PHYSICAL REVIEW B 99, 104109 (2019)

Effect of Cu intercalation and pressure on excitonic interaction in 1T -TiSe2
S. Kitou,1,2 A. Nakano,1,* S. Kobayashi,1,† K. Sugawara,1,‡ N. Katayama,1 N. Maejima,3,§ A. Machida,3 T. Watanuki,3
K. Ichimura,4,5 S. Tanda,4,5 T. Nakamura,2 and H. Sawa1,
1

Department of Applied Physics, Nagoya University, Nagoya 464-8603, Japan
2
Institute for Molecular Science, Myodaiji, Okazaki 444-8585, Japan
3
Synchrotron Radiation Research Center, National Institutes for Quantum and Radiological Science and Technology,
Sayo, Hyogo 679-5148, Japan
4
Department of Applied Physics, Hokkaido University, Sapporo 060-8628, Japan
5
Center of Education and Research for Topological Science and Technology, Hokkaido University, Sapporo 060-8628, Japan(Received 6 February 2019; published 28 March 2019)
1T -TiSe2 has a semimetallic band structure at room temperature and undergoes phase transition to a triple-q
charge-density wave (CDW) state with a commensurate superlattice structure (2a × 2a × 2c) below Tc ≈ 200 K
at ambient pressure. This phase transition is caused by cooperative phenomena involving electron-phononand electron-hole (excitonic) interactions, and cannot be described by a standard CDW framework. By Cu
intercalation or the application of pressure, this phase-transition temperature is suppressed and superconductivity(SC) appears. However, it is not clear what kind of order parameters are affected by these two procedures. We
investigated the crystal structure of Cux TiSe2 and pressurized 1T -TiSe2 around the SC state by synchrotron x-ray
diffraction on single crystals. In the high-temperature phase, the variations of structural parameters for the caseof Cu intercalation and application of pressure are considerably different. Moreover, the relationship between thecritical points of the CDW phase transition and the SC dome are also different for the two cases. The excitonic
interaction appears to play an important role in the P-T phase diagram of 1T -TiSe2 , but not in the x-T phase
diagram.
DOI: 10.1103/PhysRevB.99.104109

I. INTRODUCTION

In strongly correlated electronic systems, exotic electronic
states are often realized by changing the balance between
interactions through external pressure and/or carrier doping.
For example, superconductivity (SC) in cuprates appears by
suppressing the antiferromagnetic interaction through carrier doping [1]. Hence, in these materials, it is very important to understand which of the fundamental parameterschange by applying external pressure and carrier doping. The
electronic state of transition-metal dichalcogenides (TMDs),
which changes on carrier doping or application of externalpressure, is interesting from this point of view.
TMDs often show various charge-density wave (CDW)
states, with SC often appearing in its vicinity in materials suchas 1T -TaS2 [2,3] and 2H-NbSe2 [4,5]. In this series, 1T -TiSe2
has been one of the most vigorously researched systems because of its exotic electronic states [6–10] such as chiral CDW*
Present address: Department of Physics, Nagoya University,
Nagoya 464-8602, Japan.
†
Present address: Japan Synchrotron Radiation Research Institute,SPring-8, 1-1-1 Kouto, Sayo 679-5198, Japan.
‡
Present address: Synchrotron Radiation Research Center, National
Institutes for Quantum and Radiological Science and Technology,
Sayo, Hyogo 679-5148, Japan.
§
Present address: Department of Chemistry, Rikkyo University,
Toshima-ku, Tokyo 171-8501, Japan.
z47827a@cc.nagoya-u.ac.jp2469-9950/2019/99(10)/104109(10)[11] and exciton condensation [12]. Although 1T -TiSe2 has
both electron-phonon and electron-hole interactions, several
aspects of its electronic ground state remain to be understood.
In this compound, the formal valence states of Ti4+ (3d 0 ) andSe2− (4p6 ) correspond to closed shells. According to reports,
a semimetallic band structure is formed by Se 4p and Ti 3dorbitals [13]. Near the Fermi energy, a hole pocket of the Se 4p
and electron pockets of the Ti 3d exist at the  point and the
L points, respectively. The electrical resistivity shows metallic
characteristics at room temperature [14].
By decreasing temperature, a hump appears in electric
resistivity at Tc ≈ 200 K [14]. Below 200 K (β phase), a
triple-q CDW state with a commensurate superlattice structure (2a × 2a × 2c) is formed by folding of the band near
L points to  point [15–17]. However, because the Fermi
surface in 1T -TiSe2 is three dimensional and the size of
two Fermi surfaces contributing to the nesting between
electrons and holes is different, the triple-q nesting condition from the hole pocket to the electron pockets (qnest =a∗ /2 + c∗ /2, −b∗ /2 + c∗ /2, −a∗ /2 + b∗ /2 + c∗ /2) is not
good. Therefore, the origin of this phase transition cannot be
explained within a simple CDW framework. In this phasetransition mechanism, it is argued that not only the electronphonon coupling (EPC) [17–21] but also the electron-hole(excitonic) interaction [12,22–25] plays an important role.
However, because the electronic system and the lattice system
are strongly coupled in this compound, it is difficult to accurately estimate the contribution of the excitonic interaction
exclusively. Ta2 NiSe5 , which is a direct-gap semiconductor

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PHYSICAL REVIEW B 99, 104109 (2019)that has similarities to 1T -TiSe2 [26,27], is considered anothercandidate as an excitonic insulator [28–33]. Comparing theelectronic states of both compounds is important for understanding the excitonic insulator system.
Recently, SC was achieved in 1T -TiSe2 by intercalation[34–37], external pressure [38], and electric field [9]. For
MAX=
example, SC was reported for 0.04  x  0.10 (TSC
4.15 K at x = 0.08) in Cu-intercalated Cux TiSe2 [34], andMAX= 1.8 K at P =in the pressure range of 2–4 GPa (TSC
3 GPa) in pristine 1T -TiSe2 [38]. These two SC states are
summarized using similar pressure-temperature (P-T ) and Cu
content x-temperature (x-T ) phase diagrams. It is of prime
interest to understand how the change of the electronic and/or
the lattice system influences the triple-q CDW state and the
SC state in 1T -TiSe2 . Indeed, multilateral experiments andcalculations are performed in Cux TiSe2 [39–49] and pressurized 1T -TiSe2 [49–52].
The crystal structure of pristine 1T -TiSe2 has been studied
using neutron diffraction by Di Salvo et al. in 1976 [14], but
detailed information about the crystal structure around TSC is
hardly reported because of the experimental and analyticaldifficulties described later. The theoretical investigations of
the SC state in 1T -TiSe2 [47–49,52] were calculated by using
the crystal structure of 1T -TiSe2 or Cux TiSe2 in the high temperature (HT). Cu intercalation changes the chemical potential
and pressurization changes the phonon modes by changing
lattice structures. It is strange that the two phase diagramsof Cu-intercalated [34,39] and pressurized [38,50] 1T -TiSe2
resemble each other. Therefore, to understand the anomalous
electronic state of 1T -TiSe2 , it is important to understandthe structural changes associated with Cu intercalation andpressurization.
In this study, we conducted the synchrotron radiation xray-diffraction (XRD) experiments and crystal-structure analysis of 1T -TiSe2 under ambient- and high-pressure conditions
as well as Cu-intercalated 1T -TiSe2 under ambient pressure.
In Cux TiSe2 , detailed structural parameters and a complete
phase diagram with the information of phase transitions andthe SC dome are reported. Furthermore, for 1T -TiSe2 underhigh pressure, structural parameters were determined with ahigh degree of precision by using multiple single crystals
and by performing structure analysis including superlatticereflections.
II. EXPERIMENT

Single-crystal samples of 1T -TiSe2 used under ambientand high-pressure experiments were synthesized using theprocedure outlined in Ref. [14], and five kinds of singlecrystal samples of Cux TiSe2 (x = 0.05−0.13) were preparedaccording to Ref. [53]. The content of Cu in Cux TiSe2 wasdetermined by crystal-structure analysis using the synchrotron
XRD at room temperature, in which weak diffuse scatteringcorresponding to disordered Cu position was ignored. The
XRD measurements at ambient pressure were carried out atbeamline BL02B1 at the synchrotron facility SPring-8, Japan[54]. A helium gas blow was employed to cool the sample
to 25 K at BL02B1. The XRD measurements under highpressure were performed using a diamond-anvil cell (DAC)
apparatus at beamline BL22XU at SPring-8 [55], using awavelength λ = 0.4133 Å. The single crystals of 1T -TiSe2
were loaded into a hole (220-μm diameter) in a stainlesssteel gasket. The incident x-ray beam was shaped into a
40 × 40 μm2 square and impinged into the samples. Helium
was used as the pressure medium and helium-gas-membrane
system was used for pressurization. The pressure was calibrated by measuring the fluorescence of small rubies placed
beside the 1T -TiSe2 crystal in the sample chamber [56]. A
refrigerator was employed to decrease the temperature to
5 K at BL22XU. A two-dimensional imaging plate (IP) wasused as the diffractometer’s detector at the two beamlines toperform structure analysis including superlattice reflections.
For the crystal-structure analysis, we used original softwarefor extracting the peak intensity [57]. Because the diffraction
from the single crystals of diamond cannot be ignored in asingle-crystal XRD experiment using DAC, these are also
taken into consideration for the analysis. Peak-intensity averaging and structure analysis were performed using SORTAV[58] and JANA2006 [59], respectively.
The electric resistivity measurements were performed ina Quantum Design physical properties measurement system(PPMS) instrument using the standard four-probe technique.
Additional resistivity measurements down to 100 mK werecarried out by using an adiabatic demagnetization refrigerator cell combined with the PPMS. dc magnetization measurements were conducted using a superconducting quantum
interference device magnetometer in a Quantum Design magnetic properties measurement system instrument.
III. RESULT
A. 1T -TiSe2 at ambient pressure

Figure 1(a) shows the crystal structure of 1T -TiSe2 in the
HT phase (a × a × c; P3̄m1). Ti and Se each form a triangularlattice. Below 200 K, reflections appeared at (h/2, k/2, l/2)
(shown in Fig. 2), and a superlattice structure (2a × 2a × 2c;P3̄c1) is realized [Fig. 1(b)] in the β phase of 1T -TiSe2 . The
structural parameters obtained from our XRD experiment at
30 K (Table I) are qualitatively consistent with the results
reported by Di Salvo et al. [14]. As a result of the atomic
displacements accompanying the phase transition, hybridization of Se 4p and Ti 3d orbitals creates the triple-q structure[15–17]. These displacements also correspond to softeningof the transverse optical (TO) phonon mode observed by theinelastic x-ray scattering (IXS) [20]. Each of the Ti and Se
atoms has one symmetry site in the HT phase, whereas they
are divided into two symmetry sites each in the β phase. The
ratio of the number of Ti and Se sites is 1:3 in the β phase.
As a result, TiSe6 octahedra with symmetry D3d are divided
into two sets of octahedra with symmetries D3 and C2 during
the structural phase transition [the dotted circle and the solid
circle shown in Fig. 1(b), respectively]. The volumes of the3
two TiSe6 octahedra are nearly equal (D3 : 22.1402 Å , C2 :3
22.1452 Å ) at 30 K.
In TiSe6 octahedra with symmetry C2 , Ti and a part of Se
are displaced in opposite directions. Therefore, the electricdipole moments exist locally despite the large electrical conductivity in the β phase [14], whereas no dipole moments in
TiSe6 octahedra with symmetry D3 . These electric-dipole mo-

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PHYSICAL REVIEW B 99, 104109 (2019)

FIG. 2. Temperature dependence of the intensity of the(1/2, 3/2, 5/2) superlattice peak (black) and the lattice constants
normalized to 300 K (red and blue).

FIG. 1. (a) Crystal structure of 1T -TiSe2 (a × a × c). (b) Crystal
structure (2a × 2a × 2c) in the β phase. The black arrows on atoms
show the atomic displacement accompanying the structural phasetransition. The yellow arrows show the electric-dipole moments.
There is a threefold axis along the c axis at sites indicated by white
triangles. The dotted circle and the solid circle show the octahedrawith symmetries D3 and C2 , respectively. (c) The electric-dipole
moments form a kagome lattice (blue dotted line). The black line
shows a unit cell of size 2a × 2a. (d) Formation of an electric toroidal
moment T e . (e) Arrangement of the electric-dipole moments μ andthe electric toroidal moments T e in 1T -TiSe2 in the β phase.

ments have been calculated [60], and they correspond to thetriple-q structure [15–17], which was formed by the freezingof the TO phonon mode [20]. The intensity of the superlatticereflections is scaled to the size of the dipole moment |μ|(μ = qd). From the difference between the centroids of Ti
and Se atoms, the value of |d| is 0.066 Å. In the case of
BaTiO3 (Ti4+ 3d 0 ), which is a typical ferroelectric material,
the value of |d| is 0.134 Å in the ferroelectric phase (P4mm)[61]. Hence, the |μ| in 1T -TiSe2 , which is about half value in
BaTiO3 , is significant.
In this system, one-fourth of TiSe6 octahedra become
nodes that do not develop dipoles [the dotted circle inFig. 1(b)]. As a result, the dipoles form the kagome lattice inthe basal plane, as shown in Fig. 1(c). On this kagome lattice,
the electric dipoles form vortices around the lattice sites
indicated by white triangles, a threefold rotation axis exists[Fig. 1(b)]. Because there is an equal number of clockwise
and anticlockwise vortices, antiferroelectric arrangement ofelectric dipoles are realized within the TiSe2 plane. In thecenter of the vortex of the electric dipoles, an electric toroidal

moment T e = r × μ can be defined as shown in Fig. 1(d)[62–65]. Because r is a vector from the center of the vortex
to the dipole moment μ, T e is along the c axis at the center ofthe vortex. An antiferrotoroidic state, where the neighboring
electric toroidal moments are arranged in opposite directions both within and between layers, is realized [Fig. 1(e)].
Figure 2 shows the temperature dependence of lattice constants normalized to 300 K. The rate of change in the c-axis
lattice constant is lower below Tc . This unusual behavior,consistent with the reported data [66], may be due to theantiferrotoroidic state in 1T -TiSe2 .
B. Cux TiSe2 at ambient pressure

The formation of electric dipoles is important in the triple-q
CDW state of pristine 1T -TiSe2 because these dipoles correspond to the triple-q structure, which is formed by the freezingof the TO phonon mode. Our interest here is to understandhow these electric dipoles change by Cu intercalation orapplication of an external pressure.
For Cu-intercalated samples, the lattice constants and a/c
at room temperature for Cu-intercalated samples Cux TiSe2
with different x are shown in Fig. 3(a). By increasing x,
the c-axis parameter increases appreciably, while the a-axis
parameter also increases monotonically. There is a linear relationship between a/c and x, as shown in the inset of Fig. 3(a).
Compared to the results of previous work by Morosan et al.
[34], nearly the same values of a/c were observed for Cu
content x at room temperature. A linear equation
a/c = −2.237 × 10−2 x + 0.589,(1)

can be obtained for approximating the linear relationshipbetween x and a/c [black line in inset of Fig. 3(a)].
Table I shows the resulst of the structure analysis for
x = 0, 0.0798(12), and 0.129(2) at room temperature. The
Cu ion occupies the 1b site (Wyckoff letter) of P3̄m1 spacegroup, which is the site between TiSe2 layers. Since it has

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PHYSICAL REVIEW B 99, 104109 (2019)
TABLE I. Crystallographic data for 1T -TiSe2 and Cux TiSe2 .
β phaseHigh-temperature phase
Pressure (GPa) 00
Temperature (K) 300
300
Cu content x
00.079 8(12)Wavelength (Å) 0.354 22 0.353 74
Space group
P3̄m1
P3̄m1
a (= b) (Å)
3.539 5(3) 3.544 7(8)c (Å)
6.008 2(4) 6.037 5(9)3V (Å )Z
F (000)dmin (Å)aNTot,obs
NUniq,obs
R1 (%)(σ cut)65.187(9)
1
90
0.4
504
300
2.77
(I > 4σ )65.70(2)
1
119
0.45
452
223
1.94
(I > 4σ )

0
3.12
0
0
300
110
30
30
0.129(2) 000.050 0(11)0.353 74 0.4133
0.354 220.388 14
P3̄m1
P3̄m1
P3̄c1
P3̄c1
3.548 1(3) 3.4763(17) 7.059 30(10) 7.059 7(2)6.053 0(4) 5.7481(17) 11.992 9(3) 12.020 0(8)

2.82
5
0
0.4133P3̄c1
6.955(3)11.524(3)65.992(9)
1
119
0.35
5 106
663
2.25
(I > 4σ )482.8(3)
8
720
0.69
190
76
4.71
(I > 2σ )60.16(5)
1
90
0.64
118
47
4.77
(I > 4σ )517.581(17)
8
720
0.3
108 669
7 344
2.62(I > 2σ )β phase (P3̄c1)

High-temperature phase (P3̄m1)
Atom

Site

Position [x, y, z]

518.81(4)8732
0.3
76 8336 606
2.77(I > 2σ )2Beq (Å )(P = 0 GPa, T = 300 K, x = 0)Se2d[2/3, 1/3, 0.25 514(5)] 0.659(6)Ti
1a[0, 0, 0]0.896(10)[P = 0 GPa, T = 300 K, x = 0.079 8(12)]Se
2d[2/3, 1/3, 0.25 399(4)] 0.592(7)Ti
1a[0, 0, 0]0.835(10)Cu
1b[0, 0, 1/2]
1.35(11)[P = 0 GPa, T = 300 K, x = 0.129(2)]Se
2d[2/3, 1/3, 0.253 39(3)] 0.708(2)Ti
1a[0, 0, 0]0.968(4)Cu
1b[0, 0, 1/2]
1.46(3)(P = 3.12 GPa, T = 110 K, x = 0)Se2d[2/3, 1/3, 0.267 1(6)] 0.24(7)Ti
1a[0, 0, 0]0.31(9)

Atom

Site

Position [x, y, z]

2

Beq (Å )(P = 0 GPa, T = 30 K, x = 0)
Se(1)
12g
[0.164 01(2), 0.333 12(2), 0.121 51(4)] 0.238(2)Se(2)
4d[2/3, 1/3, 0.122 08(5)]0.141(3)Ti(1)
6f[0, 0.491 48(3), 1/4]
0.270(5)Ti(2)
2a[0, 0, 1/4]
0.313(8)[P = 0 GPa, T = 30 K, x = 0.050 0(11)]
Se(1)
12g
[0.165 50(3), 1/3, 0.122 098(5)]0.1993(2)0.1993Se(2)4d[2/3, 1/3, 0.122 098]Ti(1)6f[0, 0.494 93(9), 1/4]
0.3142(2)Ti(2)
2a[0, 0, 1/4]
0.3142Cu(1)6e[0, 1/2, 0]0.47(2)Cu(2)2b[0, 0, 0]0.47(P = 2.82 GPa, T = 5 K, x = 0)
Se(1)
12g
[0.164 86(16), 1/3, 0.116 9(2)]0.16(7)Se(2)4d[2/3, 1/3, 0.116 9]
0.16
Ti(1)
6f
[0, 0.49 53(4), 1/4]
0.24(9)Ti(2)2a[0, 0, 1/4]
0.24

admin indicates the resolution limit used for the crystal-structure analysis. NTot,obs and NUniq,obs indicate the number of the total reflections and theunique reflections in the dmin region, respectively. In P = 0 GPa, T = 30 K, x = 0.0500(11), to reduce the parameters we restricted y[Se(1)] =1/3 and z[Se(1)] = z[Se(2)] and Beq [Se(1)] = Beq [Se(2)] and Beq [Ti(1)] = Beq [Ti(2)] and Beq [Cu(1)] = Beq [Cu(2)]. In P = 2.82 GPa, T =5 K, x = 0, to reduce the parameters we restricted y[Se(1)] = 1/3 and z[Se(1)] = z[Se(2)] and Beq [Se(1)] = Beq [Se(2)] and Beq [Ti(1)] =Beq [Ti(2)].

been reported that the physical properties are affected by the
Se vacancy in 1T -TiSe2 [67], we also investigated this fact.
We confirmed that there was no Se vacancy in all Cux TiSe2
samples including nondoped 1T -TiSe2 . The interlayer Se-Se
distance [Fig. 1(a)] increases with increasing x [Fig. 3(b)].
The volume of TiSe6 octahedra increases with increasing x[inset of Fig. 3(b)], indicating a decrease in the valence of
Ti. This corresponds to electron doping from Cu ions to
TiSe2 layers, which has been also verified through the densityfunctional-theory calculations [48]. Assuming the valence ofSe (2-) in 1T -TiSe2−δ , since Se vacancy δ also corresponds

to electron doping, δ dependence of the Ti–Se bond length
similar to Cux TiSe2 is predicted. However, the result of thestructure analysis reported in Ref. [67] shows that the Ti–Se
bond length decreases with increasing δ, which is an inverse
correlation with Cu-intercalation system. The Se vacancy
cannot be understood by the simple valence change of Ti.
Figure 4(a) shows the temperature dependence of the electric resistivity for Cux TiSe2 . The value x of single-crystal samples used for electric resistivity measurements was determinedfrom XRD experiments by using Eq. (1). SC was confirmed inMAX= 3.79 K
samples with 0.052(6)  x  0.123(8), with TSC

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FIG. 3. (a) Lattice parameters of Cux TiSe2 with Cu content
x = 0, 0.0500(11), 0.0753(17), 0.0798(12), 0.118(4), and 0.129(2)at room temperature. Inset: a/c as a function of x at room temperature. (b) The distances Se-Se (intralayer) and Se-Se (interlayer)at room temperature for x = 0, 0.0798(12), and 0.129(2) [refer toFig. 1(a)]. Inset: Volume of TiSe6 octahedra as a function of x at
room temperature.

occurring at x = 0.076(8), consistent with reported composition [34]. In x = 0.130(5), the SC was absent down to
139 mK. Figure 4(c) shows the magnetic susceptibility of
Cu0.075 TiSe2 , TSC = 3.8 K, the SC volume fraction is large
enough to constitute bulk SC.
The phase-transition temperature was determined asaround 80 K for x = 0.052(6) from the dρ/dT curve[Fig. 4(b)]. Furthermore, the same superlattice pattern aspristine 1T -TiSe2 was confirmed in Cu0.05 TiSe2 below 80 K
from XRD data [Fig. 5(a) and Fig. 6(a)]. We confirmed thatsome superlattice peaks with the strong intensity show abroadening along qnest = a∗ /2 ± c∗ /2 vectors in Cu0.05 TiSe2
at 30 K [Fig. 5(a)]. For example, a superlattice reflection(−5/2, 3, −1/2) extends in two directions of −a∗ /2 + c∗ /2and −a∗ /2 − c∗ /2. These directions correspond to theqnest vectors in two directions passing through an L point[Fig. 5(d)]. The correlation length was calculated to be about
10 unit cells× 72 + 122 ≈ 140 Å from the peak broadening
in the qnest direction of the superlattice reflections. This is
the same order of magnitude as the domain size reported
from earlier XRD [39] and scanning tunneling microscopy
measurements [41].
Recently, incommensurate superlattice reflections were reported in Cux TiSe2 (at ambient pressure) [39] and 1T -TiSe2(under pressure) [50]. In our XRD measurement of Cux TiSe2(and pressurized 1T -TiSe2 to be discussed later), we cannot

FIG. 4. (a) Temperature dependence of the electric resistivity
for Cux TiSe2 . Inset: Resistivity below 5 K. (b) dρ/dT curve for
x = 0.052(6), Tc ≈ 80 K. (c) Magnetic susceptibility of Cu0.075 TiSe2 .

estimate the degree of incommensurability due to the limited
resolution of our IP detector (0.03 deg/pixel). However, both
additional superlattice reflections and the change of symmetry
suggesting the incommensurate long-range structure were notobserved in Cu0.05 TiSe2 (and pressurized 1T -TiSe2 ).
The crystal-structure analysis was carried out using theextracted intensity of the superlattice reflections. A triple-q
structure identical to pristine 1T -TiSe2 in the β phase was obtained from our analysis (Table I). The size of the dipole moment |μ| decreased to 58% to that observed in 1T -TiSe2 at 30
K. It is noted that the SC and the triple-q structure coexist in
the ground state in Cu0.05 TiSe2 . In Cu0.05 TiSe2 , an unusual behavior of lattice constants in the stacking direction due to thestructural phase transition is not observed [Fig. 6(c)] as seen in
1T -TiSe2 (Fig. 2). The compression ratio of c axis was larger
than that of a axis, akin to many common layered compounds.
For 0.075  x  0.13, no additional superlattice reflections or diffuse scattering were observed above 25 K down to104109-5

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FIG. 5. (a) X-ray-diffraction data of Cu0.05 TiSe2 at 30 K. The
white square parts are shown as 2.5 times as large. (b)–(d) Brillouinzone layout of 1T -TiSe2 at high-temperature phase (a × a × c)
where  (0, 0, 0), A (0, 0, 1/2), M (1/2, 0, 0), L (1/2, 0, 1/2),
K (1/3, 1/3, 0), and H (1/3, 1/3, 1/2). The red arrows show
the qnest vector corresponding to the elongation of the superlattice
peaks in (a).

10−6 times the intensity of the main reflections. For example,
Fig. 6(b) shows the XRD data in Cu0.075 TiSe2 at 25 K in
which there are no superlattice reflections. This fact indicatesthe absence of structural phase transitions and electric-dipole
moments.
Figure 6(d) shows the x-T phase diagram of Cux TiSe2 from
our XRD and electric resistivity measurements. The criticalconcentration xc of the phase transition is x ≈ 0.07. It isnoted that xc is inside the SC dome. While this differs fromthe previous XRD data [39], the present result shows good
agreement with those obtained by earlier Raman scattering[42] and IXS [49].

C. 1T -TiSe2 at high pressure

Our x-T phase diagram of Cux TiSe2 is different fromprevious reports of the XRD measurement of Cux TiSe2 [39]and pressurized 1T -TiSe2 [50]. Hence, we carefully investigated the crystal structure across the P-T phase diagram.
To discuss the electronic state under the high pressure withhighly accurate structural parameters, the structure analysis
by the synchrotron XRD experiment under the high-pressure
were carried out. The intensity of superlattice reflections
is approximately three orders of magnitude lower than theintensity of main reflections in the β phase of 1T -TiSe2 .
Powder samples are often used for structure analysis underpressure, but it is difficult to accurately extract superlatticeintensities with weak intensity. Therefore, it is required toperform structure analysis using single-crystal samples in thiscase. However, the accessible reciprocal space is limited dueto the constraints imposed by the use of a DAC. It is difficult

FIG. 6. X-ray-diffraction data of (a) Cu0.05 TiSe2 at 30 K and (b)Cu0.075 TiSe2 at 25 K. (c) Lattice constants normalized to 300 K of
Cu0.05 TiSe2 . (d) x−T phase diagram of Cux TiSe2 . White squares
denote that x values for which no superlattice reflections or diffuse
scattering are observed above 25 K, indicating absence of any phasetransition.

to perform a comprehensive structure analysis using only one
single crystal under high pressure.
To clarify the crystal structure of 1T -TiSe2 under pressure,
two single-crystal samples with different crystal orientations[(i) 30 × 25 × 10 μm3 and (ii) 20 × 20 × 10 μm3 ] were measured at the same time in the DAC [inset of Fig. 7(a)]. The
independent reciprocal space that could be measured was 24%of the total region (resolution limit of d > 0.75 Å) with only
crystal 1, whereas it improved to 69% by using two crystals.
The ratio of diffracted intensities from the two crystals wascrystal 1:crystal 2 = 1:0.74, in which common reflections
were used as the calibration standard.
Figure 7(a) shows the XRD data of 1T -TiSe2 under highpressure in the HT phase (3.12 GPa and 110 K). The pink and104109-6

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FIG. 7. (a) X-ray-diffraction data from 1T -TiSe2 at 3.12 GPa and 110 K, which is the high-temperature phase. Inset: Two single crystalsof 1T -TiSe2 with different crystal orientations used in the experiment with a diamond-anvil cell. (i) and (ii) indicate crystal 1 and crystal 2,
respectively. The pink and black circles show diffraction peaks of crystal 1 and crystal 2, respectively. (b) P-T phase diagram. The green
dots show our measurement points. The phase boundary described by the black dotted line and the SC dome described by red line are takenfrom Ref. [50] and Ref. [38], respectively. (c) The (−1/2, 7/2, −3/2) superlattice peak of crystal 1 for several temperatures, under an appliedpressure of around 3 GPa [corresponding to the five points in (b)]. Right Inset: Diffraction peaks of 1T -TiSe2 at 2.82 GPa and 5 K. (i) and (ii)indicate (−1/2, 7/2, −3/2) of crystal 1 and (0, 2, −5) of crystal 2, respectively. Left Inset: The (−3, 3, −2) peak of the crystal 1 at 2.82 GPaand 5 K.

the black circles correspond to diffraction peaks of crystal 1
and crystal 2, respectively. The information about a∗ b∗ -planeand c∗ -stacking direction are extracted mainly from crystal 1
and crystal 2, respectively. Figure 7(b) shows the measurement points on the P-T phase diagram. Crystal-structure
analyses at the high-pressure HT phase (3.12 GPa and 110 K)
and the high-pressure low-temperature phase (2.82 GPa and5 K) were carried out by using the diffraction intensity fromthe two crystals. From the analysis of the high-pressure HTphase data, the value of R1 (I > 4σ ) was 4.77%, which
is sufficiently reliable (Table I). The volume of the TiSe6
3octahedra decreases to 96% (from 22.2081 to 21.4241 Å )and the distance between the interlayer Se atoms decreases
to 91% [from 2.936 78(16) to 2.677(6) Å] at 3.12 GPa and
110 K, when compared to 0 GPa and 215 K. These results areopposite to the structural changes observed with increasing x
in Cux TiSe2 .
Figure 7(c) shows the temperature dependence of the peak
profile of a superlattice reflection (−1/2, 7/2, −3/2) fromcrystal 1. The plot point shows the changes in the peak profileas the temperature is lowered from 110 to 5 K at an appliedpressure of about 3 GPa [corresponding to the five data
points near 3 GPa in Fig. 7(b)]. By decreasing temperature at
3.12 GPa, superlattice reflections appeared below 65 K. This
result is consistent with earlier XRD reports [50]. Because allsuperlattice reflections satisfy the extinction rule of c glide
in the 2a × 2a × 2c lattice, the space group is determined
to be P3̄c1, the same as the β phase. The full width at half
maximum of the superlattice reflection was almost equal to themain peak (−3, 3, −2) at 5 K [left inset of Fig. 7(c)]. Hence,
crystal-structure analysis could be performed including thedata from the superlattice reflections. At the high-pressure andβ phase (2.82 GPa and 5 K), the value of R1 (I > 2σ ) was
4.71%, which was comparable to that of the high-pressure
HT phase. The similarity of this triple-q structure to the onesin unpressurized 1T -TiSe2 and Cu0.05 TiSe2 was confirmed(Table I). The size of the dipole moment |μ| was reduced to56% compared to that of 0 GPa and 30 K. It was confirmedthat there were no superlattice reflections at 6.49 GPa and10 K. This result is consistent with earlier reports [50], which
mentioned that superlattice reflections were not observed
above Pc = 5.1 GPa. The positional relationship between thecritical point (xc and Pc ) and the SC dome is different between
Cux TiSe2 and pressurized 1T -TiSe2 . This is also consistent
with the previously reported Raman scattering [42,51] andIXS measurements [49].
IV. DISCUSSION

The phase transition of 1T -TiSe2 is suppressed by pressureand electron doping. These behaviors resemble those of a general CDW transition in low-dimensional materials. The suppression of the CDW transition can be explained by changes inband filling and dimensionality of the system. Changes in EPC
and excitonic interaction due to external pressure and carrier
doping in 1T -TiSe2 system have been discussed in several
experiments [12,20,22–25] and calculations [17–19,21]. From
our structural findings, the nature of the phase transition in thissystem becomes clearer as follows.
As the interlayer Se-Se distance shrinks [hinter (P=3.12)/
hinter (P = 0) ≈ 0.91, dhinter /dP ≈ −0.083 Å/GPa] due to increasing pressure in the HT phase, the interlayer interaction
in 1T -TiSe2 becomes strong. The volume of TiSe6 octahedra decreases [V (P = 3.12)/V (P = 0) ≈ 0.96, dV/dP ≈3−0.25 Å /GPa] on applying pressure. In the P-T phase diagram of other TMDs such as 1T -TaS2 [3], 2H-NbSe2 [5],and 1T -TiTe2 [68], the SC is stabilized for a wide range ofpressures. On the other hand, the critical pressure Pc occurs
in the higher-pressure region rather than the SC dome in pressurized 1T -TiSe2 [Fig. 7(b)]. From our results under pressure,
2a × 2a × 2c structure is realized within the SC dome. The
triple-q structures were observed even around the SC dome
in pressurized 1T -TiSe2 , while the size of the electric-dipole
moments |μ| was reduced to 56% compared to the β phase at

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PHYSICAL REVIEW B 99, 104109 (2019)

ambient pressure. This result suggests the possibility that theexcitonic interaction and SC coexist.
Recently, the similar P-T phase diagram and SC was
reported in Ta2 NiSe5 [69,70], which is another excitonic insulator candidate. Electric toroidal moments are also observedin the excitonic phase of Ta2 NiSe5 [26]. However, Ta2 NiSe5
is a ferrotoroidic state, while 1T -TiSe2 is an antiferrotoroidic
state [Fig. 1(e)]. These similarities between 1T -TiSe2 andTa2 NiSe5 are important factors in the fundamental understanding of these compounds with excitonic interactions. The
excitonic interaction and SC may be closely related in both
1T -TiSe2 and Ta2 NiSe5 under applied pressure.
The balance between the number of electrons and holes
is an important consideration in the context of excitonic
interactions. Because the band dispersion itself does notessentially change in Cux TiSe2 [48,71], a positive shift ofthe chemical potential occurs by electron doping. In thiscase, because hole carriers are reduced by electron doping,
the excitonic interaction is weakened. From our structural
studies of Cux TiSe2 , as the interlayer Se-Se distance increases [hinter (x = 0.08)/hinter (x = 0) ≈ 1.010, dhinter /dx ≈0.35 Å/x] with increasing x in the HT phase, the interlayerinteraction in 1T -TiSe2 becomes weak. This affects the temperature dependence of the lattice constants [Figs. 2 and 6(c)],in which the anomalous behavior of the compression ratioof c axis disappears by Cu intercalation. The volume of
TiSe6 octahedra increases [V (x = 0.08)/V (x = 0) ≈ 1.003,
3
dV/dx ≈ 0.91 Å /x] by Cu intercalation. These are opposite
to the changes caused by pressure.
With regard to the x-T phase diagram, xc exists within the
SC dome [Fig. 6(d)], which is different from the position of
Pc in the P-T phase diagram. This difference may be related
to the presence or absence of the excitonic interaction in
1T -TiSe2 . On the other hand, the structural change accompanying the β phase transition in TiSe2 layers suppressed by
Cu intercalation is similar to that by pressure. These atomic
displacements in the β phase cannot be explained by changes
in the spatial charge disproportionation because there is nodifference in the volume of the two types of TiSe6 octahedra
as mentioned above. For this reason, the β phase of 1T -TiSe2
cannot be described by a standard CDW framework.
Recently, studies from our group have confirmed the pure
CDW due to electron-electron nesting on the high Cu-doped
region (x ≈ 0.33) [71], in which there are two kinds of TiSe6
octahedra with different volumes from each other. In the CDW
state in Cu0.33 TiSe2 , the charge disproportionation occurs in

TiSe2 layers and there is no excitonic interaction because of
no hole pockets. This pure CDW state is different from that inthe β phase. This result also seems to indicate that not only
the EPC but also the excitonic interaction are important in theβ phase of 1T -TiSe2 .

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V. SUMMARY

We investigated the crystal structure of pristine 1T -TiSe2
under ambient- and high pressure and Cux TiSe2 under ambient pressure by using synchrotron XRD. In pristine 1T -TiSe2
in the triple-q CDW state, the characteristic antiferroelectricarrangement of the electric dipoles and the possible electric
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ACKNOWLEDGMENTS

We thank T. Kaneko, S. Murakami, S. Ishihara, andT. Hasegawa for fruitful discussions. This work was supported by a Grant-in-Aid for Scientific Research (Grants No.
JP23244074, and No. JP17K17793) from JSPS, the Kato
Foundation for Promotion of Science, and the Daiko Foundation. The synchrotron radiation experiments were performed
at SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (Proposals No. 2013B0083,
No. 2016B1270, No. 2016B3783, and No. 2017B1733). Apart of this work was performed under the Shared Use Program of QST Facilities (Proposal No.2016B-H10) supported
by QST Advanced Characterization Nanotechnology Platform
under the remit of “Nanotechnology Platform” of the Ministry of Education, Culture, Sports, Science and Technology(MEXT), Japan (Proposal No. A-16-QS-0023). In addition,a part of this work was carried out under the Visiting Researcher’s Program of the Institute for Solid State Physics,
the University of Tokyo, and the Institute for Molecular Science (IMS), supported by Nanotechnology Platform Program(Molecule and Material Synthesis) of the MEXT, Japan.

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