# On the floating of the topological surface state on top of a thick lead
layer:
The case of the Pb/Bi2Se3 interface

Oreste De Luca  Laboratorio di Spettroscopia Avanzata dei Materiali, STAR IR,
Via Tito Flavio, Università della Calabria, 87036, Rende (CS), Italy
Dipartimento di Fisica, Università della Calabria, Via P.Bucci, 87036
Arcavacata di Rende (CS), Italy  Igor A. Shvets  Tomsk State University,
634050 Tomsk, Russia  Sergey V. Eremeev  Institute of Strength Physics and
Materials Science, Russian Academy of Sciences, 634055 Tomsk, Russia  Ziya S.
Aliev  Baku State University, AZ1148 Baku, Azerbaijan  Marek Kopciuszynski
Sincrotrone Trieste S.C.p.A., Area Science Park, I-34012 Basovizza, Trieste,
Italy  Alexey Barinov  Sincrotrone Trieste S.C.p.A., Area Science Park,
I-34012 Basovizza, Trieste, Italy  Fabio Ronci  Istituto di Struttura della
Materia-CNR (ISM-CNR), Via del Fosso del Cavaliere, 00133 Roma, Italy  Stefano
Colonna  Istituto di Struttura della Materia-CNR (ISM-CNR), Via del Fosso del
Cavaliere, 00133 Roma, Italy  Evgueni V. Chulkov  Departamento de Polímeros y
Materiales Avanzados: Física, Química y Tecnología, Facultad de Ciencias
Químicas, Universidad del País Vasco UPV/EHU, 20080 San Sebastián/Donostia,
Spain  Donostia International Physics Center (DIPC), 20018 Donostia-San
Sebastián, Basque Country, Spain  Centro de Física de Materiales (CFM-MPC),
Centro Mixto CSIC-UPV/EHU, 20018 Donostia-San Sebastián, Basque Country, Spain
Saint Petersburg State University, 199034 Saint Petersburg, Russia  Raffaele
G. Agostino  Laboratorio di Spettroscopia Avanzata dei Materiali, STAR IR, Via
Tito Flavio, Università della Calabria, 87036, Rende (CS), Italy  Dipartimento
di Fisica, Università della Calabria, Via P.Bucci, 87036 Arcavacata di Rende
(CS), Italy  Marco Papagno  Laboratorio di Spettroscopia Avanzata dei
Materiali, STAR IR, Via Tito Flavio, Università della Calabria, 87036, Rende
(CS), Italy  Dipartimento di Fisica, Università della Calabria, Via P.Bucci,
87036 Arcavacata di Rende (CS), Italy  Roberto Flammini
<EMAIL_ADDRESS>Istituto di Struttura della Materia-CNR (ISM-CNR), Via
del Fosso del Cavaliere, 00133 Roma, Italy

(today)

###### Abstract

The puzzling question about the floating of the topological surface state on
top of a thick Pb layer, has now possibly been answered. A photoemission study
of the interface made by Pb on Bi2Se3 for different temperature and adsorbate
coverage condition, allowed us to demonstrate that the evidence reported in
the literature can be related to the surface diffusion phenomenon exhibited by
the Pb atoms, which leaves the substrate partially uncovered. Comprehensive
density functional theory calculations show that despite the specific
arrangement of the atoms at the interface, the topological surface state
cannot float on top of the adlayer but rather tends to move inward within the
substrate.

##  I Introduction

Triggering the migration of a topological surface state (TSS) from a substrate
into an adsorbate layer is an important goal as it means the
topology–protected properties of a substrate could be transferred to a
suitable conventional material. Research fields like superconductivity,
Majorana physics or spintronics might strongly benefit from the spin-orbit
texture or from the resilience to disorder and defects, inherited from the
topological matter [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13].

The subtle details underlying this phenomenon have not been fully explained.
Underpinning of the TSS migration is a transformation of the spin–orbit
texture of electronic bands of the substrate and of the adlayer due to
matching at the interface. Provided that the spin-orbit coupling strength is
comparable to other relevant terms of the Hamiltonian describing the
topological insulator (TI), [5, 8, 14] band hybridization can take place and
new physical phenomena may occur, such as the migration of the TSS. [4, 15, 9,
10, 13]

The first reports on the effects of Pb growth on top of a TI have led to
contrasting results. On Bi2Te3 D.A. Estyunin et al. [16] predict the
withdrawal of the TSS towards the substrate bulk, while C.X. Trang et al. [17]
claim the possibility to transfer the TSS of a TlBiSe2 substrate up to the 20
monolayer (ML) thick Pb adlayer. If that proved true, there could be a huge
step towards the incorporation of topological matter into functional
electronic devices [18].

The recent studies about Pb on layered TI reported in the literature mainly
focus on the superconducting nature of the interface [19, 20] or on the
exploitation of its magnetic properties [16, 21]. Interestingly, these
investigations also shed light on the delicate phase of the growth and on the
subsequent formation of a wetting layer (WL), within which the adsorbate and
substrate atoms strongly interact forming an alloy of unknown stoichiometry.

Stimulated by these recent results we undertook an experimental and
theoretical study of the Pb/Bi2Se3 interface. Scanning photoemission
microscopy (SPEM), spatially resolved X-Ray photoelectron spectroscopy (XPS)
and angle resolved photoelectron spectroscopy ($\mu$–ARPES) measurements were
carried out at the Elettra synchrotron radiation source. Moreover, Density
Functional Theory (DFT) calculations were performed considering a sharp
interface to predict the localization of the TSS in the case of a thin (1 ML)
and of a thick (7 ML) Pb layer to unveil the nature of the interface and of
its electronic structure as it starts to form.

##  II Experimental and Computational details

The Bi2Se3 samples are (0001)-oriented single crystals grown by the modified
Bridgman method. These samples have been previously characterized by X-ray
diffraction. The Bi2Se3 surface was prepared by in-situ exfoliation, in an
ultra-high-vacuum (UHV) chamber. Lead was sublimated from a temperature-
controlled Knudsen cell. All depositions were performed at liquid nitrogen
(LN) temperature with a deposition rate of 0.33 Å/min. We considered 1 ML of
Pb equal to 0.286 nm, a value corresponding to the interplane distance along
the (111) direction.

The measurements were carried out at the Spectromicroscopy beamline [22]. The
photons were focused through a Schwarzschild objective in order to obtain a
sub–$\mu$m beam size spot. For the present measurements, the total energy
resolution was set to 70 meV with an angle resolution of 0.6∘. The ARPES maps
were acquired at 74 eV and 27 eV photon energies, along the
${\bar{\text{K}}}{\bar{\Gamma}}{\bar{\text{K}}}$ direction. The vertical
stripes appearing in the ARPES maps are due to a imperfections of the entrance
slit of the detector. The subtraction of such stripes would have led to a loss
of relevant information, this is why we decided to display the maps as
measured, without any data handling. The stripes do not influence in any way
the results and the conclusions of our work. The measurements were performed
under UHV in the 10-10 mbar range. The SPEM intensity images were obtained by
integrating the photoemission spectra within the relative energy window
($\approx$ 3.5 eV). The XPS spectra were acquired at 74 eV and angle
integrated, with an acceptance angle of $\pm$ 7.5${}^{\circ}\times\pm
0.3^{\circ}$ corresponding to $\pm$ 0.3 Å${}^{-1}\pm$ 0.012 Å-1, around the
${\bar{\Gamma}}$ point. The photoemission measurements were performed at LN
temperature.

Electronic structure calculations were carried out within the density
functional theory using the projector augmented-wave (PAW) method [23] as
implemented in the VASP code [24, 25]. The exchange-correlation energy was
treated using the Perdew-Burke-Ernzerhof (PBE) type generalized gradient
approximation (GGA) [26]. The Hamiltonian contained scalar relativistic
corrections and the spin-orbit coupling was taken into account. In order to
describe the van der Waals interactions we made use of the DFT-D3 approach
[27]. Spin-orbit coupling was always included when performing relaxations. For
analysis of interactions between Pb atoms and the Bi2Se3 substrate we used the
projected crystal orbital Hamilton population (pCOHP) method [28, 29]
implemented within Local-orbital basis suite towards electronic structure
reconstruction code [30]. To simulate the Pb films on the Bi2Se3-$1\times 1$
surface we used a slab consisting of 8 quintuple layers (QLs) of the substrate
with the PBE-optimized bulk lattice constants with Pb layers placed on both
slab surfaces. The atomic positions of Pb as well as atoms of the topmost QL
of Bi2Se3 were optimized. For consideration of the $6/5\times 6/5$
Pb(111)/Bi2Se3 models the supercells composed of the single Pb(111)-$6\times
6$ layer on top of the single QL of Bi2Se3-$5\times 5$ was used. The geometry
optimization was performed until the residual forces on atoms became smaller
than 1 meV/Å. The 10$\times 10\times$1 and 2$\times 2\times$1 $k$-point meshes
were used to sample the $1\times 1$ and $5\times 5$ surface Brillouin zones,
respectively.

##  III Results and Discussion

In Fig. 1(a) the ARPES map displaying the band structure of the pristine
substrate is shown. The TSS and the Dirac point (DP) at about –0.3 eV below
the Fermi level are readily visible at ${\bar{\Gamma}}$, along with the bulk
valence bands [31, 32]. Fig. 1(b) features the ARPES map recorded after
deposition of 20 ML of Pb. The several electron–like parabolas with vertex at
${\bar{\Gamma}}$ are attributed to, at least, four quantum well states (QWS)
[33, 34], demonstrating the flatness and uniformity of the adlayer, owing to
the growth protocol. In Fig. 1(c), the energy distribution curve (EDC)
extracted from Fig. 1(b) better highlights the features corresponding to the
QWS. The complete burial of the substrate surface is demonstrated by the
corresponding survey scan displayed in Fig. 1(d). After the Pb growth no
traces of Bi or Se were recorded. The most noticeable feature, however, is the
absence of the TSS in Fig. 1(b).

This result suggests that either the topological protection is destroyed or
the TSS is buried under the thick Pb adlayer. To this aim, a Pb wedge was
fabricated on the Bi2Se3 substrate, as the TSS migration process may have
taken place below the probing depth of the photoemission process. In Fig. 2(a)
a SPEM intensity image of the wedge is displayed. The wedge is composed of
four areas with 1, 2, 4 and 10 ML of Pb, where $\mu$-ARPES spectra were
collected. The use of the SPEM allowed us to pick up the different areas of
the wedge without spatial superposition. A notable difference is seen between
Fig. 2(b,c) where traces of the Bi2Se3 TSS are recorded, and Fig. 2(d,e),
where the TSS is, at variance, absent. The QWS are not detected, as they start
to form for larger deposits [35, 36].

Figure 1: (a) ARPES map of the pristine Bi2Se3 surface along the
${\bar{\text{K}}}$${\bar{\Gamma}}$${\bar{\text{K}}}$ high symmetry direction.
At ${\bar{\Gamma}}$ the Dirac point and the TSS are noted. (b) ARPES map of
the same sample surface after deposition of 20 ML of Pb. QW states are visible
without any feature related to the TSS. (c) Line profile (EDC) corresponding
to the dashed line of panel (b). In (d) the corresponding XPS survey scans are
shown. All spectra have been taken at h$\nu$=74 eV. The zero binding energy
corresponds to the Fermi level. Figure 2: (a) SPEM intensity map ($6000\times
6000$ $\mu$m2) taken on the Pb-5$d_{5/2}$ core level at about 18 eV binding
energy. The areas exhibiting different adsorbate thickness are displayed in
false colors. The ARPES images (b-e) and the core level spectra (f-h) were
taken on the corresponding zones of the Pb wedge, at $h\nu=74$ eV photon
energy. The dashed rectangle highlights the blow-up shown in panel (g). Panel
(h) features the corresponding Se-$3d$ spectra.

The core levels in Fig. 2(f) feature the Pb-5$d$ doublet consisting of two
components of which one, at lower binding energy, can be attributed to the Pb
atoms in their bulk environment (Pbel, where ‘el’ stands for ‘elemental’) and
the other (Pbwl), at higher binding energy, attributed to the WL, where a
strong interaction of the Pb atoms with the substrate is expected [21, 16].
The Bi-5$d$ doublet shows two components as well: one is attributed to the
Bi2Se3 environment, Bisub, while the other, at low binding energy, to the
wetting layer (Biwl) [37, 21, 16]. The overall intensity of the Bi-5$d$ peaks
decreases and becomes negligible as the amount of Pb increases, demonstrating
that an effective burial of the substrate occurs only for high coverage. It is
known from the literature that Pb follows the “electronic growth” mode: flat-
topped islands start to form whose height and stability are driven by the
compromise between the quantum size effect and adsorbate kinetics. [38, 39,
40]

In the blow-up of the dashed square area displayed in Fig. 2(g), it is noticed
that the intensity of the WL component increases comparing it to the substrate
component and eventually becomes dominant. Our hypothesis is that either
residual areas of the WL remain uncovered or a segregation process of Bi atoms
on top of the Pb layer occurs. The Se-3$d$ core levels shown in Fig. 2(h) on
the other hand, confirm that the Bi2Se3 is fully covered by the Pb layer at
higher coverage.

Yet, as is well known, when a Pb layer is prepared at low temperature and then
brought to room temperature (RT), a diffusion process occurs, inducing a
reduction of the surface coverage [41]. In order to verify this phenomenon,
the sample was allowed to return to RT, keeping it on a carousel under UHV.
After 12 hours the sample was checked for contamination, and new measurements
were performed. In Fig. 3(a-d), the ARPES maps taken on the same wedge areas
as before are displayed. All areas show some intensity in correspondence to
the Bi2Se3 TSS, as indicated by the black arrows.

In the corresponding core level spectra displayed in Fig. 3(e), it is noticed
that Pbel almost disappears for low coverage while surviving for a coverage
higher than 4 ML; The intensity of the Pbwl component is clearly larger than
Pbel up to 10 ML. Comparing the Bi-5$d$ doublet components in Fig. 3(f) with
those of Fig. 2(g), we notice a reversed evolution of Bisub and Biwl. For low
coverage, the Bisub of Fig. 3(f), is completely transformed in Biwl, owing to
the increased Bi-Pb chemical reaction. Increasing the coverage, the Biwl
component loses intensity in favour of Bisub. This can only be explained by
the formation of large uncovered areas. In the literature, this phenomenon was
reported in the case of thin films of Pb grown on both insulators and metals
(namely Pb/Si and Pb/Cu), where the increase of the island height occurs at
the expense of the surface coverage, as verified by photoemission [35, 42],
spatially resolved techniques [43, 44], and explained by a model based on the
confinement of free electrons to a quantum well. [45].

Figure 3: In panels (a-d) the ARPES maps and in (e-g) the core level spectra
taken on the Pb wedge after leaving the sample to return to RT. h$\nu$=74 eV
photon energy. The arrows indicate the faint TSS of the substrate. The dashed
rectangle highlights the blow-up shown in panel (f). In panel (g), the
corresponding Se-$3d$ core level spectra are displayed.

Accordingly, the Se-3$d$ doublet in Fig. 3(g), does not show any change in the
lineshape or intensity, suggesting a poor interaction with the lead atoms.
This can be rationalised by considering a chemically shifted component below
our energy resolution or showing a negligible intensity. In the case of the
Pb/MnSb2Te4 [21] and at the Pb/Mn(Bi0.7Sb0.3)2Te4 [16] interfaces, the PbTe
bond does form, retaining the –2 valence state, and thus not showing any
chemical shift with respect to the Te in the Bi2Te3 substrate [21]. Moreover,
the photoionization cross-section of the Se-3$d$ with respect to the Bi-5$d$
results 10 times smaller [46].

The evolution of the valence bands and of the loss spectra, as shown in Fig.
S1 and Fig. S2 of the Supplemental Material [[SeeSupplementalMaterialat]supp],
seems to confirm that the surface gets uncovered: during the growth at low
temperature the spectra gradually show the features of an elemental Pb layer;
Instead if the sample is left to return to RT, the spectra show evidence again
of the Bi and Se outer shells [48]. We also notice the photoemission intensity
just below the Fermi level that, starting from the peak related to the TSS of
the substrate, evolves in a strong metallic behaviour upon growth at low
temperature, eventually decreasing at RT (Fig. S1 [47], black arrows).

Some metals, such as Ag or Au, when deposited using the two–step procedure
(where firstly the deposition is made at low temperature and subsequently the
sample is allowed to return to RT), undergo an improvement of their flatness
and uniformity [49]. Pb is an exception [50, 36] and the above results
represent another hint that its peculiar behaviour at different temperatures
can explain the detection of the TSS at RT after growth of a thick Pb deposit.
In this regard, we cannot exclude the hypothesis of a collective motion of the
lead atoms in contrast to the classical nucleation: an explosive island
formation could take place owing to the large mismatch (18%) between the
Pb(111) and the Bi2Se3(0001) lattices [51, 52, 53]. However, the presence of
the WL could mitigate the lattice strain and should be taken into account.

Figure 4: (a) SPEM intensity map of the wedge after an additional deposit of
10 ML at LN temperature. The image, displayed in false colors, was measured on
the Pb-5$d_{5/2}$ core level peak and acquired at $h\nu=74$ eV photon energy.
The size of the image is of $6000\times 6000$ $\mu$m2. Panels (b-d) and (f-h),
ARPES maps recorded at low and room temperature, respectively. In panel (e)
evidence of 3 QWs as from the EDC taken at 0.4 Å-1 in panel (d).

In order to ascertain the influence of the temperature, we deposited further
10 ML at LN temperature, trying to bury again the whole interface. In Fig.
4(a) the image of the novel wedge is displayed. It is now formed by only three
zones as the thin one on top was too small to allow a reliable measurement.
The ARPES results displayed in Fig. 4(b-d) show no evidence of the TSS. We
emphasize that at 74 eV photon energy, the technique is extremely sensitive to
the surface, probing only few Å of the Pb/Bi2Se3 interface. The 20 ML region,
though, displays QWS, as proved by the EDC presented in Fig. 4(e). As a matter
of fact, if the deposit as well as the measurements, are carried out with no
increase of the temperature, the burial of the TSS is again ensured. By
leaving the sample to return to RT, the maps of Fig. 4(f–h) show only blurred
features recalling the substrate bulk valence band of the pristine surface
(below –0.5 eV) and still no TSS.

With the aim to understand what happens to the interface we used a photon
energy of 27 eV so as to increase the bulk sensitivity. The result is shown in
Fig. 5 : panel (a) features the map recorded on the pristine surface for
comparison, while in panels (b–d) a clear evidence of the TSS is shown again,
demonstrating incontrovertibly that the TSS is not floating on top of the Pb
layer, but survives underneath. In Fig. 5(d), we also attribute the “V-shape”
feature (grey dashed line) to the Bi2Se3 bulk valence band. At lower binding
energy, we notice a bright feature displaying an electron-like curvature
(dotted line), absent in the pristine surface. We tentatively attribute this
band to a QW state. Paradoxically, the TSSs in the present case are more
evident with respect to the low coverage case of Fig. 3(a-d), suggesting an
increase of the uncovered areas. The reason can be related to the elastic
energy accumulated by a thicker adlayer that overcomes the interaction of the
Pb atoms with the substrate, favouring the dewetting phenomenon. One can argue
that QSE effects are better seen for smaller height islands and for lower
temperatures due to the increased energy stability however, in the present
case, due to the strong interaction with the substrate, a larger amount of Pb
is needed to form pure and crystalline islands, as part of the adsorbate atoms
compose the WL.

Figure 5: ARPES maps taken at 27 eV photon energy on the pristine sample (a)
and on the three different zones relative to the wedge of Fig. 4(a),
corresponding to 12 ML, 14 ML and 20 ML, panels (b,c,d), respectively. The
sample was allowed to return to RT. See text.

It is remarkable that the maps of Fig. 5(c) and (d) reproduce well enough the
map reported by C.X. Trang et al. [17] for 17 ML of Pb on TlBiSe2, where the
TSS survives among the QWS. Our interpretation of the data based on the
probing depth of the photoelectrons however, does not invoke band
hybridization, but rather the dewetting phenomenon. The electronic structure
most probably results from the overlap of the features relative to the flat
lead islands with those relative to the substrate. Nonetheless, a question
remains on the precise localization of the TSS.

Figure 6: (a) Side view of the relaxed 1 ML Pb/Bi2Se3-$6/5\times 6/5$
interface (one of three models is shown, see text). (b) Top view of the
structure; Only two topmost (Pb and Se) layers are shown. (c) In-plane
averaged electrostatic potentials $V_{z}$ for Pb/Bi2Se3 with Pb in bridge
position obtained within $1\times 1$ relaxed cell and for those with
interatomic distances extracted from $6/5\times 6/5$ model with Pb in bridge
(br-$\langle E_{b}\rangle$) and fcc-hollow (fcc-$\langle E_{b}\rangle$)
positions (red and blue rhombuses in (b), respectively). Zero $z$ corresponds
to the middle of the first vdW gap. (d) Surface electronic structure of the 1
ML Pb/Bi2Se3 interface with Pb in the bridge position. Spatial distributions
of the surface states I, II, and III marked with black squares are shown in
right outsets. (e) Potential bending $\Delta V_{z}$ within the Bi2Se3 slab
($z=0$ corresponds to the middle of the third vdW gap). (f) The electronic
spectrum of 7 ML Pb/Bi2Se3. Black squares mark the Dirac-like TSS (I) and the
interface state (II) for which the in-plane averaged charge densities are
shown in panel (g); $z=0$ corresponds to the interface plane.

To clarify the interaction of the adsorbed layer with the substrate and reveal
how the formation of the Pb/Bi2Se3 interface affects the TSS we performed DFT
calculations. Considering 1 ML of Pb(111) placed on top of the Bi2Se3 surface
within a $1\times 1$ cell we found that the most favored geometry is that when
Pb atom is in the fcc-hollow position. The next preferred geometry is the
bridge position having total energy higher by 120 meV/cell. The hcp-hollow and
most unfavorable top positions follow. However, the Pb ML stability determined
in this way cannot be relied upon, since the lateral lattice constant of
Pb(111) is by $\approx$18 % smaller than that of Bi2Se3 and hence the Pb ML
placed on the substrate within a $1\times 1$ cell is unrealistically expanded.

To overcome the huge lattice mismatch we constructed the ($6\times
6$)/($5\times 5$) (briefly $6/5\times 6/5$) superlattice models simulating
incommensurate Pb/Bi2Se3 interface (Pb(111) - $6\times 6$ on top of the Bi2Se3
– $5\times 5$) for which the initial Pb–Pb interatomic distance (3.44 Å) is
compressed only by $\approx 1.7$ %, with respect to the experimental one (3.5
Å). Three possible ($6/5\times 6/5$) models, corresponding to A (0,0), B
($\frac{1}{3}$, $\frac{2}{3}$), and C ($\frac{2}{3}$, $\frac{1}{3}$) hexagonal
layers of Pb(111), were constructed. The relaxed structure of the latter model
is shown in Fig. 6(a,b). After relaxation, the Pb–Pb distances vary from 3.37
to 3.64 Å and the Pb layer acquires a corrugation with a rippling of
$\Delta_{z}\approx 0.75$ Å (see side view in the Fig. 6(a)). In these
superlattice models the Pb atoms appear in more or less distorted ”top” (with
single Pb-Se bond), ”bridge” (where Pb atoms are two-fold coordinated with
surface Se atoms) and ”hollow” (three-fold coordinated) positions. Estimation
of Pb–Se bonding energies via integrated projected crystal orbital Hamilton
population (IpCOHP) calculations [28, 29, 30] shows that the bond strength
between Pb and neighboring Se atoms can vary in a wide range: from 1.77 (1.97,
2.10) eV to 3.14 (3.56, 3.65) eV for A(B,C)-derived ($6/5\times 6/5$) models.
Remarkably, there is no correspondence between the number of nearest Se
neighbors and the value of the bonding energy. For example, three-fold
coordinated Pb atoms can be found both at the lower and upper limits of this
range. The mean Pb–Se bond energy $\langle E_{b}\rangle$ averaged over 36 Pb
atoms of each ($6/5\times 6/5$) model and over three models, amounts to 2.55
eV. The Pb atoms possessing the Pb–Se bond energies closest to $\langle
E_{b}\rangle$ are found in distorted top and bridge positions. Among the
three-fold coordinated Pb atoms also can be found those having bond energy
relatively close to $\langle E_{b}\rangle$. Two of such Pb atoms, in ”bridge”
and ”fcc-hollow” positions are outlined in Fig. 6(b) with red and blue
rhombuses, respectively.

Extracting the local interlayer distances within these $1\times 1$ rhombuses
(averaging the $z$ coordinates in the Se and Bi layers, which also have a
small rippling), we constructed the $1\times 1$ cells with Pb in bridge and
fcc-hollow positions (br-$\langle E_{b}\rangle$ and fcc-$\langle
E_{b}\rangle$, respectively). The in-plane averaged electrostatic potentials
$V_{z}$ for these artificial slabs are shown in Fig. 6(c). As can be seen,
they are close to each other as well as close to the $V_{z}$ of the cell with
the Pb atom in the bridge position. In the latter case, the positions of Pb
layer and of the topmost Bi2Se3 QL were obtained directly within relaxation of
the $1\times 1$ cell (br-($1\times 1$)). In contrast, the comparison of
fcc-$\langle E_{b}\rangle$ and fcc-($1\times 1$) electrostatic potentials
highlights the large difference when considering the topmost QL (Fig. S3(a)
[47]). This is due to the difference between the Pb–Se interlayer spacing
obtained from ($6/5\times 6/5$) model (2.29 Å) and from the relaxation of the
overstretched Pb(111) layer (1.86 Å). Thus, one can conclude that although the
bridge position (within $1\times 1$ cell) is energetically the second
preferred one, it represents much better the average bonding at the
incommensurate interface between 1 ML Pb(111) and the Bi2Se3 surface.

The electronic band structure calculated for the 1 ML Pb/Bi2Se3 interface with
the Pb atom in the bridge ($1\times 1$) position, is shown in Fig. 6(d). Apart
from the bulk projected bands shaded in tan, the weights of the surface states
are shown by circles of different colours corresponding to the localization in
the Pb layer, in the first and in the second QLs (as shown in the key). In
order to visualize the position of the maximum density of the states within
the atomic lattice we added three outsets, corresponding to the three black
boxes in the band structure (labelled I, II and III).

As can be seen in Fig. 6(e), due to the large potential bending $\Delta
V_{z}$, obtained by subtracting the potentials of Bi2Se3 with and without the
Pb adlayer, the states localized in the first, and even in the second QL,
result to be shifted downward in energy. As a consequence, the DP of the
former TSS inherited from the Bi2Se3 substrate falls in the local gap, at
about $-1$ eV binding energy. This state is spread within the topmost QL in
the close vicinity of the DP, then it mixes with the Pb states far from the
Brillouin zone center, where it experiences a strong localization on the Se
and Pb atomic layers (see outsets in Fig. 6(d)).

It is remarkable that the electronic spectrum of the less realistic
fcc-($1\times 1$) structure, leads to very similar results (Fig. S3(b) [47]).
Nonetheless, in this case, the Pb and Bi2Se3 states are mixed to a greater
extent. Thus, it can be concluded that regardless of the position of the Pb
monolayer on the Bi2Se3 surface (and one can expect the same effect in the
incommensurate Pb layer), the potential bending shifts the former TSS into a
local gap, in striking contrast with the ARPES observation, where the TSS
remains in the principal gap. The latter should indicate that the continuous
Pb monolayer is not formed, but a more complex interaction of Pb with the TI
surface takes place.

Next, we considered a relatively thick Pb film of 7 ML (Fig. 6(f)). The
spectrum contains a large number of Pb-film states, which cannot be compared
with the dispersion of the measured Pb quantum well states, since the Pb
adlayer is overstretched in this geometry and we will focus here on the states
of the Bi2Se3 substrate. Similarly to earlier studies on Bi2Se3 and other
related TIs [54, 4, 55, 56, 57, 58], the formation of the interface results in
the appearance of an interface state along with the development of a new Dirac
state in the principal band gap which departs from the interface region and
moves back to the second QL. Indeed, we see the interface state showing the
Dirac-like crossing dispersion in the local gap at about $-1$ eV. Traces of
this state can be followed up the Fermi level for large $k_{\|}$, where it
overlaps with the set of Pb states and undergoes a localization between the
topmost QL and the adlayer.

The new TSS with the DP is observed in the middle of the principal band gap
(at about $-0.35$ eV), mostly localized in the second QL, but decaying
outwards and penetrating even into the Pb film (Fig. 6(g)). The precursor of
this state is visible below the bulk conduction band at $\approx-0.2$ eV, in
the spectrum of the heterostructure with a single Pb layer (Fig. 6(d)).
Therefore, we can conclude that the TSS of the Bi2Se3 substrate can survive
below the relatively thick Pb adlayer, by shifting into the second QL
regardless of the peculiarities of the atomic structure at the interface.

All results reported above lead to a fundamental question on whether a TI made
by V-VI layered compounds coupled with Pb, can represent a suitable system to
induce the migration of the TSS. Apart from the issues related to the
stability of the a nanometric-thin Pb layer at different temperatures, the
formation of a WL possibly made of a disordered ternary alloy can strongly
affect the electronic structure. Ultimately, even in the case of a sharp model
interface, the main condition for the relocation of the TSS in the adlayer, is
the absence of an interface potential.

##  IV Conclusions

A joint theoretical and experimental study of the behaviour of the TSS at the
Pb/Bi2Se3 interface was carried out. DFT calculations reveal that the TSS of
the substrate escapes the interface region moving downward into the bulk. The
detection of the TSS after lead deposition should be attributed to the
uncovering of the TI substrate, as a result of surface diffusion of the lead
atoms, as demonstrated by the core-level and angle resolved photoemission
measurements done for different temperature and adsorbate coverage conditions.

##  V Acknowledgements

S.V.E. acknowledges support from the Government research assignment for ISPMS
SB RAS, project FWRW-2022-0001. I.A.Sh. gratefully acknowledges ﬁnancial
support from the Ministry of Education and Science of the Russian Federation
within State Task No. FSWM-2020-0033. E.V.C. acknowledges support from Saint
Petersburg State University (Project ID No. 94031444).

## References

  * Hutasoit and Stanescu [2011] J. A. Hutasoit and T. D. Stanescu, Phys. Rev. B 84, 085103 (2011).
  * Hirahara  _et al._ [2011] T. Hirahara, G. Bihlmayer, Y. Sakamoto, M. Yamada, H. Miyazaki, S.-i. Kimura, S. Blügel, and S. Hasegawa, Phys. Rev. Lett. 107, 166801 (2011).
  * Hirahara  _et al._ [2012] T. Hirahara, N. Fukui, T. Shirasawa, M. Yamada, M. Aitani, H. Miyazaki, M. Matsunami, S. Kimura, T. Takahashi, S. Hasegawa, and K. Kobayashi, Phys. Rev. Lett. 109, 227401 (2012).
  * Wu  _et al._ [2013] G. Wu, H. Chen, Y. Sun, X. Li, P. Cui, C. Franchini, J. Wang, X.-Q. Chen, and Z. Zhang, Scientific Reports 3, 1233 (2013).
  * Bahramy  _et al._ [2012] M. S. Bahramy, P. D. C. King, A. de la Torre, J. Chang, M. Shi, L. Patthey, G. Balakrishnan, P. Hofmann, R. Arita, N. Nagaosa, and F. Baumberger, Nature Communications 3, 1159 (2012).
  * Yoshimi  _et al._ [2014] R. Yoshimi, A. Tsukazaki, K. Kikutake, J. G. Checkelsky, K. S. Takahashi, M. Kawasaki, and Y. Tokura, Nature Materials 13, 253 (2014).
  * Essert  _et al._ [2014] S. Essert, V. Krueckl, and K. Richter, New Journal of Physics 16, 113058 (2014).
  * Shoman  _et al._ [2015] T. Shoman, A. Takayama, T. Sato, S. Souma, T. Takahashi, T. Oguchi, K. Segawa, and Y. Ando, Nature Communications 6, 6547 (2015).
  * Seixas  _et al._ [2015] L. Seixas, D. West, A. Fazzio, and S. B. Zhang, Nature Communications 6, 7630 (2015).
  * Soumyanarayanan  _et al._ [2016] A. Soumyanarayanan, N. Reyren, A. Fert, and C. Panagopoulos, Nature 539, 509 (2016).
  * Costa  _et al._ [2018] M. Costa, A. T. Costa, W. A. Freitas, T. M. Schmidt, M. Buongiorno Nardelli, and A. Fazzio, ACS Omega 3, 15900 (2018), pMID: 31458234, https://doi.org/10.1021/acsomega.8b01836 .
  * Chae  _et al._ [2019] J. Chae, S.-H. Kang, S. H. Park, H. Park, K. Jeong, T. H. Kim, S.-B. Hong, K. S. Kim, Y.-K. Kwon, J. W. Kim, and M.-H. Cho, ACS Nano 13, 3931 (2019), pMID: 30951288, https://doi.org/10.1021/acsnano.8b07012 .
  * Holtgrewe  _et al._ [2020] K. Holtgrewe, S. K. Mahatha, P. M. Sheverdyaeva, P. Moras, R. Flammini, S. Colonna, F. Ronci, M. Papagno, A. Barla, L. Petaccia, Z. S. Aliev, M. B. Babanly, E. V. Chulkov, S. Sanna, C. Hogan, and C. Carbone, Scientific Reports 10, 14619 (2020).
  * Waugh  _et al._ [2016] J. A. Waugh, T. Nummy, S. Parham, Q. Liu, X. Zhang, A. Zunger, and D. S. Dessau, npj Quantum Materials 1, 16025 (2016).
  * Wang  _et al._ [2013] X. Wang, G. Bian, T. Miller, and T.-C. Chiang, Phys. Rev. B 87, 235113 (2013).
  * Estyunin  _et al._ [2022] D. A. Estyunin, T. P. Makarova, K. A. Kokh, O. E. Tereshchenko, A. M. Shikin, and I. I. Klimovskikh, Phys. Rev. B 106, 155305 (2022).
  * Trang  _et al._ [2020] C. X. Trang, N. Shimamura, K. Nakayama, S. Souma, K. Sugawara, I. Watanabe, K. Yamauchi, T. Oguchi, K. Segawa, T. Takahashi, Y. Ando, and T. Sato, Nature Communications 11, 159 (2020).
  * Breunig and Ando [2022] O. Breunig and Y. Ando, Nature Reviews Physics 4, 184 (2022).
  * Surnin  _et al._ [2018] Y. A. Surnin, I. I. Klimovskikh, D. M. Sostina, K. A. Kokh, O. E. Tereshchenko, and A. M. Shikin, Journal of Experimental and Theoretical Physics 126, 535 (2018).
  * Stolyarov  _et al._ [2021] V. S. Stolyarov, S. Pons, S. Vlaic, S. V. Remizov, D. S. Shapiro, C. Brun, S. I. Bozhko, T. Cren, T. V. Menshchikova, E. V. Chulkov, W. V. Pogosov, Y. E. Lozovik, and D. Roditchev, The Journal of Physical Chemistry Letters 12, 9068 (2021), pMID: 34516738, https://doi.org/10.1021/acs.jpclett.1c02257 .
  * Klimovskikh  _et al._ [2022] I. I. Klimovskikh, D. A. Estyunin, T. P. Makarova, O. E. Tereshchenko, K. A. Kokh, and A. M. Shikin, The Journal of Physical Chemistry Letters 13, 6628 (2022), pMID: 35834754, https://doi.org/10.1021/acs.jpclett.2c01245 .
  * Dudin  _et al._ [2010] P. Dudin, P. Lacovig, C. Fava, E. Nicolini, A. Bianco, G. Cautero, and A. Barinov, Journal of Synchrotron Radiation 17, 445 (2010).
  * Blöchl [1994] P. E. Blöchl, Phys. Rev. B 50, 17953 (1994).
  * Kresse and Furthmüller [1996] G. Kresse and J. Furthmüller, Phys. Rev. B 54, 11169 (1996).
  * Kresse and Joubert [1999] G. Kresse and D. Joubert, Phys. Rev. B 59, 1758 (1999).
  * Perdew  _et al._ [1996] J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).
  * Grimme  _et al._ [2011] S. Grimme, S. Ehrlich, and L. Goerigk, Journal of Computational Chemistry 32, 1456 (2011).
  * Dronskowski and Bloechl [1993] R. Dronskowski and P. E. Bloechl, The Journal of Physical Chemistry 97, 8617 (1993).
  * Deringer  _et al._ [2011] V. L. Deringer, A. L. Tchougréeff, and R. Dronskowski, The Journal of Physical Chemistry A 115, 5461 (2011).
  * Maintz  _et al._ [2016] S. Maintz, V. L. Deringer, A. L. Tchougréeff, and R. Dronskowski, Journal of Computational Chemistry 37, 1030 (2016).
  * Zhang  _et al._ [2009] H. Zhang, C.-X. Liu, X.-L. Qi, X. Dai, Z. Fang, and S.-C. Zhang, Nature Physics 5, 438 (2009).
  * Kuroda  _et al._ [2010] K. Kuroda, M. Arita, K. Miyamoto, M. Ye, J. Jiang, A. Kimura, E. E. Krasovskii, E. V. Chulkov, H. Iwasawa, T. Okuda, K. Shimada, Y. Ueda, H. Namatame, and M. Taniguchi, Phys. Rev. Lett. 105, 076802 (2010).
  * Wei and Chou [2002] C. M. Wei and M. Y. Chou, Phys. Rev. B 66, 233408 (2002).
  * Mans  _et al._ [2002] A. Mans, J. H. Dil, A. R. H. F. Ettema, and H. H. Weitering, Phys. Rev. B 66, 195410 (2002).
  * Upton  _et al._ [2004] M. H. Upton, C. M. Wei, M. Y. Chou, T. Miller, and T.-C. Chiang, Phys. Rev. Lett. 93, 026802 (2004).
  * Upton  _et al._ [2005] M. H. Upton, T. Miller, and T.-C. Chiang, Phys. Rev. B 71, 033403 (2005).
  * Li  _et al._ [2015] C. Li, W. Chen, M. Li, Q. Sun, and Y. Jia, New Journal of Physics 17, 053006 (2015).
  * Menzel  _et al._ [2003] A. Menzel, M. Kammler, E. H. Conrad, V. Yeh, M. Hupalo, and M. C. Tringides, Phys. Rev. B 67, 165314 (2003).
  * Budde  _et al._ [2000] K. Budde, E. Abram, V. Yeh, and M. C. Tringides, Phys. Rev. B 61, R10602 (2000).
  * Jia  _et al._ [2006] Y. Jia, B. Wu, H. H. Weitering, and Z. Zhang, Phys. Rev. B 74, 035433 (2006).
  * Jia  _et al._ [2011] Y. Jia, M. Özer, H.H.Weitering, and Z. Zhang, “Quantum size effects in the growth and properties of ultrathin metal films, alloys, and related low-dimensional structures,” in  _Nanophenomena at Surfaces_ , Springer Series in Surface Sciences, edited by M. Michailov (Springer Berlin, Heidelberg, 2011) pp. XX, 284.
  * Dil  _et al._ [2004] J. H. Dil, J. W. Kim, S. Gokhale, M. Tallarida, and K. Horn, Phys. Rev. B 70, 045405 (2004).
  * Hupalo  _et al._ [2001] M. Hupalo, V. Yeh, L. Berbil-Bautista, S. Kremmer, E. Abram, and M. C. Tringides, Phys. Rev. B 64, 155307 (2001).
  * Calleja  _et al._ [2009] F. Calleja, A. L. V. de Parga, E. Anglada, J. J. Hinarejos, R. Miranda, and F. Yndurain, New Journal of Physics 11, 123003 (2009).
  * Czoschke  _et al._ [2004] P. Czoschke, H. Hong, L. Basile, and T.-C. Chiang, Phys. Rev. Lett. 93, 036103 (2004).
  * Yeh and Lindau [1985] J. J. Yeh and I. Lindau, Atomic Data and Nuclear Data Tables 32, 1 (1985).
  * [47] URL_will_be_inserted_by_publisher, dependence of the valence bands and of the loss spectra as a function of the thickness and of the temperature; Surface electronic structure of the 1 ML Pb/Bi2Se3 interface, with Pb in the fcc-hollow position.
  * Thuler  _et al._ [1982] M. R. Thuler, R. L. Benbow, and Z. Hurych, Chemical Physics 71, 265 (1982).
  * Chiang [2000] T.-C. Chiang, Surface Science Reports 39, 181 (2000).
  * Zhang  _et al._ [2005] Y.-F. Zhang, J.-F. Jia, Z. Tang, T.-Z. Han, X.-C. Ma, and Q.-K. Xue, Surface Science 596, L331 (2005).
  * Man  _et al._ [2013] K. L. Man, M. C. Tringides, M. M. T. Loy, and M. S. Altman, Phys. Rev. Lett. 110, 036104 (2013).
  * Hershberger  _et al._ [2014] M. T. Hershberger, M. Hupalo, P. A. Thiel, C. Z. Wang, K. M. Ho, and M. C. Tringides, Phys. Rev. Lett. 113, 236101 (2014).
  * Jaroch  _et al._ [2019] T. Jaroch, S. Chen, R. Zdyb, M. Jałochowski, P. Thiel, and M. Tringides, Journal of Crystal Growth 523, 125137 (2019).
  * Eremeev  _et al._ [2013] S. V. Eremeev, V. N. Men’shov, V. V. Tugushev, P. M. Echenique, and E. V. Chulkov, Phys. Rev. B 88, 144430 (2013).
  * Men’shov  _et al._ [2014] V. N. Men’shov, V. V. Tugushev, T. V. Menshchikova, S. V. Eremeev, P. M. Echenique, and E. V. Chulkov, Journal of Physics: Condensed Matter 26, 485003 (2014).
  * Eremeev  _et al._ [2015] S. V. Eremeev, V. N. Men’shov, V. V. Tugushev, and E. V. Chulkov, Journal of Magnetism and Magnetic Materials 383, 30 (2015).
  * Men’shov  _et al._ [2015] V. N. Men’shov, V. V. Tugushev, S. V. Eremeev, P. M. Echenique, and E. V. Chulkov, Phys. Rev. B 91, 075307 (2015).
  * Menshchikova  _et al._ [2020] T. V. Menshchikova, S. V. Eremeev, V. M. Kuznetsov, and E. V. Chulkov, Materials 13 (2020), 10.3390/ma13204481.