheme, the
$\mathrm{(Bi_{0.15}Sb_{0.85})_{2}Te_{3}}$ is only growing in the predefined Si
trenches which expose the Si(111) surfaces. During the crystal growth, the
sample is under constant rotation to assure a homogeneous distribution of the
components from the different effusion cells and a smooth growth underneath
the $\mathrm{Si_{3}N_{4}}$ bridge. Subsequently, a 11 nm thick Nb film is
deposited by electron beam evaporation under a fixed angle. During this
evaporation the $\mathrm{Si_{3}N_{4}}$ bridge is shadowing part of the
$\mathrm{(Bi_{0.15}Sb_{0.85})_{2}Te_{3}}$ and pre-defines the contacts. For
passivation a stoichiometric 3 nm $\mathrm{Al_{2}O_{3}}$ layer is deposited on
the whole sample under rotation (d). Afterwards, the shadow mask is removed by
mechanical scratching with a cleanroom tissue (e), while the sample is covered
with a thin layer of PMMA.

For the fabrication normal contact fingers Ti is deposited by electron beam
evaporation and lift-off with a previous Ar-milling step to remove residual
surface oxides (f). In the next step, the superconducting contacts are
structured by another lithography step (g) and reactive ion etching (h). Prior
to the etching, the $\mathrm{Al_{2}O_{3}}$ capping on top of the Nb is removed
by a dip in 0.2$\%$ hydrofluoric acid. In the last step, the Ti top-gate
contact is fabricated (i). Therefore, 16 nm $\mathrm{HfO_{2}}$ are deposited
with atomic layer deposition. Subsequently, the Ti top-gate contact is
prepared by a PMMA-based lift-off procedure. Scanning electron micrographs of
the device measured in this work are depicted in Figs. 1(c) and (d). The
100-nm-wide selectively-grown $\mathrm{(Bi_{0.15}Sb_{0.85})_{2}Te_{3}}$
nanoribbon is contacted on both ends by superconducting Nb electrodes. The two
Ti normal contacts are placed at different positions along the nanoribbon. In
the high-angular annular dark-field scanning transmission electron microscopy
(HAADF-STEM) image shown in Fig. 1(a) it can be seen that the interface region
between Nb and BST is limited to an intermixing region of a couple quintuple
layers (See detailed larger scale image in Supplementary Material VIII) [37].
The atomic resolution gives no indication for a damage of the BST underneath
the Nb layer, which confirms the expectations of a clean interface.

###  IV.2 Magnetortransport measurements

Our measurements have been conducted in a He-4 variable temperature insert
setup with a base temperature of 1.5 K and a perpendicular magnetic field of
up to 6 T. Thereby, we conducted quasi-DC lock-in amplifier based current
driven differential conductance measurements at a frequency of $31.7\,$Hz and
with an amplitude of $I_{\mathrm{AC}}=100\,$nA. The bias dependence was
investigated by superimposing a DC current in the range
$\pm$30$\,\mathrm{\upmu A}$ between both superconducting electrodes. As
illustrated in Fig. 1(d), the differential conductance was measured between
one superconducting contact and one of the normal contacts.

###  IV.3 Density functional theory

In our density functional theory (DFT) calculations we employ the full-
potential relativistic Korringa-Kohn-Rostoker Green function method (KKR) [38]
as implemented in the JuKKR code [39]. Superconducting properties are
calculated with the help of the Kohn-Sham-Bogoliubov-de Gennes extension to
the JuKKR code [31]. We parametrize the normal state exchange correlation
functional using the local density approximation (LDA) [40]. We use an
$\ell_{\mathrm{max}}=2$ cutoff in the angular momentum expansion of the space
filling Voronoi cells around the atomic centers, where the exact (i.e. full-
potential) description of the atomic shapes is taken into account [41, 42].

The structure we study is an interface between the $s$-wave superconductor Nb
and the prototypical TI Bi2Te3, which was previously discussed in Ref. 43. The
TI film we use in the calculations for this work consist of 2QL thick Bi2Te3
in contact to nine layers of Nb(111) lattice matched to the in-plane unit cell
of the TI. In order to study a shift of the TI Fermi level relative to the
electronic structure of the superconductor we employ a renormalization of the
energy integration weights during self-consistency in accordance to Lloyd’s
formula in the KKR method [44].

The series of DFT calculations in this study are orchestrated with the help of
the AiiDA-KKR plugin [45] to the AiiDA infrastructure [46]. This has the
advantage that the full data provenance (including all values of numerical
cutoffs and input parameters to the calculation) is automatically stored in
compliance to the FAIR principles of open research data [47]. The complete
data set, that includes the full provenance of the DFT calculations, is made
publicly available in the materials cloud archive [48, 49]. The source codes
of the AiiDA-KKR plugin and the JuKKR code are published as open source
software under the MIT license [50, 39].

##  V Author Contributions

K.J., S.L. and A.R.J. designed the devices. K.J. and S.L. fabricated the
samples in the clean room. F.L. and S.T. performed all e-beam writing steps.
M.S., P.S., G.M. were responsible for TI growth and optimization. B.B. grew
the Nb, $\mathrm{Al_{2}O_{3}}$ and $\mathrm{HfO_{2}}$ layers. K.J. performed
the electrical measurements of the devices and the analysis. E.Z. helped with
the setup of the electrical measurement system. X.H. and A.R.J. performed the
HAADF-STEM measurements. P.R. performed the DFT calculations. K.J., P.R., and
T.S. wrote the manuscript with contributions of all coauthors. T.S., L.P.
supervised the project.

##  VI Acknowledgement

We thank Elmar Neumann for TEM preparation and Joachim Mayer for feedback on
STEM measurements. We thank the board of directors at Forschungszentrum Jülich
for financial support doctoral projects within the framework of the strategic
further development of method-oriented research. PR and SB acknowledge funding
by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under
Germany’s Excellence Strategy – Cluster of Excellence Matter and Light for
Quantum Computing (ML4Q) EXC 2004/1 – 390534769 and PR thanks the Bavarian
Ministry of Economic Affairs, Regional Development and Energy for financial
support within High-Tech Agenda Project “Bausteine für das Quantencomputing
auf Basis topologischer Materialien mit experimentellen und theoretischen
Ansätzen”. We are grateful for computing time granted by the JARA
Vergabegremium and provided on the JARA Partition part of the supercomputer
CLAIX at RWTH Aachen University (project number jara0191).

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Supplementary Material: Single in situ Interface Characterization Composed of
Niobium and a Selectively Grown (Bi1-xSbx)2Te3 Topological Insulator
Nanoribbon

##  SI Hall measurements of the topological insulator layer

Hall measurements have been conducted on 100 nm wide reference devices of the
exact same molecular beam epitaxy growth and Nb deposition run as the sample
presented in the main manuscript. Hall measurements on two reference devices
were conducted. The data with corresponding Hall slopes is shown in
Supplementary Fig. S1.

Supplementary Figure S1:  Hall voltage as a function of magnetic field
measured for two reference devices. The colors blue and red distinguish
between the forward and backward scan of the magnetic field. Scanning electron
micrographs of the corresponding devices and the electrical contacting are
shown in the inset. The superconducting contacts are highlighted in grey, the
normal contacts in yellow, the $\mathrm{(Bi_{0.15}Sb_{0.85})_{2}Te_{3}}$
ribbon in green.

The charge carrier density is determined from:

$n_{\mathrm{2D}}=\frac{I_{\mathrm{x}}}{e}\cdot\frac{1}{\frac{dV_{\mathrm{Hall}}}{dB_{\mathrm{z}}}}=4.44\cdot
10^{13}\,\mathrm{cm}^{-2}\,,$ (S1)

with $I_{\mathrm{x}}=100\,$nA the bias current, $e$ the electron charge, and
$dV_{\mathrm{Hall}}/dB_{\mathrm{z}}$ the mean slope of both measurements
consisting of forward and backward sweep direction. The slope of the Hall
curve reveals p-type doping of the $\mathrm{(Bi_{0.15}Sb_{0.85})_{2}Te_{3}}$
ribbon. Furthermore, we determined the resistivity $\rho$ from the results of
our linear regression presented in Supplementary Sec. SI:

$\rho=a\cdot w\cdot t=4.94\cdot 10^{-4}\,\Omega\mathrm{cm}\,,$ (S2)

with $a=4.94\,\mathrm{k\Omega/\upmu m}$ resistance per unit length,
$w=100\,$nm the ribbon width and $t=10$ nm the ribbon thickness. The mobility
of our $\mathrm{(Bi_{0.15}Sb_{0.85})_{2}Te_{3}}$ ribbon can then be estimated
by:

$\mu=\frac{t}{\rho\cdot e\cdot
n_{\mathrm{2D}}}=285\,\frac{\mathrm{cm}^{2}}{\mathrm{Vs}}\,.$ (S3)

##  SII Characterisation of the niobium layer

The thickness of the Nb layer has been determined to 11 nm and the
$\mathrm{Al_{2}O_{3}}$ capping to 3 nm using X-ray-reflectometry. The critical
temperature and critical magnetic field were determined to $T_{c}=7.0\,$K and
$B_{c}=3.5\,$T, respectively, by two-point-measurements of the left Nb contact
(cf. Supplementary Fig. S2). The offset value of 268 $\Omega$ is the residual
resistance of the cables in the measurement setup.

Supplementary Figure S2:  Resistance of Nb layer measured in a two-point
configuration for (a) varying temperature and (b) varying perpendicular
magnetic field. The colors blue and red distinguish between the forwards and
backwards direction.

The measured temperature values were re-calibrated by an additional
temperature curve with a Lakeshore CX-1030-SD-HT-1.4L temperature sensor
(Serial number X147729) on the exact sample position. Afterwards, the scaling
of the temperature axis was adjusted to these re-calibrated temperature
values. The superconducting gap was determined according to BCS theory:

$\Delta_{\mathrm{BCS}}=1.764\,k_{\mathrm{B}}T_{\mathrm{c}}=1.06\,\mathrm{meV}\;.$
(S4)

##  SIII Resistance per length of topological insulator ribbon

In order to estimate the additional resistance of the
$\mathrm{(Bi_{0.15}Sb_{0.85})_{2}Te_{3}}$ (BST) nanoribbon from the interface
to the superconductor until the normal contact is reached, the resistance has
been measured for several distances of the normal contact to the interface
using the transmission line method. The measurements were conducted on 100 nm
wide devices on a reference sample. The
$\mathrm{(Bi_{0.15}Sb_{0.85})_{2}Te_{3}}$ and the Nb on this sample have been
processed in the exact same run as the presented device in the main
manuscript. Supplementary Fig. S3 shows the acquired resistances for different
normal contact distances to the superconducting interface.

Supplementary Figure S3:  Differential resistance $R$ at zero bias voltage for
different interfaces and distances $d$. The different colors distinguish
between different devices. The black line shows the linear regression of the
data, leaving out the two data points for $d$ larger 1$\,\mathrm{\mu m}$.

Note that for distances above 1$\,\mu$m a low film quality was observed on
certain parts of the $\mathrm{(Bi_{0.15}Sb_{0.85})_{2}Te_{3}}$ nanoribbon by
scanning electron microscopy. The reason for this is the very large
$\mathrm{Si_{3}N_{4}}$ shadow mask on these particular devices, which impedes
a uniform growth. Consequently, this leads to exceptionally high resistance
values which do not describe the behaviour of a closed high quality film.
Therefore, the two data points for distances above 1$\,\mu$m were left out
from the linear regression. The resistance of the nanoribbons segment can be
described by:

$R=a\cdot d+b\;,$ (S5)

where $a$ is the resistance per unit length and $b$ is the residual
resistance, which is the $\mathrm{(Bi_{0.15}Sb_{0.85})_{2}Te_{3}}$/Nb
interface resistance. For our measurement data we extracted:

$a=(4.94\pm 0.34)\,\mathrm{k}\Omega/\mu\mathrm{m}\,,$ (S6)

and

$b=(0.20\pm 0.20)\,\mathrm{k}\Omega\,.$ (S7)

Note, that the error on the interface resistance $b$ is equally large to the
value itself. Therefore, the value can only be used as an indication when
compared to other results.

##  SIV Raw Data of the differential conductance spectra

In Supplementary Fig. S4 the raw data of the differential conductance at 1.5 K
and zero gate voltage are shown.

Supplementary Figure S4:  Raw data of the differential conductance $dI/dV$ for
different bias voltages.

##  SV Gate Dependence of the Differential Conductance

In Supplementary Fig. S5 the differential conductance after subtraction of the
influence of the gate voltage at zero bias voltage is shown. Therefore, the
change in resistance at zero bias voltage has been subtracted from the curves
with non-zero gate voltage, before calculating the differential resistance.
Fig. S5 shows that no systematic behavior with gate voltage is present.

Supplementary Figure S5:  Differential conductance after subtracting the
influence of the gate voltage at zero bias voltage.

##  SVI Raw Data of the differential conductance for various temperatures

In Supplementary Fig. S6 the raw data of the differential conductance for
different temperatures at zero gate voltage are shown.

Supplementary Figure S6:  Raw data of the temperature dependence of the
differential conductance $dI/dV$ for different bias voltages.

##  SVII Zero bias dip in the magnetoconductance of the topological insulator
ribbon

In several of our differential conductance measurements we observe a zero bias
conductance dip for magnetic fields above 3.6 T. At this magnetic field
strength the superconductivity of the Nb contacts is completely suppressed
since the magnetic field is above the critical field of our Nb film. However,
when suppressing the superconductivity by increasing the temperature above the
critical temperature $T_{\mathrm{c}}$ this zero bias resistance peak was not
observed, as can be seen in the main manuscript. Stehno et. al. also observed
a zero bias dip in their measurements of a exfoliated BiSbTeSe single crystal
[21]. The conductance dip has also been stable with magnetic field but
unstable with increasing temperature, which is consistent with our
observations. They suggested that the origin is the Altshuler–Aronov effect
(electron-electron interaction) which develops in the crystal due to disorder.

In order to investigate the origin of this zero bias resistance peak in our
devices, we conducted four-point measurements of our
$\mathrm{(Bi_{0.15}Sb_{0.85})_{2}Te_{3}}$ nanoribbon (see Supplementary Fig.
S7(a)).

Supplementary Figure S7:  (a) Four-point differential conductance measurement
as a function of voltage of a $\mathrm{(Bi_{0.15}Sb_{0.85})_{2}Te_{3}}$ ribbon
for various magnetic fields. (b) Waterfall plot of the differential
conductance of the left interface with a 200 nm distant close normal contact.
The curves are offset by $0.1\,\mathrm{e^{2}/h}$. (c) Waterfall plot of the
differential conductance of the right interface for the same device. The
curves are offset by $0.02\,\mathrm{e^{2}/h}$. In this case with a 800 nm
distant far normal contact. Scanning electron micrographs of the corresponding
devices and the electrical contacting are shown in the inset. The
superconducting contacts are highlighted in grey, the normal contacts in
yellow, the $\mathrm{(Bi_{0.15}Sb_{0.85})_{2}Te_{3}}$ ribbon in green.

We observed a zero bias conductance dip which is stable up to 6 T, which is
the highest field we applied. Due to the four-point configuration of the
measurement the voltage drop only occurs over the
$\mathrm{(Bi_{0.15}Sb_{0.85})_{2}Te_{3}}$ nanoribbon. Considering that
temperature and a bias voltage, which is microscopically a change of the
electron band structure, destroys this effect which leads to the zero bias
conductance dip and magnetic field does not, this behaviour fits the expected
behavior of the Altshuler-Aronov effect. Furthermore, this is also consistent
with our observation that the dip is more pronounced when the normal contact
is further apart from the interface, as can be seen in Supplementary Fig.
S7(b-c). When the normal contact is close to the interface the contribution of
the $\mathrm{(Bi_{0.15}Sb_{0.85})_{2}Te_{3}}$ nanoribbon segment to the
measurement signal is comparably small and no zero bias conductance dip is
observed (cf. Supplementary Fig. S7(b)). In contrast, for a large contact
separation, the contribution of the nanoribbon to the measurement signal is
high and the conductance dip is observed (cf. Supplementary Fig. S7(c)).

##  SVIII Transmission Electron Microscopy Data

In Supplementary Fig. S8 a large scale transmission electron microscopy image
of the interface region is shown. It can be seen that the interdiffusion
region is limited to 2-3 quintuple layers, which roughly corresponds to 2-3
nm. The width of the interdiffusion region agrees well with the results of
Jalil et al. [37]. Furthermore, it can be seen that the BST is brighter on the
bottom half, than on the top half. This indicates that the lower part is more
Bi heavy compared to the upper part, concerning its composition.

Supplementary Figure S8:  Large-scale high-angle annular dark-field scanning
transmission electron microscopy image of the Nb/BST interface region. The
interdiffusion region of 2-3 nm is highlighted by the green box.

##  SIX Density functional theory data for bulk-insulating and $p$-type SC/TI
heterostructures

In Supplementary Fig. S9 we compare the normal state charge density at the
Fermi level for bulk-insulating (a) and $p$-type TI (b) in contact to Nb. This
illustrates the increased availability of states for hybridization. The
superconducting density of states (b,d) for these two situations show a
broadening of the Nb coherence peak indicated by the larger FWHM, which is
discussed in the main text. Note, due to the limited resolution of the energy
sampling points of the DOS, the absolute high of the coherence peaks can not
be compared between Fig. S9(a) and Fig. S9(b).

Supplementary Figure S9:  Comparison of bulk-insulating (a,b) and $p$-type TI
(c,d) in the SC/TI heterostructure. (a,c) Distribution of the normal state
density at the chemical potential throughout the Nb/Bi2Te3 heterostructure.
(b,d) Superconducting density of states showing a broadening of the coherence
peak if $\mu$ resides not in the TI bulk band gap (indicated by the larger
FWHM in d compared to b).