Photo-Induced Displacive Phase Transition in Two-dimensional MoTe₂ from First-Principle Calculations

Abstract

The discovery and control of new phases of matter are a central endeavor in materials research. Phase transition in two-dimensional (2D) materials has been achieved through laser irradiation, strain engineering, electrostatic doping, and controlled chemical vapor deposition growth, and laser irradiation is considered as a fast and clean technique for triggering phase transition. By using first-principles calculations, we predict that the monolayer MoTe2 exhibits a photo-induced phase transition (PIPT) from the semiconducting 2H phase to the topological 1T′ phase. The purely electronic excitations by photon soften multiple lattice vibrational modes and lead to structural symmetry breaking within sub-picosecond timescales, which is shorter than the timescale of a thermally driven phase transition, enabling a controllable phase transition by means of photons. This finding provides deep insight into the underlying physics of the phase transition in 2D transition-metal ditellurides and show an ultrafast phase-transition mechanism for manipulation of the topological properties of 2D systems. More importantly, our finding opens a new avenue to discover the new families of PIPT materials that are very limited at present but are essential to design the next generation of devices operated at ultrafast speed.

1. Introduction

1.1 Current status of photo-induced phase transition (PIPT)

Phase transition is a process by which matter changes from one phase to another. The discovery, characterization, and control of materials at different phase are a central endeavor in condensed matter physics and materials science [1]. The traditional methods using theoretical and experimental methods including thermal annealing, strain engineering, charge doping, adsorption, alloying and electron injection have been adopted to understand the transformation of phase transition [2]. However, the abovementioned phase transformation states are all stabilized in the so-called equilibrium phases, and some require a complex environment to generate the phase transition. Meanwhile, with the increasing importance of optical modulation in the aspect of modulating materials structures and properties in recent years, PIPT has become an important tool in adjusting materials in the aspect that the abovementioned traditional methods are ineffective [2].

PIPT is a phase transition directly by light that can be precisely controlled toward target structures with desired physical properties at transient speeds, which is much more convenient than using heat or electric field to control the phase transition. The process of phase transition is basically a non-equilibrium process, and it is especially important to understand the evolution process of this non-equilibrium phase transition. Therefore, it is necessary and extremely important to obtain basic information such as timescale and driving force of PIPT. Using light to control ultrafine transformation between different forms of matter to realize ultrafast functional devices is the goal that scientific researchers have been pursuing since the discovery of PIPT in the 1990s, which takes place in one-dimensional (1D) corrected organic charge-transfer molecular system tetrathiafulvalene-p chloranil (TTF-CA) [3]. Actually, because light-induced charge transfer excitation and/or carrier generation can excite the instability of 1D properties inherent in electronic states through strong electron (spin)-electron (spin) interactions, researchers treat the PIPT of 1D correlated electron systems as their targets.

Although PIPT has the advantages of ultrafast dynamics and simple operation, the areas where PIPT phase transition can be successfully implemented are limited, such as: (1) time-resolved spectroscopy of the dynamics of photo-induced ionic-to-neutral or semiconductor-to-metal phase transition [4]: mixed-stack organic charge transfer crystal, color-phase transitions in polydiacetylene and polythiophene, for example. In such PIPT system, it has strong electron-lattice coupling during the cooperative relaxation interactions; (2) low-spin to high-spin state conversion related magnetic materials or light-induced full topological physics in magnetic semiconductors: [Fe(2pic)₃]Cl₃· EtOH and RbMn [Fe(CN)₆], for example [5, 6]. Phase transition in magnetic materials under the action of light is caused by the coupling between volume striction effect and acoustic modes, and the abrupt step transition observed in the experiment is attributed to the depinning effect of volume shrinkage; (3) femtosecond/picosecond dynamics of the photo-induced lattice rearrangements: [Pt(en)₂] [Pt(en)₂X₂](ClO₄)₄ with X = Cl, Br and I, for example [4]. The formation and decay dynamics of self trapped excitons are the starting point of various metastable formation processes accompanied by lattice rearrangement as the excited states of electrons induced by photo-excitation change chemical bonds or generate metastable states; (4) PIPT also presented in ferroelectric materials: barium titanate (BaTiO₃) and lead titanate (PbTiO₃) in perovskite oxides system, for example [7]. With the typical property of polar distortions in ABO₃ perovskite oxides, the polarization within it nearly disappears under the stimulation of light, nonpolar phases such as antiferroelectric come into being with the tilt of the oxygen octahedra in ABO₃ perovskite oxides.

The emergence of 2D and the layered van der waals materials gives the research a new platform of the diffusive, displacive, and quantum phase transitions with distinct physical properties arised from the dimensionality confinement, chemistry, electrostatics, elasticity, and defects [8]. Recently, experimental evidence has shown that the laser irradiation induced phase transition observed in MoTe₂ and WTe₂ often along takes place with the abrupt changes of electronic structure, especially with the spring up of some new topological phases [9, 10, 11]. Taking few-layer MoTe₂ under laser irradiation, for example, it experiences an irreversible transition from the semiconductor hexagonal 2H phase to the topologically distorted octahedral 1T′ phase. And it can be used in the desired area for the fabrication of an ohmic heterophase homojunction with the accurate command of micrometer patterning. Despite the intensive investigations, the microscopic mechanism of the laser irradiation induced phase transition in these 2D materials is still not very clear. These experimental findings also suggest that 2D materials may provide a new platform to discover the PIPT materials that is the focus of this theoretical study.

1.2 Scientific importance of PIPT

Recently, experimental observation of ultrafast disordering of atomic motions in PIPTs has challenged the convertional knowledge of phase transition that the atomic motion in PIPTs is always treated as a coherent process [12]. Actually, ultrashort laser pulses manipulate the structure and function of materials, transforming the electronic or magnetic properties with a timescale in the limit of atomic motion and providing a powerful approach under photo-excitation. Active optical control or interplay between optical and other external influences impact matter or materials are desirable in the field of scientific disciplines, which may display fresh fundamental theoretical and device concepts by optically induced electron-electron correlations, electron-lattice coupling, altering band structures and topology, and so on [4]. Photoexcitation is not only widely used in one-dimensional material systems over the past three decades [13], but also emerging in other fields in recent years, such as memory devices, twistronics field, in-sensor computing field, ultrafast dynamics, and ultra-high frequency acoustic devices and so on. It’s all due to the rich physics effects of PIPT.

Light can introduce the charge density wave as the phase competition in far-from-equilibrium system of LaTe₃ [14], with the presentation of topological defects under the influence of slower re-establishment of phase coherence [15]. This result paves the way for understanding the mechanical nature of topological defects with non-equilibrium defect-mediated transitions and providing a framework for the production, control, and manipulation of optically introduced other ordered phases. PIPT can also be used in the emerging in-sensor computing field [16, 17]. Under oxygen stoichiometry engineering, VO₂ films can show non-volatile multi-level control under ultraviolet irradiation, with integrated processing, sensing, and memory functions at 300 K. It can significantly improve the recognition accuracy from 24 to 93% because this artificial neural network can exact UV information from ambient environment consisting of the abovementioned neuromorphic sensor. This PIPT observed in the application of neuromorphic ultraviolet sensors not only provides an avenue of the design of neuromorphic sensors but also facilitates its potential applications in artificial vision systems.

Furthermore, in various field such as complex liquids, biological and sensing nanostructures systems, ultrafast light-generated giga–terahertz (GHz–THz) frequencies acoustic phonons have attracted much attention [18, 19, 20]. For example, ferroelectric BiFeO₃ has photogeneration/photodetection of coherent phonons [21], with the generation of strain under giant ultrafast light because of the generation of stress by inverse piezoelectric effect under the screening of the internal electric fields by light-induced charges. This giant opto-acoustic response opens up a new prospect for the application of ferroelectric oxides in ultra-high-frequency acoustic devices and promoting the development of some new GHz-THz sound sources. Meanwhile, the corresponding ultrafast dynamics of materials at far from equilibrium states under laser irradiation are one of the ultimate problems in modern science and technology [22, 23]. Actually, PIPT is always treated as a coherent process, but ultrafast disordering of atomic motions in PIPT is observed in recent experiments [24]. It is very important to understand the evolution process of the non-equilibrium phase transition and obtain the basic information such as timescale and driving force of the structural phase transition.

In fact, there are various opinions on the basic information of timescale and driving force in PIPT. The competitive relationship of all driving forces such as photo-excitation, thermal phonon vibration, strain, and so on, has been the focus of scientific attention. With low laser fluence, the timescale of phase transition is always long under the combination of the atomic driving forces caused by thermal phonon vibration and photo-excitation, due to influence of photo-excited hot carriers cooling. In VO₂, at high laser fluence, the smallest timescale of phase transition is indeed saturated to a minimum value of about 55 fs, which is due to the saturation of the population of the V–V bonding states by the photo-excited holes [24]. In this work, the structural transition takes place within 1 picosecond, shorter than the timescale for the photo-excited electrons to transfer their energy to the lattice. We also rule out a thermally driven or a strain-induced phase transition under laser irradiation by comparing the thermodynamic stability.

1.3 Novel two-dimensional PIPT material family predicted from ab-initio calculations

Although PIPT has some applications, its physical mechanism has not been clearly defined, and there is still no unified method to explain this physical phenomenon. The microscopic nature of optically driven phase transition is still unclear. With the changes of strain, lattice vibrational modes, chemical state, electronic excitation, and temperature in the studied system excited by light, the corresponding phase transition may be triggered by one of these factors or on a combination of them. It is of great physical importance to understand the dynamic process of PIPT-induced evolution. However, there are still many technical difficulties to understand the evolution of the ultrafast phase transition both experimentally and theoretically. In this work, we adopt a mature computational method: first-principles calculation, combining ultrafast dynamics and Landau theory to predict the emergence of PIPT in 2D materials for the first time, which opens a new direction for the future search of PIPT materials.

Several models have been proposed to explain this phase transition mechanism: (1) local phase transition induced by Te vacancies created by irradiation [25]: in the presence of nearby vacancies, the contraction of the migration energy makes the higher rate of larger defects accumulation than that expected from the isolated migration. Therefore, it acts as a seed for gathering more vacancies around the photo-induced Te vacancy region, producing nucleus arrangement, increasing the growth rate of 1T′ phase; (2) accumulated heat is a main driving force for the phase transition [26]: the local instantaneous heating from a laser leads to a certain number of Te vacancies, which significantly reduces the potential energy barrier between 1T′- and 2H-MoTe₂; (3) laser-induced thermal strain contributes to phase transition [27]: strain effect originating from thermal expansion can tune the electronic properties and induce a phase transition between 1T′- and 2H-MoTe₂; (4) the electronic excitation plays a critical role in the phase transition [2, 28, 29]: with the increase of excited charge carriers density, the energy barrier between 1T′ crystal and electronically excited 2H phase decreases monotonically and decreases to the thermal energy fluctuation range under the carrier concentration.

Due to electronically excited population inversion, a new distorted trigonal prismatic phase of 1T′ MoTe₂ was generated in previous work [29], which will significantly broaden the application spectrum of these materials. The discovery and control of this phase transition are expressively important to electron regulation science of 2D materials, and the characterization of PIPT is quite less explored with its uncertainty. It is necessary to correctly explain the phase transformation mechanism or the relationship between the magnitude of activation barriers and the potential energy surface in the excited state. Here, based on the first-principle calculations, the microscopic nature of PIPT was studied by a pure photo-induced excitation processes, not by thermal accumulation, defects, or thermal strain as previously assumed. In our calculations, available electrons are stimulated by photo-excitation energies of 1.58 eV (785 nm), 1.96 eV (633 m), 2.34 eV (532 nm), and 2.63 eV (473 nm) respectively. On the premise of unchanging the chemical composition of 2D materials, electrons are excited by light, and the electronic distribution state and lattice vibration mode in the crystal are fundamentally changed in the process of excitonic excitation, which leads to the significant change of chemical bond. Meanwhile, the appearance of ultrafast phase transition to 1T′ MoTe₂ driven by lattice vibration mode softening when the photon energy is larger than 1.96 eV for 2H MoTe₂, and this phase transition by electron excited state is very similar to Peierls phase transition.

In this chapter, we not only demonstrate that the phase transition of monolayer MoTe₂ can be triggered by photo-excitation of carriers alone, but also successfully using Landau theory for the first time to reveal the difference between the physical mechanism of PIPT and the traditional equilibrium thermodynamic phase transition caused by temperature or pressure. The starting point of Landau’s theory is that the symmetry of thermodynamic functions should be the same as the symmetry of the crystal structure of the system. The key point of Landau theory is that symmetry is broken by mean-field approximation or saddle-point approximation and the phase transition with non-zero order sign is obtained. The theory of Landau phase transition is based on the construction of Landau Free Energy after selecting the state variables corresponding to the order parameters of phase transition [30]. For a soft-mode displacive phase transition, the order parameter can be chosen as the amplitude of the distortion of the soft-mode eigenvector u [31]. In this work, we applied the Landau phase transition theory to the explanation of PIPT, the lattice vibration barrier of the E “and A2” uses Landau expansion, which gives the relationship between vibration mode frequency and excitation photon energy. Finally, the vibration mode frequency will drop to zero with the lattice vibration mode completely softened when the excitation energy reached 1.96 eV, which leads to the emergence of the structural phase transition. Our findings not only reveal the microscopic origin of PIPT 2D transition metal tellurides but also provide hope to motivate both fundamental and applied studies of ultrafast phase transitions in these new class of materials for topological switching and neuromorphic computing.

2. Numerical method: First-principle calculations

We use Vienna ab-initio simulation package (VASP) to calculate the ground electron states and phonon properties and stimulate the photo-excitation processes [32]. For the pseudopotentials, we use the PBE potentials of Mo($4s^{2}4p^{6}5s^{1}4d^6$) and Te($5s^{2}5p^4$) atoms [33]. The structural optimization, self-consistent field calculation are conducted under energy cutoff of 500 eV, kmesh of 19 × 19 × 1, energy threshold of ${10}^{-6}\mathit{eV}$, Hellman-Feynman force threshold of ${10}^{-4}\mathit{eV}/\mathring{\mathrm{A}}$.

In the stimulation of optical excited electrons, we neglect the electron-phonon scattering process and all the thermal effects. We approximately assume that the distribution function of electron states is by quasi-Fermi-Dirac function with infinite smearing, thus the distribution becomes stepwise, as follows:

$$f\left(\epsilon \right)=\left\{\begin{array}{l}1,\epsilon <{\epsilon }_{\mathit{FV}}\\ 0,\epsilon >{\epsilon }_{\mathit{FC}}\end{array}\right.$$E1

During the excited state simulation, we manually lift and lower the quasi-Fermi levels by,

$$f\left(\epsilon \right)=\left\{\begin{array}{l}1,\epsilon <{\epsilon }_{\mathit{FV}}\\ 0,{\epsilon }_{\mathit{FV}}<\epsilon <{\epsilon }_F\\ 1,{\epsilon }_F<\epsilon <{\epsilon }_{\mathit{FC}}\\ 0,\epsilon >{\epsilon }_{\mathit{FC}}\end{array}\right.$$E2

The energy difference between the quasi-Fermi level ${\epsilon }_{\mathit{FC}}$ for electrons and the quasi-Fermi level ${\epsilon }_{\mathit{FV}}$ for holes is used as a merit of photo-excitation, which takes five discrete values, 1.58, 1.96, 2.34, and 2.63 eV respectively.

3. Results and discussions: PIPT in 2D MoTe₂

Firstly, we calculate the phonon spectra of high-symmetry hexagonal 2H phase and low-symmetry monoclinic 1 T′ phase. The results are depicted in Figure 1 and fit well with previous reports [34]. The color from light yellow to dark red indicates the Bose-Einstein distribution of phonon states calculated at 300 K. Since the 2H phase has $D_{3h}$ point group at $\mathrm{\Gamma }$ point, the vibration modes can be decomposed by irreducible representations as [35]

Figure 1.

Phonon dispersion of (a) high-symmetry 2H and (b) low-symmetry 1 T′ MoTe₂ monolayer and irreducible representation for optical phonons at the $\mathrm{\Gamma }$ point. The occupation number (calculated by Bose-Einstein distribution at 300 K) is marked by the colormap.

$${\mathrm{\Gamma }}_{2H}=E^{\text{'}\text{'}}+A_1^{\text{'}}+E^{\text{'}}+A_2^{\text{'}\text{'}}$$E3

We find that the $E^{\text{'}}$, $E^{\text{'}\text{'}}$, $A_2^{\text{'}\text{'}}$ phonons display well correspondance to the character of 2H to 1 T′ phase transition. The microscopic atomic displacements are shown in Figure 2(d–f) by arrows. Under photo-excitation by photons with energies of 1.58, 1.96, 2.34, and 2.63 eV, we calculate the one dimensional potential energy surface (PES) along these vibrations to figure out the responsible modes of phase transition. The results are summarized in Figure 2(a–c). The 0 eV photo-excitation represents the displacement in dark environment for reference. Without photo-excitation, there is an energy barrier of 80 meV between 2H phase and $1T^{\text{'}}$ phase. As the optical excitation increases, the origin energy minimum of 2H phase bifurcates and the newly emergent energy minima correspond to 1T′ phase [2, 29].

Figure 2.

One-dimensional potential energy surface at different excitation energies in the eigenspaces of (a) E”, (b) E’, and (c) A₂” phonons, and their corresponding structures (d–f) at the minima of the potential energy surface at 2.63 eV.

The upper and lower layers of Te atoms move in the monolayer plane along opposite directions in E” mode (Figure 2(d)). In the dark environment, the Te atoms do not experience any damping force that drives into another phase. With increasing portion of excited electron states, the potential energy surface becomes flattened and finally forms a lineshape of Mexican hat at critical photon energy of 1.96 eV. This indicates a frozen soft mode that leads to a displacive phase transition. For the A₂” phonon, both Mo atoms layer in the middle and Te atom layer at the side move vertically in different directions (Figure 2(f)). Similar with the foregoing circumstance of E” phonon, a Mexican hat lineshape also forms if the photon energy is larger than the critical one. But the E’ mode shows totally different behaviors under photo-excitation (Figure 2(e)). For E’ mode, both Mo atom layer and Te atom layers move in the monolayer plane, but along opposite directions. The one-dimensional potential surface of E’ phonon shows asymmetric feature where the right-hand-side energy maximum gradually lowers down and finally becomes an valley at 2.63 eV of photon-excitation, which indicates that a new metastable phase emerges. We notice that for the photons with energy between 1.96 and 2.63 eV, the energy maximum does not become an energy minimum, thus the E’ does not anticipate the phase transition process and only E” and A₂” phonons make a contribution. After 2.63 eV excitation where the energy minimum along E’ mode emerges, the E’ mode starts to make a contribution simultaneously.

Besides the total energy surface, we can justify the stability of a phase by inspecting the phonon spectra. Since new energy minima emerge from a parabolic potential, which reveal new metaphases, the phonon spectra are also expected to collap and become softened. The frozen phonon mode can lead to structural phase transition, which breaks the original high symmetry [31, 36]. The E” and A₂” phonon frequencies are investigated using density functional perturbation theory under different photon excitations. The results are shown in Figure 3. The phonon frequencies of E” and A₂” phonon become imaginary as expected, which indicates a finite damping force and energy decreasing along the phonon mode. The critical photon energy fits well with the one of previous potential energy surfaces.

Figure 3.

(a) Phonon frequency of the E” and A₂” modes as a function of photo-excitation energy.

In the general Landau framework, we can choose an order parameter, which becomes finite at the vicinity of phase transition region, and the Landau free energy is expanded as a fourth-order polynomial of it, as follows:

$$F\left(u\right)=F_0+{\mathit{au}}^2+{\mathit{bu}}^4$$E4

The coefficients $a,b$ are related with the external condition. The change of sign of $a$ can lead to an emergence of new energy minimum at $u\propto \sqrt{-\frac{a}{2b}}$. By choosing here the photon energy as an external condition indication and the phonon frequencies as the corresponding order parameter. We fit the frequency of E” and A₂” modes against the photo-excitation energy and obtain good agreement given by $\omega \propto {\left(E_C-E\right)}^{\frac{\gamma }{2}}$, where E_C = 1.96 eV and $\gamma =0.24$, as shown in Figure 3. The result is similar as the well-known Curie-Weiss law, except that the critical exponent is 0.12. We can call it as the modified Cuire-Weiss law for PIPT. The sudden softening of E” and A₂” phonon modes further proves the PIPT.

The high-dimensional potential energy surface (PES) in the configuration space as a direct product of E” and A₂” modes under different photo-excitation is depicted in Figure 4(a–d). The photo-excitation is chosen as 1.0, 2.0, 3.0, 4.0% per unit cell. These results suggest that at $\sim$ 3.0% excitation, the energy minimum bifurcates and two new asymmetric PES minima emerge. Besides, in comparison to the E” mode, the A₂” mode apparently contributes more, which indicates that the phase transition is mostly triggered by A₂” mode.

Figure 4.

The two-dimensional potential energy surface spanned by E” and A₂” modes under (a) 1.0%, (b) 2.0%, (c) 3.0%, (d)4.0% photo-excitation per unit cell. Energies are in unit of eV.

The excited electron states that contribute to the electron localization function (ELF) are shown in Figure 5. The PIPT is caused because the charge distribution exerts forces to the ions [37]. In Figure 5(a) we plot ELF of high-symmetry MoTe₂ under different photo-excitation. In the dark environment, the electron gas connects the Mo atoms to form hexagons. As the electron gradually excited from the valance states, the electron gas becomes more localized into the center of Mo atoms triangles. The more electrons excited, the more localized into the triangle vertices. The localization in the triangle vertices is viewed as the microscopic reason that exerts forces on Mo and Te atoms to soften the E” and A₂” phonon modes and induces displacive phase transition.

Figure 5.

(a) 3D and (b) top view of the electron localization function of 2H MoTe₂ at different excitation energies. The iso-energy surface for the electron localization function in a is 0.2.

The second law of thermodynamics shows that free energy is the criterion of spontaneous process, and here we calculate the Helmholz free energy to describe the thermodynamic stability of MoTe₂ at 2H and 1T′ phases [38]. As shown in Figure 6, at 0 K, the calculated free energy difference between the two phases of MoTe₂ is only 33 meV per rectangular unit cell at 0 K, indicating that 2H phase and 1T′ phase of MoTe₂ have similar stability at this environment. Furthermore, with the temperature rising, 1T′ MoTe₂ becomes more thermodynamically stable than 2H MoTe₂ at temperatures higher than 190 K as shown in green line in Figure 6. When taking thermal strain into account as shown in orange line in Figure 6, the temperature of phase transition decreases to 110 K.

Figure 6.

Helmholtz free energy difference between 2H and 1 T′ MoTe₂ monolayers as a function of temperature.

4. Conclusions and perspective

In this chapter, it is demonstrated that a PIPT from 2H to 1T′ phase occurs in monolayer MoTe₂ as the excitation energy of photon is higher than the critical value of 1.96 eV by using first-principles calculations. Such structural phase transition is intermediated by the charge distribution transition after photo-excitation, contributing to phonon mode softening and newly emergent potential energy minima. The structural phase transition can be induced under the photo-excitation of $\sim$ 3.0% electrons per unit cell. Further, this work expresses the phonon frequencies as order parameter and fit it with the external condition indication, namely the photon-excitation energy, and the result fits excellent with the modified Cuire-Weiss law. This research reveals the microscopic nature of the 2H-1T′ PIPT and facilitates the fundamental research of non-equilibrium transient phase transition between normal semiconductor and the topological phase. Also, this theoretical finding is expected to trigger the experimental investigations of PIPT materials in the 2D materials.

By now, stimulated by the advanced experimental methods such as four-dimensional ultrafast electron diffraction (UED), and the recently developed real-time time-dependent functional theory (rt-TDDFT) method, the studies on the PIPT in newly emergent systems such as three-dimensional VO₂ and two-dimensional IrTe have been able to manifest the atomic motions induced by light at femtosecond scale. Furthermore, it has been shown by rt-TDDFT simulations that, by laser pulse excitation, a large part of electrons are excited from valence bands to conduction bands, which not only enlarges the electron occupation in antibonding states, leading to the enhancement of intrinsic Coulumb repulsion and thus enlarged interatomic bond length, but also forms the so-called electron-hole plasma. The dense plasma softens and stabilizes acoustic phonon modes, which drives the distortion of crystal lattice. Recent studies also reveal the competition between coherent light-induced nonthermal collective motions and thermally induced disorded motions, when PIPT takes place. However, there are two important problems still existing. One problem is the nature of PIPT in different kinds of materials. In this work, the microscopic theory based on the Landau phase-transition theory has been developed to explain the PIPT in two-dimensional materials, but whether it is applicable for one- or three-dimensional materials remains unclear. Moreover, the relation between different PIPT-based phases is still needed to clarify. Therefore, it is believed that, it is still challenging to develop a globally microscopic theory for PIPT in this field. The other problem is related to the intentional control over the PIPT-based phases. If the different hidden phases of materials can be induced by light, is it feasible to control by laser pulse to induce a special phase? More experimental and theoretical works are still needed to be conducted.