# Topological superconductivity in a topological insulator

Hao Yu1,2,5 Noah F. Q. Yuan1,5 Wei-Jian Li3,2 Liu-Cheng Chen1,2 Zi-Yu Cao1 Di
Li4 Xiaoying Qin4 Chang-De Gong3 & Xiao-Jia Chen1,2∗

###### Abstract

Topological superconductivity as an exotic quantum phenomenon with coupled
nontrivial topological order and superconductivity together in a single
substance has drawn extensive attention because of its novelty as well as the
potential for quantum computation[1, 3, 2, 4, 5, 6]. A direct idea for
producing topological superconductors is to create superconductivity based on
the well recognized topological insulators[7, 8, 9, 10, 11, 12, 13, 14]. The
topological insulating states in highly efficient thermoelectric materials
Bi2Te3 and Bi2Se3 and their alloy Bi2Te3-xSex have been established from
angle-resolved photoemission[15, 16, 17] and transport[18] experiments.
Superconductivity was also observed based on these popular topological
insulators by the application of pressure[19, 20, 21], chemical dopant[22],
and heterostructures[23, 24]. However, the experiments mainly focusing on
Bi2Se3 doped by metals such as Cu[25, 26, 27, 28, 29, 30, 31, 34, 35, 32, 33],
Sr[36, 37, 38, 39], and Nb[40, 41, 42, 43, 44, 45, 46] have not provided the
consistent evidence to support the topological superconductivity. Here we
carry out a systematic high-pressure study on a topological insulator
Bi2Te2.7Se0.3 to provide the convincing evidence for the expected topological
superconductivity. Four phases with different structures are found upon
compression by the X-ray diffraction, Raman scattering, and electrical
transport measurements. The Hall resistivity and electronic structure
calculations help to identify the topological surface state in the entire
initial phase, while superconductivity is found to coexist with such a state
of the compressed material after its passing the electronic topological
transition, followed by three other superconducting phases without topological
character. For these superconducting phases, we observe that the upper
critical field follows with the temperature in the critical exponent ${2/3}$
for the first one with the topological surface state and $1$ for the left.
These observations support the realization of the topological
superconductivity in the initial phase according to the theoretically proposed
critical field measure. Therefore, this work points out a big pool and new
direction for finding topological superconductors from topological
thermoelectric materials. The results also demonstrate that the critical field
measure is an easy and powerful method for the identification of topological
superconductivity in the system where topological surface states and
superconductivity coexist.

School of Science, Harbin Institute of Technology, Shenzhen 518055, China

Center for High Pressure Science and Technology Advanced Research, Shanghai,
201203, China

National Laboratory of Solid State Microstructures and School of Physics,
Nanjing University, Nanjing 210093, China

Key Laboratory of Materials Physics, Institute of Solid State Physics, Chinese
Academy of Sciences, Hefei 230031, China

These authors contribute equally to this work.
∗E-mail<EMAIL_ADDRESS>
Symmetry and topology are two of the main themes of modern physics, especially
the condensed matter physics in recent decades. In two dimensions (2D),
quantum (anomalous) Hall effects emerge with nontrivial electronic topology
when the time-reversal symmetry is broken[7]. When the time-reversal symmetry
is preserved, quantum Hall states then develop into the quantum spin Hall
(QSH) phase[8, 9]. In three dimensions (3D), stacked QSH states evolve into
topological insulators (TIs)[10, 11, 12]. The crystal symmetries further
intertwine with the electronic topology, leading to topological crystalline
insulators[47, 48, 49]. These topological insulating phases have been
experimentally verified with high precision in several materials, in
particular highly efficient thermoelectric materials Bi2Te3 and Bi2Se3 and
their alloy Bi2Te3-xSex[12, 13, 14, 15, 16, 17, 18]. Importantly, such TI
materials have also been found to be intrinsically superconducting by the
application of pressure[19, 20, 21] or chemical dopant[22, 36, 37, 40, 41],
which naturally invites two questions on the nature of this kind of
superconductivity. From the symmetry wise, one needs to determine the pairing
symmetry of the intrinsic superconductivity. From the topology wise, one needs
to know whether and how the topological superconductivity can be realized in
these topologically nontrivial materials.

Theoretical proposals followed by various experimental measurements have been
carried out to address these two questions. Classified by the irreducible
representations of the point group $D_{3d}$, the possible pairing symmetry of
Bi(Te,Se) systems has been theoretically proposed as $A_{1g}$ phase
($s$-wave), odd-parity $A_{1u}$ phase[31, 32, 33] or two-component $E_{u}$
phase (nematic[34, 35] versus chiral[42]). For doped topological insulators,
some experimental data support the $A_{1g}$ phase ($s$-wave)[27] without
topological superconductivity[30] for Cu-doped Bi2Se3, while others support
the nematic $E_{u}$ phase for Bi2Se3 doped with Cu[26, 28, 29], Sr[36, 37, 38,
39] or Nb[41, 43, 44, 45, 46], which are believed to host topological
superconductivity, although discrepancy still remains[46, 35]. For topological
insulators under pressure, experimental data indicate unconventional
superconductivity in Bi2Se3[21], while no direct evidence on unconventional
superconductivity has been provided in Bi2Te3[20]. The issue regarding whether
topological superconductivity can take place in topological insulators has not
been settled yet but is highly desired from the science community. To address
this issue, we conduct a careful experimental and theoretical study on both
the normal phase and superconducting phase of Bi2Te2.7Se0.3 at high pressures.
The details are given as follows.

The room-temperature phase and structure behaviours of Bi2Te2.7Se0.3 at
ambient pressure and high pressures were determined by X-ray diffraction
measurements. The details for the experiments and refinements are given in
Methods. The diffraction patterns and profiles indicate the occurrence of
several phases at high pressures (Fig. 1a). The Rietveld refinements for four
representative pressures yield good agreement between the measurements and
calculations (Fig. 1b). The obtained structural parameters are summarized in
Extended Data Table 1. The results support the formation of three new phases
besides the initial one. All the obtained phases are named as I to IV with
space groups of $R$-3$m$, $C$2/$m$, $C$2/$c$, and $Im$-3$m$ from the ambient
to high pressure, respectively. The evolution of the volume per formula of
these phases and the atomic arrangements for Bi and Te(Se) in each structure
are presented in Fig. 1c. Phase I can maintain its initial rhombohedra
structure up to 10 GPa. For Phase IV, all three kinds of atoms could occupy
the same position with equal possibility and are hence geometrically
indistinguishable. The obtained phases and structures of Bi2Te2.7Se0.3 are
consistent with the previous studies on the two ending compounds Bi2Te3[50]
and Bi2Se3[51]. Interestingly, the axial ratio $c/a$ of the lattice parameters
exhibits non-monotonic behaviour under pressure with a minimum at around 2 GPa
(Fig. 1d). Such a minimum was also observed in both Bi2Te3[52] and Bi2Se3[51].
It has been proposed to be associated with the Lifshitz transition, also known
as the electronic topological transition (ETT)[52]. The experimental evidence
for pressure-induced ETT in Bi2(Te,Se)3-based system through various
techniques is summarized in Methods. For $n$-type Bi2Te2.7Se0.3, the ETT near
2 GPa has been firmly confirmed through the pressure dependence of $\sigma$,
$S$, their power factor $\sigma S^{2}$, effective mass, and charge
mobility[53].

The structural characters of the obtained four phases were further examined
through high-pressure Raman scattering measurements. The phonon modes appear
in accordance with the structural symmetry of each phase (Extended Data Figs.
1a and 1b). For example, the $R$-3$m$ symmetry predicts four phonon modes for
the first phase (I)[54]. We do observe these modes in the pressure range up to
8 GPa. The pressure dependence of the low-frequency $E_{g}^{1}$ mode is the
first report in history[51, 54]. The flat background at high pressures is just
the feature of Phase IV with space group of $Im$-3$m$ because no active Raman
modes are expected from the symmetry consideration. The details for the mode
assignment are given in Methods. The pressure dependence of the frequencies of
the obtained phonon modes provide the accurate boundaries between phases and
their coexistence (Extended Data Fig. 1c). Note that the slope change of the
pressure-dependent frequency can be observed at around 2 GPa for all the
phonon modes in Phase I. Meanwhile, the full width at half maximum (FWHM) has
the maximum (minimum) for the $E_{g}^{1}$ ($E_{g}^{2}$) mode at pressure near
2 GPa where the FWHM of the $A_{1g}^{1}$ and $A_{1g}^{2}$ mode changes slope
(Extended Data Fig. 1d). These offer additional spectroscopic evidence for the
ETT in Phase I of the studied material.

Hall effect measurements at low temperature of 10 K were carried out to
examine the validity of the nontrivial topological surface states under
pressure. The Hall resistivity $\rho_{xy}$ vs magnetic field curves for
representative pressures reveal the different nature of the carriers in the
obtained four phases (Fig. 2a). The first phase (I) and the last two phases
(III and IV) hold the $n$-type feature, while Phase II becomes a $p$-type
material. This indicates that the electrical transport properties of the two
intermediate phases (II and III) are controlled by the different types of the
carriers. The robust topological order in Bi2Te3-xSex has been reported from
the angle-resolved photoemission measurements[17]. The Hall conductivity data
of Phase I at various pressures exhibit a nonlinear resonant structure when
applying magnetic fields (Extended Data Fig. 2), evidencing the existence of
the surface state in topological insulators[18]. The Hall conductivity can be
decomposed into the surface and bulk components based on the method developed
recently[18]. The details for determining the mobility of the surface
$\mu_{s}$ and bulk $\mu_{b}$ state as well as the carrier concentration $n$ of
the bulk are described in Methods. Fitting our experimental data yields the
Hall conductivity for the surface $\sigma_{xy}^{s}$ and the bulk
$\sigma_{xy}^{b}$, supporting the existence of the nontrivial topological
states in Phase I (Fig. 2b and Extended Data Fig. 2). However, the topological
states does not survive in the rest three high-pressure phases reflected from
the absence of the resonant structure of the Hall conductivity.

The obtained surface mobility $\mu_{s}$ is one order larger in magnitude than
the bulk value $\mu_{b}$ over the whole pressure region studied in Phase I,
supporting the nontrivial topological state. As can be seen from Fig. 2c, both
mobilities increase with increasing pressure. The bulk one reaches a maximum
at the boundary between Phase I and II. The mobility decreases with increasing
pressure in Phase II. There is a minimum at the boundary between Phase III and
IV. The distinct phase boundaries can be clearly established from the pressure
dependence of the effective carrier concentration $n_{eff}$ for the bulk state
in Phase I and the Hall concentration $n_{H}$ in the rest three phases
(Extended Data Fig. 3). These boundaries seemingly do not shift with
temperature when keeping pressure unchanged. Now the phases and their
boundaries are well determined for Bi2Te2.7Se0.3 from X-ray diffraction, Raman
scattering, and Hall effect measurements.

We perform the first-principles calculations of the Bi2Te2.7Se0.3 alloy in the
$R$-3$m$ phase under pressures (Fig. 3a). For the chosen first Brillouin zone
and the projection along the (001) surface (Fig. 3b), the metallic surface
state appears in all the pressure range studied up to 8 GPa (Fig. 3c), in good
agreement with the transport measurements at temperature of 10 K (Fig. 2b).
Furthermore, the evolution of energy contours of the top bulk valance band
with increasing pressure (Fig. 3d) indicates the ETT around 2 GPa, where
energy contours merge together and the number of distinct contours at the same
energy changes from 3 to 2 as pressure increases. The numerical result of ETT
is consistent with the transport and Raman scattering measurements.

Among the obtained four phases, only Phase I carries on the topological states
at room temperature. Therefore, topological superconductivity can be only
expected in this phase. To verify this expectation, we then cool down the
material and perform transport measurements.

As expected, superconducting transitions are observed at low temperatures with
a sudden resistivity drop at 4.3 GPa and even to zero value at 5.5 GPa, and
the zero-resistivity states are always achievable for pressures higher than
5.5 GPa (Fig. 4a) within the experimentally achievable pressure range. The
suppression of superconductivity by the applied magnetic fields is
demonstrated in Fig. 4b for selected pressures of interest. The
superconducting phase diagram in the pressure-temperature plane is presented
in Fig. 4c. A comparison of the present results with the other experiments is
given in Methods.

The same spectroscopic features at room temperature (Extended Data Fig. 1),
low temperature of 3.6 K (Extended Data Fig. 4), and the temperatures across
$T_{c}$ (Extended Data Fig. 6) indicate that the compound keeps the same
electronic phases at low temperatures as determined at room temperature. The
nontrivial topological states can coexist with the superconducting state in
Phase I at pressures up to 10 GPa (Extended Data Fig. 4). This topological
state maintains when the material enters the superconducting state (below
$T_{c}$) (Extended Data Fig. 6). In other words, among the obtained four
superconducting phases, the superconducting state in Phase I is the only one
to coexist with the nontrivial topological states in the studied compound.
Therefore, the region at pressures of 5.5-10 GPa and temperatures less than
$T_{c}$ in Phase I provides the only window to examine the possibility of
topological superconductivity in Bi2Te2.7Se0.3.

Now we turn to the identification of the coexistence between superconductivity
and topological surface states by investigation of critical fields in the
Ginzburg-Landau regime near $T_{c}$. In Fig. 4b, two distinct types of
critical fields have been obtained. In the three high-pressure phases (II,
III, IV) without the topological surface states, the linear temperature
dependence $H_{c2}\propto 1-T/T_{c}$ is found, while in Phase I it can be
found that $H_{c2}\sim(1-T/T_{c})^{2/3}$ near $T_{c}$ (Inset of Fig. 4b and
Extended Data Fig. 5). This sharp contrast is in excellent agreement with the
theoretical prediction of the critical fields in trivial versus topological
superconductors. To understand this mechanism, we need to work out the order
parameter and the critical field by minimizing Ginzburg-Landau free energy, as
elaborated in Ref.[55]. In the following we stretch the outline of the theory.

In the trivial superconductors without surface states, the critical field is
linear in temperature. Denote $\xi\propto(1-T/T_{c})^{-1/2}$ as the coherence
length of the superconductor, then superconductivity is killed when a flux
quantum $\Phi_{0}=h/(2e)$ is trapped in the area $\sim\xi^{2}$. As a result,
$H_{c2}\propto 1/\xi^{2}\propto 1-T/T_{c}$, which corresponds to the high-
pressure cases as shown for 14.0 GPa and 16.8 GPa (Fig. 4b and Extended Data
Fig. 5).

In the topological superconductors with surface states, the critical field can
have critical exponent of 2/3 in the temperature dependence. After the bulk
superconductivity is killed, as we further increase magnetic field strength,
the surface layer of the thickness $\sim l_{s}$ prefers to remain
superconducting. The new length scale $l_{s}$, known as the extrapolation
length, measures the coupling strength between the topological states and
superconductivity on the surface. When a flux quantum is trapped in the area
$\sim\zeta^{2}$ near the surface, superconductivity is killed, where
$\zeta=(l_{s}\xi^{2})^{1/3}$ combines the extrapolation length of the surface
superconductivity and the coherence length of the bulk superconductivity. We
then derive $H_{c2}\sim\Phi_{0}/\zeta^{2}\sim(1-T/T_{c})^{2/3}$, which
corresponds to the 6.4 GPa case of Fig. 4b (also see Extended Data Fig. 5).

From the obtained experimental evidence for surface states, we believe the
superconducting state of the Bi2Te2.7Se0.3 alloy in Phase I can have
nontrivial topology. When the bulk pairing is $A_{1g}$ phase ($s$-wave), the
bulk is fully gapped, surface states form the Fu-Kane model[56] in 2D, and
Majorana zero modes should be found in the vortex cores on the surfaces. When
the bulk pairing is $A_{1u}$ phase, the fully-gapped bulk realizes topological
superconductivity in class DIII in 3D[57], and the the surface states are
recognized as helical Majorana surface states, which should lead to an
asymmetric surface tunneling spectroscopy[31, 32, 33]. The bulk pairing
symmetry can also be two-component $E_{u}$ phase according to recent data,
which can spontaneously break in-plane rotation (time-reversal) symmetry and
falls into the nematic (chiral) phase. In the nematic phase, topological
superconductivity in class DIII is realized in 3D, and the surface states are
helical Majorana surface states[34, 35], where the in-plane critical fields
should be anisotropic[35, 46]. While in the chiral phase, bulk
superconductivity is nodal with point nodes, and Weyl superconductivity is
realized. The surface states are thus Majorana arc states connecting surface-
projected Weyl points with opposite Chern numbers[42]. In the chiral phase,
time-reversal breaking signals such as Kerr rotation should be observed. These
results and discussions above are summarized in Table 1.

The search for topological superconductivity in topological materials such as
topological insulators has been longed for in condensed matter physics
community during the recent decade. In this work, from carefully designed
experiments, and detailed electrical transport, X-ray diffraction, and Raman
scattering measurements, we first narrow down the coexisting window of the
topological surface states and superconductivity for the same compound. We
then apply the detection method proposed recently to measure the critical
exponent of critical fields in the temperature dependence, regardless of
microscopic details. Finally, we find both the topologically nontrivial and
trivial cases for the different superconducting phases predicted by the
theory, and hence besides evidence for topological superconductivity, at the
same time we also validate this recently proposed method for identifying and
distinguishing topological and conventional superconductivity. The current
work thus realizes the long-standing dream for the topological
superconductivity in most popular topological insulators Bi2Se3-xTex $-$ the
alloy compounds of Bi2Se3 and Bi2Te3.

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  * [58] [Acknowledgements] This work was funded through the Shenzhen Science and Technology Program (Grant No. KQTD20200820113045081), the Basic Research Program of Shenzhen (Grant No. JCYJ20200109112810241), and the National Key R$\&$D Program of China (Grant No. 2018YFA0305900). N.F.Q.Y. acknowledges the National Natural Science Foundation of China (Grant. No. 12174021) for the financial support. The sample preparation in CAS was supported by National Natural Science Foundation of China under Grant Nos. 51672278, 11674322, and 11374306. The synchrotron X-ray diffraction measurements were performed at GeoSoilEnviroCARS (The University of Chicago, Sector 13), Advanced Photon Source (APS), Argonne National Laboratory. GeoSoilEnviroCARS is supported by the National Science Foundation$-$Earth Sciences (EAR$-$1634415) and Department of Energy- GeoSciences (DE-FG02-94ER14466). The research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357.

Figure 1 $\mid$ High-pressure structures of Bi2Te2.7Se0.3 at room temperature.
a, Synchrotron X-ray diffraction patterns at various pressures up to 28.0 GPa
with the radiation wavelength of 0.3100 Å. b, Rietveld refinement results at
pressure of 1.0, 13.3, 20.6, and 28.0 GPa for representative phase with space
group of $R$-3$m$ (Phase I), $C$2/$m$ (Phase II), $C$2/$c$ (Phase III), and
$Im$-3$m$ (Phase IV), respectively. The open cycles are the measured data
points. The curves are the refinement results. Their difference profiles are
shown at the bottoms. The positions of the Bragg reflections are marked by the
vertical lines for each phase. The agreement between the experiments and
structure models is evaluated by the residual parameters $R_{wp}$=2.2%,
$R_{p}$=1.6%, and $\chi^{2}$=0.049 for pressure of 1.0 GPa; $R_{wp}$=2.3%,
$R_{p}$=1.7%, and $\chi^{2}$=0.070 for pressure of 13.3 GPa; $R_{wp}$=8.8%,
$R_{p}$=7.5%, and $\chi^{2}$=0.096 for pressure of 20.6 GPa; and
$R_{wp}$=7.4%, $R_{p}$=7.2%, and $\chi^{2}$=0.083 for pressure of 28.0 GPa,
respectively. c, Evolution of the volume per formula of each phase with
pressure. The atomic arrangement in a unit cell is shown for the corresponding
phase pointed by arrow. The atoms of Bi and Te/Se are drawn in two different
balls with different colours for the first three phases. These atoms share the
same positions in Phase IV with the space group of $Im$-3$m$. d, Pressure
dependence of the axial ratio $c$/$a$ in Phase I with the space group of
$R$-3$m$. The dashed line is drawn for the guide of the eye. There is a
minimum at a pressure close to 2 GPa. The open squares in c and d are the data
points at ambient pressure.

Figure 2 $\mid$ High-pressure Hall effect of Bi2Te2.7Se0.3 at temperature of
10 K. a, Representative Hall resistivity $\rho_{xy}$ vs magnetic fields up to
$\pm$3 Tesla for each phase from the bottom to top with the space group of
$R$-3$m$, $C$2/$m$, $C$2/$c$, and $Im$-3$m$ at pressure of 4.3 , 14.0, 18.4,
and 40.6 GPa, respectively. The data points are denoted by the open cycles.
The lines are the the fitting results to the experiments. The nonlinear
profile of the Hall resistivity in Phase I at pressure of 4.3 GPa is a result
of the combination from the contributions of the bulk and surface states. b,
Separation of the bulk and surface contributions to the Hall conductivity in
Phase I with the space group of $R$-3$m$ for selected pressures. The surface
Hall conductivity $\sigma_{xy}^{s}$ is obtained by subtracting the bulk
component $\sigma_{xy}^{b}$ from the observed Hall conductivity $\sigma_{xy}$.
c, Pressure dependence of the mobility in the surface ($\mu_{s}$) and bulk
($\mu_{b}$) states in Phase I with the space group of $R$-3$m$ and the bulk
mobility in the followed phases at higher pressures.

Figure 3 $\mid$ Electronic structures of Bi2Te2.7Se0.3 in the $R$-3$m$ phase
at high pressures. a, A unit cell with the space group of $R$-3$m$. b, The
first Brillouin zone of the alloy with high symmetry points (upper panel) and
the two-dimensional projection along the (001) surface (lower panel). c, The
slab band structures at various pressures up to 8.0 GPa. The blue curves
represent the metallic surface bands and the black ones are the bulk
electronic structures. d, The evolution of energy contours of the top bulk
valence band with pressure. As pressure increases, the number of distinct
energy contours changes from 3 to 2, indicating the electronic topological
transition around 2 GPa.

Figure 4 $\mid$ Temperature-pressure phase diagram of Bi2Te2.7Se0.3. a,
Temperature dependence of the resistivity $\rho$ for selected pressures up to
40.6 GPa. The $\rho$ drop appears at 4.3 GPa and down to zero to low
temperatures at higher pressures. Inset: Photograph for the sample attached by
four electrodes in the chamber made by cubic boron nitride. b, Temperature-
dependent resistivity curve with the applied magnetic fields at pressure of
6.4, 14.0, and 16.8 GPa, respectively. Insets: The upper critical field as a
function of the reduced temperature ($T/T_{c}$) with $T_{c}$ being the
superconducting transition temperature for representative pressures in
different phases. The zero-field $T_{c}$ value for pressure of 6.4, 14.0, and
16.8 GPa is 4.50(4), 8.21(8), and 8.92(8) K, respectively. $T_{c}$ is chosen
as the onset temperature of superconductivity to avoid the influence of
possible superconducting vortex phases. The fitting to the experimental data
points near $T_{c}$ in the $T/T_{c}$ range of 0.5 to 1 in the curve by using
$\mu_{0}H_{c2}\sim(1-T/T_{c})^{\alpha}$ with $\alpha$ being $2/3$ for pressure
of 6.4 GPa and 1.0 for pressure of 14.0 and 16.8 GPa, respectively. c,
Pressure dependence of $T_{c}$ crossing different phases. The phase region is
indicated by the different type of mark. The phases and their boundaries are
determined from the results of the X-ray diffraction, Raman scattering, and
Hall effect measurements. Errors are smaller than the size of the data points.

Table 1 $\mid$ Possibilities of topological superconductivity. Corresponding to the bulk pairing symmetry, the pairing topology is listed in the bulk and on the surface.  Symmetry | Bulk | Surface
---|---|---
$A_{1g}$ | Trivial, fully gapped | Fu-Kane model
$A_{1u}$ | DIII in 3D, fully gapped | Helical Majorana surface states
$E_{u}$ nematic | DIII in 3D, fully gapped | Helical Majorana surface states
$E_{u}$ chiral | Weyl superconductor, point nodes | Chiral Majorana arc states

METHODS: Sample synthesis. Alloyed powders of Bi2Te2.7Se0.3 were synthesized
according to the stoichiometry with appropriate amounts of element Bi
(99.999%), Te (99.999%), and Se (99.999%) purchased from Alfa Aesar. The
powder mixture was loaded into quartz ampoule and sealed under vacuum at 10-3
Pa, and then heated at 1123 K for 24 hours. The obtained ingot was then ground
using a mortar type grinder for 30 minutes with a speed of 125 rpm. The
obtained powders were compacted with tungsten carbide mould by hot-pressing at
633 K at pressure of 300 MPa in vacuum for one hour. Consequently, disk-shaped
bulk samples with 2 mm in height and 13 mm in diameter were obtained. The
specimens for transport, structure, and spectroscopy measurements under
pressure were cut from the as-prepared bulk samples. The synthesized samples
are the $n$-type. High-pressure X-ray diffraction measurements. The ambient-
pressure structure of the sample was investigated by using a
RigakuD/MAX-2550PC diffractometer with Cu-K$\alpha$ radiation in wavelength of
1.5406 Å. For the high-pressure structural study, synchrotron X-ray
diffraction (XRD) patterns were collected at GeoSoilEnviroCARS (Sector 13),
Advanced Photon Source, Argonne National Laboratory, USA. The wavelength of
0.3100 Å and the size of the focus beam of less than 2 $\mu$m were chosen for
the measurements. The sample was pressed into powders before being placed into
the chamber. Neon was loaded as the transmitting medium. The obtained
two$-$dimensional XRD patterns were integrated into one$-$dimensional patterns
with the help of the Fit2D software[59]. The integrated intensity vs 2$\theta$
diffraction patterns were analyzed through the Rietveld method using the GSAS
package[60]. The pressure was calibrated by using the ruby fluorescence
shift[61] and implemented at room temperature. The collected room-temperature
XRD patterns for selected pressures are shown in Fig. 1a. The refinements to
the obtained data for four representative phases with different structure
symmetries are shown in Fig. 1b. The details of the refinement results for
these selected pressures are summarized in Extended Data Table 1. The
evolution of the obtained volume per formula at each phase with pressure is
presented in Fig. 1c. The pressure dependence of the obtained axial ratio of
$c$/$a$ for the first phase is plotted in Fig. 1d. High-pressure Raman
scattering measurements. Raman spectra were measured using a single$-$stage
spectrograph equipped with a thermoelectrically cooled charge-coupled device.
The Raman notch filters were of a very narrow bandpass, allowing Raman
measurements down to 10 cm-1 in the stokes and anti-stokes. The 488 nm
excitation incidents were used to illuminate an approximately 5$\times$5
$\mu$m2 spot on the surface of the sample. The excitation strength was
monitored by using a power meter. The power of 1.5 mW (0.5 mW) was chosen for
the measurements at room temperature (low temperatures). In both measurements,
neon was loaded as a transmitting medium. The pressure was gauged by the the
ruby fluorescence shift[61]. The results for the room temperature and low
temperatures are shown in Extended Data Figs. 1, 4, and 6, respectively. High-
pressure resistivity and Hall effect measurements. For the high-pressure
resistivity and Hall effect measurements, a nonmagnetic diamond anvil cell
made of Cu-Be alloy was used for Physical Properties Measurements System from
U.S. Quantum Design[62]. This customized cell has two symmetrical diamond
anvils and the diameter of the anvil culets is 300 $\mu$m. A steel flake was
used as the gasket with the sample chamber of 150 $\mu$m diameter. The gasket
was insulated with cubic boron nitride and silver epoxy. A cut piece of the
polycrystalline sample was placed into the sample chamber. Four Pt wires were
placed on the surface of one side of the insulated gasket with the linkage of
the sample and the external Cu wires. A standard four-probe method was used
for the electrical transport measurements. The resistivity and Hall
coefficient were determined in terms of the van der Pauw method[63]. For this
method, the thickness of the measured sample is the only needed dimensional
parameter. The sample thickness for the electrical transport measurements is
32 $\mu$m. No pressure transmitting medium was used for such electrical
transport measurements. The loaded ruby chip was used to determine pressure.
The Hall effect measurements were taken at low temperature of 10 K. The
results are shown in Fig. 2. The Hall conductivity $\sigma_{xy}$ and the
contributions from the bulk and surface states for pressures of interest in
Phase I are shown in Fig. 2b and Extended Data Figs. 2 and 3, respectively.
The temperature-dependent resistivities at selected pressures up to 40.6 GPa
are shown in Figs. 4a and 4b. Structural evolution with pressure. Our
experiments support the following structural evolution path of Bi2Te2.7Se0.3
with pressure: from its initial rhombohedra structure (Phase I) with the space
group of $R$–3$m$ to the final disordered body-centered cubic structure (Phase
IV) with the space group of $Im$-3$m$ after passing two intermediate
monoclinic phases with the space group of $C$2/$m$ for Phase II and $C$2/$c$
for Phase III. We observed the anomaly of the axial ratio $c/a$ in Phase I
with the minimum at a pressure close to 2 GPa. This phenomenon was also
observed in the other studies on the similar compounds Bi2Te3[52, 64, 65] and
Bi2Se3[51, 65]. The obtained structural evolution path with pressure for
Bi2Te2.7Se0.3 is in good agreement with the observations for the similar
systems such as Bi2Te3[52, 50], Bi2Se3[51], and Sb2Te3[66]. Assignment of the
phonon modes. There are four phases at high pressures from the structural
study. Phonon modes can be observed at low pressures but become invisible at
high pressure (Extended Dada Figs. 1 and 4). The spectra change profiles at
the boundary for a certain pressure where the phase transition takes place.
The critical pressures for the profile changes from the Raman spectra are
consistent with those for the phase transformation detected from the XRD
measurements (Fig. 1). The initial phase (I) of Bi2Te2.7Se0.3 has the
rhombohedra structure with the space group of $R$–3$m$. Group theory predicts
10 zone-center modes with the irreducible representations:
$\Gamma_{I}=2A_{1g}+3A_{2u}+2E_{g}+3E_{u}$. Here $A_{2u}$ and $E_{u}$ are two
acoustic branches, and $A_{1g}$ and $E_{g}$ are from optical branches. Only
two $A_{1g}$ modes and two $E_{g}$ modes are Raman active. The first
intermediate phase (II) of Bi2Te2.7Se0.3 possesses the monoclinic structure
with the space group of $C$2/$m$. There are 30 vibrational modes from the
group theory prediction with the representation:
$\Gamma_{II}=10A_{g}+10B_{u}+5A_{u}+5B_{g}$. Among them, the $A_{u}$ and
$B_{u}$ are from the acoustic branches and the rest are optical phonons.
Therefore, 10 $A_{g}$ and 5 $B_{g}$ modes are Raman active. The second
intermediate phase (III) of Bi2Te2.7Se0.3 adopts the monoclinic structure with
the space group of $C$2/$c$. Group theoretical considerations predict 30
vibrational modes with the following representation form:
$\Gamma_{III}=7A_{g}+7A_{u}+8B_{g}+8B_{u}$. Here the $A_{u}$ and $B_{u}$ modes
are from the acoustic branches and the $A_{g}$ and $B_{g}$ modes are from the
optical branches. Thus, 15 zone-center Raman active modes (7$A_{g}$+8$B_{g}$)
are expected to be observed for this phase. The last phase (IV) of
Bi2Te2.7Se0.3 has the disordered body-centered cubic structure with the space
group of $Im$-3$m$. No Raman active modes are expected for this symmetry. Our
in-house built Raman system captures almost all these assigned features. For
example, we observed the four Raman active modes for Phase I over the whole
pressure range at both the room temperature (Extended Data Fig. 1) and low
temperatures down to 3.6 K (Extended Data Figs. 4 and 6). The featureless
background in Phase IV was also observed in both cases. The rather rich
features below the wavenumber of 50 cm-1 in the two intermediate phases were
found from the current study. The phonon peaks and profiles above 50 cm-1 for
these two phases are similar to the observations for Bi2Se3[51]. We observed
four Raman-active modes (2$A_{1g}$+2$E_{g}$) in the studied Bi2Te2.7Se0.3 in
the wavenumbers down to 10 cm-1 for Phase I. At both room temperature and low
temperature, the frequencies of all these phonon modes change slope at around
2 GPa when increasing with pressure. Interestingly, the FWHM changes with
pressure in different manners for the $A_{1g}$ and $E_{g}$ mode. The two
$E_{g}$ modes correspond to atomic vibrations in the plane of the layers,
while the $A_{1g}$ modes correspond to vibrations along the $c$ axis
perpendicular to the layers[54]. Upon compression, the FWHM has the maximum
(minimum) for the $E_{g}^{1}$ ($E_{g}^{2}$) mode at a pressure close to 2 GPa.
For the two $A_{1g}$ modes, their FWHM just changes slope when narrowing down
with increasing pressure. These results are summarized in Extended Data Figs.
1, 4, and 6. The non-monotonic pressure dependences were also observed in the
sister systems Bi2Te3[65, 51], Bi2Se3[65, 51], and Sb2Se3[67]. Determination
of the mobility and concentration of the charge carriers. The high-pressure
Hall effect measurements were used to determine the Hall resistivity or
conductivity along the $xx$ and $xy$ directions. The components for the Hall
resistivity and conductivity along the $xx$ and $xy$ directions are related to
the two expressions $\sigma_{xx}=1/\rho_{xx}$ and
$\sigma_{xy}=\rho_{xy}/(\rho_{xx}^{2}+\rho_{xy}^{2})$. The Hall coefficient
$R_{H}$ is thus determined by fitting the obtained Hall resistivity
$\rho_{xy}$ along the $xy$ direction vs magnetic field curve for the bulk
material on the assumption that the electrical transport is dominated by free
electrons. The carrier concentration $n_{H}$ can be obtained by using the
formula $n_{H}=1/(eR_{H})$ with $e$ being the electron charge. The Hall
mobility ($\mu$) can be calculated based on the relation
$\mu=\sigma_{xx}R_{H}$ if the electrical conductivity $\sigma_{xx}$ is known.
In the absence of the topological order, the Hall resistivity varies with the
low magnetic field in a linear manner if the carrier is the single type. These
conditions are fully satisfied for the high-pressure phases with the space
group of $C$2/$m$, $C$2/$c$, and $Im$-3$m$ (Fig. 2a). We thus can determine
the bulk mobility $\mu_{b}$ of this material at each pressure of the
corresponding phase. The $\mu_{b}$ values at selected pressures are shown in
Fig. 2c. For the topological insulating state, the Hall resistivity does not
exhibit a linear behaviour but has a resonant structure in weak magnetic field
(Fig. 2a and Extended Data Fig. 2). The observed Hall conductivity
$\sigma_{xy}$ can be described as the sum of the surface Hall conductivity
$\sigma_{xy}^{s}$ and the bulk $\sigma_{xy}^{b}$[18]:
$\sigma_{xy}=\sigma_{xy}^{s}+\sigma_{xy}^{b}~{}~{}.$ (1) The surface
conductivity $\sigma_{xy}^{s}$ can be expressed as:
$\sigma_{xy}^{s}=\frac{2\pi
e^{3}}{dh^{2}}\frac{Bl^{2}}{1+(\mu_{s}B)^{2}}~{}~{},$ (2) where $d$ is the
sample thickness, $l$ is the mean free path, and $\mu_{s}$ is the surface
carrier mobility. The bulk conductivity $\sigma_{xy}^{b}$ can be expressed by
the semiclassical form:
$\sigma_{xy}^{b}=n_{eff}e\mu_{b}\frac{\mu_{b}B}{1+(\mu_{b}B)^{2}}~{}~{},$ (3)
where $n_{eff}$ is the effective carrier concentration and $\mu_{b}$ is the
bulk carrier mobility. Equations (1)-(3) can be used to fit the $\sigma_{xy}$
vs $H$ curve once the sample thickness $d$ is known. The fitting gives the
values of $\mu_{s}$ for the surface and $\mu_{b}$ and $n_{eff}$ for the bulk
along with $l$ at each pressure. The fitting is in good agreement with the
observed $\sigma_{xy}$ curve (Extended Data Fig. 2). The decomposition of
$\sigma_{xy}$ into the surface and bulk term is presented in Fig. 2b. The
obtained mobility of the two components as a function of pressure is plotted
in Fig. 2c. The results for the $n_{eff}$ and $l$ for the bulk state in Phase
I together with the bulk carrier concentration $n_{H}$ in the other phases are
summarized in Extended Data Fig. 3. Pressure-induced electronic topological
transition. The anomalies were observed in the studied Bi2Te2.7Se0.3 from
pressure dependences of the axial ratio $c/a$ (Fig. 1d) and phonon modes
(Extended Data Figs. 1c and 1d, 4b and 4c) in Phase I. The similar behaviours
were also observed in the other V2-VI3 compounds with topological insulating
states[52, 64, 65, 51, 67]. These anomalies take place within the same
structure of Phase I. These are not a result of structural transition but may
be considered as experimental evidence for the possible electronic topological
transition (ETT) in these compounds at their initial phase. Pressure-driven
ETT was confirmed in Bi2Te3 through the measurements of the Shubnikov-de Haas
oscillations[68]. Seebeck coefficient measurements were recognized as an
effective, sensitive, and powerful tool for detecting the ETT[69, 70]. In the
vicinity of the ETT, the Seebeck coefficient should exhibit an asymmetric
shape[71]. The anomaly in the pressure-dependent Seebeck coefficient in
Bi2Te3[72] was reported at the same critical point for the ETT indicated by
the Shubnikov-de Haas effect[68]. This demonstrates that the Seebeck
coefficient measurements are a rather reliable means to study the ETT
phenomenon. Meanwhile, the electrical resistivity also shows a sudden change
at such a transition[71]. Such behaviours were indeed observed from the
experiments[73, 74, 53, 76, 75]. All these experiments along with our
measurements support pressure-induced ETT in the V2-VI3 compounds in Phase I.
For Bi2Te2.7Se0.3 with $n$-type carriers, we observed a minimum of the $c/a$
ratio (Fig. 1d), anomalies of the phonon modes (Extended Data Figs. 1 and 4),
abrupt change of the bulk mobility (Fig. 3c), maximum of the effective carrier
concentration (Extended Data Fig. 3) at pressure around 2 GPa. For this
compound, the Seebeck coefficient, resistivity, and thus power factor,
mobility and its product with the effective mass also exhibited anomalies at
the same pressure[53]. Our calculated results shown in Fig. 3d clearly reveal
pressure-induced ETT. All these results can be explained by the existence of
the ETT at pressure of 2 GPa in the studied compound. Comparison of
superconducting phases in Bi2Te2.7Se0.3 with Bi2Te3 and Bi2Se3. We have
demonstrated that the nontrivial topological state of Bi2Te2.7Se0.3 only
exists in Phase I from Hall effect measurements (Fig. 2). Thus, topological
superconductivity is only expected in Phase I with the space group of
$R$-3$m$. The topological orders are absent in the rest phases with the space
group of $C$2/$m$, $C$/2$c$, and $Im$-3$m$. Now let us compare our findings in
Bi2Te2.7Se0.3 with the experiments for the two ending compounds Bi2Te3 and
Bi2Se3 in the literature. For Bi2Se3, superconductivity was reported to start
from Phase II after undertaking the first structure transition from $R$-3$m$
to $C$2/$m$[21, 77]. Since the topological orders are absent in the last three
high-pressure phases, the experiments do not support the existence of
topological superconductivity in Bi2Se3 at high pressures. For Bi2Te3, the
experiments delivered rather rich information. An early study[19] in 1972
revealed that superconductivity occurs in both $p$ and $n$-type Bi2Te3 at
pressure near 6 GPa. These findings were later confirmed by many groups after
the birth of the topological insulating states in this system. Specifically,
two groups[20, 78] reported the occurrence of superconductivity at pressure as
low as 3 GPa in $p$-type Bi2Te3 single crystal with $c$BN and NaCl as
pressure-transmitting medium, respectively. These observations suggested the
possible coexistence of superconductivity with the topological order in Phase
I of $p$-type Bi2Te3. A combined electrical transport and XRD study[79] on
$p$-type Bi2Te3 revealed that superconductivity takes place for all four
phases and can appear in the initial phase. It would be ideal if the
experimental evidence for the nontrivial topological order had been provided
from their experiments. Meanwhile, superconductivity was observed at pressure
of 11 GPa in powder sample with the mixture of Fluorinert FC-77 and FC-70 (1:1
in volume) as a pressure-transmitting medium[76] and near 7 GPa in single
crystal with glycerol as a medium[80]. Although the structure measurements on
these samples were not carried out, these authors thought that
superconductivity occurs in their samples in Phase II when the structural
transition takes place from $R$-3$m$ to $C$2/$m$. First-principles
calculations. In order to calculate the surface electronic structure, the
primitive cell of Bi2Te3 parent compound is chosen as shown in Fig. 3a. The
(001) surface has been proved to have metallic surface states in early
calculations[81]. We first prepared (001)-oriented 10-monolayers-thick crystal
slabs of Bi2Te3 with experimental lattice parameters, then three Te atoms at
one Te position are replaced by Se atom to make an alloy. The vacuum layer was
15 Å thick to ensure decoupling between neighbouring slabs. The first
Brillouin zone for Bi2Te3 and the two-dimensional Brillouin Zone of the (001)
projected surface are shown in Fig. 3b. The slab band structures at different
pressures are given in Fig. 3c. The isoenergetic surfaces close to the top of
the valence bands for the selected pressures are shown in Fig. 3d. In all
these calculations, the experimentally obtained equation of states for
Bi2Te2.7Se0.3 was used (Fig. 1c). We performed all the first-principles
calculations in the framework of the density functional theory[82, 83], as
implemented in the Vienna $ab$ $inito$ simulation package[84, 85, 86]. For
self-consistent field calculations, we used the Perdew-Burke-Ernzerhof type
generalized gradient approximation[87] by setting the plane-wave basis
expansion as 500 eV with a k-point grid taken as 8$\times$8$\times$4\. The
spin-orbit coupling was considered during the calculations.

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Extended Data Table 1 $\mid$ Detailed structural parameters of Bi2Te2.7Se0.3
at room temperature.

P (GPa) | Space group | Lattice parameters | Atom | Site | $x$ | $y$ | $z$
---|---|---|---|---|---|---|---
1.0 |  $R$-3$m$ |  $a$=4.391(3) Å | Bi | 6$c$ | 0 | 0 | 0.4080(1)
|  |  $c$=30.482(27) Å | Te/Se(1) | 6$c$ | 0 | 0 | 0.3524(1)
|  |  $R_{p}$=1.6%, $R_{wp}$=2.2% | Te/Se(2) | 3$a$ | 0 | 0 | 0
13.3 |  $C$2/$m$ |  $a$=14.624(20) Å | Bi(1) | 4$i$ | 0.1654(3) | 0 | 0.1903(7)
|  |  $b$=4.032(4) Å | Bi(2) | 4$i$ | 0.4498(9) | 0 | 0.2323(2)
|  |  $c$=17.243(19) Å | Te/Se(1) | 4$i$ | 0.2356(5) | 0 | 0.4047(8)
|  |  $\beta$=148.229(21) ∘ | Te/Se(2) | 4$i$ | 0.0098(6) | 0 | 0.5745(7)
|  |  $R_{p}$=1.7%, $R_{wp}$=2.3% | Te/Se(3) | 4$i$ | 0.3352(1) | 0 | 0.9808(8)
20.6 |  $C$2/$c$ |  $a$=10.145(29) Å | Bi | 8$f$ | 0.2586(6) | 0.1155(4) | 0.8333(4)
|  |  $b$=6.728(13) Å | Te/Se(1) | 8$f$ | 0.6013(5) | 0.3709(9) | 0.9777(5)
|  |  $c$=10.467(26) Å | Te/Se(2) | 4$e$ | 0 | 0.5946(9) | 0.25
|  |  $\beta$=134.373(39) ∘ |  |  |  |  |
|  |  $R_{p}$=7.5%, $R_{wp}$=8.8% |  |  |  |  |
28.0 |  $Im$-3$m$ |  $a$=3.611(16) Å | Bi | 2$a$ | 0 | 0 | 0
|  |  $R_{p}$=7.2%, $R_{wp}$=7.4% | Te/Se | 2$a$ | 0 | 0 | 0

Extended Data Fig. 1 $\mid$ High-pressure vibrational properties of
Bi2Te2.7Se0.3 at room temperature. a, Raman scattering spectra collected at
various pressures up to 44.3 GPa at room temperature with the laser excitation
of 488 nm and laser power of 1.5 mW. The spectra change profiles at pressures
of 8.1 and 17.4 GPa. No active Raman peaks at higher pressures above 22.8 GPa
are observed. b, From the bottom to top, Representative Raman spectra in open
cycles for the phase with space group of $R$-3$m$ at ambient pressure,
$C$2/$m$ at 9.2 GPa, and $C$2/$c$ at18.2 GPa, respectively. Lorentz fitting to
the data points is shown in the curve for individual phonon mode and their
combination. The sticks at each bottom denote the calculated frequencies of
the Raman-active modes for the corresponding structure symmetry. c, Pressure
dependence of the frequency of each phonon mode in the first three phases with
the space group of $R$-3$m$ (Phase I), $C$2/$m$ (Phase II), and $C$2/$c$
(Phase III), respectively. The regime for each phase, the boundary in between
of them, and their coexistence can be judged from the data points. d, Pressure
dependence of FWHM of the phonon mode $E_{g}^{1}$, $A_{1g}^{1}$, $E_{g}^{2}$,
and $A_{1g}^{2}$ (from the bottom to top) for the Phase I with the space group
of $R$-3$m$. There is a maximum (minimum) for the $E_{g}^{1}$ ($E_{g}^{2}$)
mode at a pressure close to 2 GPa at which the $A_{1g}^{1}$ and $A_{1g}^{2}$
mode changes curvature.

Extended Data Fig. 2 $\mid$ Hall conductivity $\sigma_{xy}$ vs applied
magnetic field for Bi2Te2.7Se0.3. The data were taken for Phase I with the
space group of $R$-3$m$ at selected pressures and at temperature of 10 K. The
open cycles are the experimental data points. The curves are the fitting
results to the experiments by considering the combination effects from the
bulk and surface states.

Extended Data Fig. 3 $\mid$ Pressure dependence of the bulk carrier
concentration in the absolute value for Bi2Te2.7Se0.3 at temperature of 10 K.
Left panel: The effective carrier concentration $n_{eff}$ of the bulk in Phase
I and the bulk carrier concentration $n_{H}$ of the rest phases. Right panel:
Mean free path $l$ of Phase I. The line is drawn for the guide to the eye. The
material is $n$-type in Phase I, III, IV but $p$ type in Phase II. This
character can be judged from Fig. 2a.

Extended Data Fig. 4 $\mid$ Evolution of the phonon modes with pressure for
Bi2Te2.7Se0.3 at temperature of 3.6 K. a, Low-temperature Raman spectra at
various pressures up to 28.1 GPa. Four phases can be identified from the
different profiles of their phonon modes. In the superconducting state of each
phase, the Raman spectra have the same profiles compared with the normal state
at the room temperature (Extended Data Fig. 1). This indicates that the
superconducting phase carries on all the features of this phase at the normal
state. The first superconducting phase thus keeps its nontrivial topological
order. b and c, Pressure dependence of the frequency and FWHM of the
$A_{1g}^{1}$, $E_{g}^{2}$, and $A_{1g}^{2}$ mode in Phase I with the space
group of $R$-3$m$.

Extended Data Fig. 5 $\mid$ Enlarged view of the upper critical field as a
function of the reduced temperature ($T/T_{c}$) of Bi2Te2.7Se0.3 at selected
pressures. The experimental data are represented by open cycles. The fitting
to the experimental data points near $T_{c}$ in the $T/T_{c}$ range of 0.5 to
1 is shown in the curve by using $\mu_{0}H_{c2}\sim(1-T/T_{c})^{\alpha}$ with
$\alpha$ of $2/3$ for pressure of 6.4 GPa and of 1.0 for pressure of 14.0 and
16.8 GPa, respectively.

Extended Data Fig. 6 $\mid$ Temperature-dependent Raman spectra for
Bi2Te2.7Se0.3 across the superconducting transition in Phase I at pressure of
6.4 GPa. a, Raman spectra at low temperatures down to 3.6 K. b and c,
Temperature dependence of the frequency and FWHM of the $A_{1g}^{1}$,
$E_{g}^{2}$, and $A_{1g}^{2}$ mode. The $T_{c}$ is indicated by the dashed
line.