Electron-phonon interactions and two-phonon modes associated with charge density wave in single crystalline 1T-VSe 2

The charge density wave (CDW) is a unique phenomenon mostly realized in two-dimensional (2D) metallic layered transition metal dichalcogenides. We report on the observation of commensurate CDW (C-CDW) and incommensurate (I-CDW) transition in single crystal 1T-VSe 2 using the spectroscopy technique in the temperature range of 50–120 K. The room temperature Raman spectra showed a sharp A 1 g mode ∼ 206 cm − 1 along with two additional modes associated to E g ∼ 257cm − 1 symmetry and two-phonon (2 ph ) ∼ 332 cm − 1 interactions. The onset temperature of I-CDW and C-CDW is estimated from resistance measurements supported by magnetic measurements. Remarkably, at the onset of I-CDW ∼ 115 K, a signiﬁcant enhancement in the intensity of the weak E g mode is observed along with emergence of a doubly degenerate E g (2) mode ∼ 144 cm − 1 , while below 70 K, the emergence of the A 1 g mode ∼ 170 cm − 1 signiﬁes the onset of C-CDW. The observation of a sudden rise in the intensity of the E g mode ∼ 257 cm − 1 mode, below I-CDW, showed the involvement of electron-phonon coupling in 1T-VSe 2 .


I. INTRODUCTION
The charge density wave (CDW) is a low-temperature ordered phase that arises from periodic modulation of conduction electron densities accompanied by periodic distortion of the atomic lattice [1][2][3].The commonly accepted argument for the origin of the CDW, in many low-dimensional systems, is based on the Peierls picture described for purely onedimensional metallic systems, where electronic instabilities result in Fermi-surface nesting.Here, the CDW is said to be driven by Fermi-surface nesting since the contour of a Fermi surface coincides with ordering vector Q [4].However, there are several recent reports suggesting that nesting alone is insufficient to explain the CDW.In many cases, especially for two dimensions (2D) and higher dimensions, the Fermi surface does not nest at the ordering vector Q [5,6].For instance, in the cases of 2H-NbSe 2 , CeTe 3 , and ErTe 3 , strong electron-phonon coupling plays a more important role for determining Q than Fermi-surface nesting [7,8].Based on the periodicity of Q, th eCDW has been classified as commensurate CDW (C-CDW), nearly commensurate (N-CDW), and incommensurate CDW (I-CDW) with a high-symmetry phase.In the C-CDW phase, the Q is an integral multiple of the reciprocal lattice vector of the undistorted phase, whereas in the I-CDW phase it is not [9].
VSe 2 is a compound that has been intensively studied for its interesting electronic band structure and CDW.The bulk VSe 2 crystallizes in the 1T polytype, where the V atoms are covalently bonded with the octahedra of Se atoms to form a single layer of VSe 2 and these layers are further stacked through van der Waals interactions [33].1T-VSe 2 shows I-CDW transition ∼110 K and C-CDW transition ∼80 K which have been studied using the x-ray diffraction technique, [9] inelastic x-ray scattering technique, angle-resolved photoemission spectroscopy [34], and transport measurement [35].However, because of the high reflectivity of this compound, the obtained optical signals are extremely poor; thus several properties such as vibrational properties, and electronphonon coupling are not well understood.Thus, in this paper, we have studied the electron-phonon coupling driven CDW transitions in bulk single crystal 1T-VSe 2 , using temperaturedependent resistivity, magnetic susceptibility, and Raman spectroscopy measurements.The coupling between electron and phonon, at low temperatures, is demonstrated from resistivity as well as magnetic measurements, while spectroscopy is used as a tool to access the CDW in VSe 2 .

II. EXPERIMENTAL SECTION
A single crystal of VSe 2 was grown by reacting a stoichiometric amount of vanadium chips and selenium pellets (both from Sigma-Aldrich, 99.9%) using the chemical vapor transport method with iodine as the transport agent (∼2 kg/m 3 ).The reactants were vacuum sealed in a quartz ampoule and placed in a two-zone furnace, which was heated slowly (∼20 h) to reach the growth temperatures of 1093 K (hot zone) and 923 K (cold zone).The samples were kept in the gradient temperature for ∼72 h followed by slow cooling to room temperature over ∼20 h.Thus, large shiny crystals of VSe 2 were obtained at the cold end of the tube.X-ray diffraction (XRD) of the prepared crystals was obtained using a rotating anode Rigaku SmartLab diffractometer in Bragg-Brentano geometry with Cu Kα radiation (λ = 1.5406Å) .To determine the crystal structure and phase purity, Rietveld refinement of the XRD patterns was done using FULLPROF SUITE software [36].
Four-probe electrical resistance (R) and magnetic susceptibility (χ ) measurements were performed from 2 to 300 K using a Quantum Design physical properties measurement system and magnetic properties measurement system, respectively.Micro-Raman measurements were done using a Horiba Jobin-Yvon LabRAM HR evolution Raman spectrometer in backscattering geometry with solid state laser excitation (∼532 nm), 1800 grooves/mm grating, and a Peltier cooled charge-doupled device (CCD) detector.Polarized Raman measurements were performed using two halfwave plates as polarizer and analyzer.Temperature-dependent micro-Raman measurement was performed by using a Montana cryostation in the temperature range of 3-300 K.All the Raman measurements are performed on the (001) plane of 1T-VSe 2 single crystal.Field emission scanning electron microscopy (FESEM) images and elemental mapping using energy dispersive spectroscopy (EDS) were recorded through JFEI Nova Nano SEM-450 (see Supplemental Material [37]).

III. RESULTS AND DISCUSSION
The XRD pattern and Rietveld refinement of the VSe 2 is shown in Fig. 1  axis.The inset shows the optical image of the grown crystals with large dimensions (∼5 mm × 5 mm).In general, the VSe 2 has trigonal crystal structure with a P 3m1 space group [Fig.1(b)]; however, there is a mild possibility of self-intercalation of V atoms between the van der Waals gap of VSe 2 , thus occupying two different sites, V1 (0, 0, 0) and V2 (0, 0, 0.5) [38].Such self-intercalation is commonly observed due to synthesis at high temperature [39].Nevertheless, the extent of self-intercalation can be minimized by synthesizing the compound at a lower temperature, ∼923 K.The layered nature of the VSe 2 crystal is observed through FESEM imaging shown in Fig. 1(c).The stoichiometry of the prepared sample has been estimated using elemental mapping (see Supplemental Material, Table S1 [37]).
The temperature-dependent electrical resistance (R) shows metallic behavior throughout the T range with an onset of the hump below 110 K [Fig.2(a)].In general, the close association of structural changes and modifications of the charge density are represented by a hump in R(T), which is a signature of CDW transition in most of the materials.The observations are in line with several layered TMDCs such as 1T-TaS 2 , 1T-TaSe 2 , and 2H-TaSe 2 [28].Additionally, the quality of the crystal plays an important role for the onset of CDW transition, and the residual resistance ratio, defined as RRR = R 300K /R 6.2K , is one of the parameters to estimate.Here, the RRR is about 8, which is in good agreement with previous reports and confirms the high quality of the synthesized VSe 2 single crystal [35].We have assessed the temperature range of the CDW transition from temperature derivative of resistivity, dR/dT , where two points of inflection at T ∼102 K and ∼50 K have been observed.In support to our observations, the temperature-dependent x-ray diffractions studies by Tsutsumi [9] described the periodic lattice distortion wave vector in the reciprocal lattice as (0.250 ± 0.003)a * +(0.314 ± 0.003)c * in the I-CDW state below 110 K and (0.250 ± 0.003)a * + (0.307 ± 0.003)c * in the C-CDW state below 85 K. Here, the a * component is independent of temperature; however, the c * component shows deviation with temperature suggesting that the origin of incommensurability is along the c axis.Thus, the observed inflections in dR/dT are associated to I-CDW ∼ 102 K and C-CDW ∼ 50 K.
The inset in Fig. 2(a) shows a low-temperature region below 10 K, where R decreases with temperature and exhibits a minimum at ∼6.2 K and then increases up to 2 K.This lowtemperature upturn in R(T) can originate from various reasons such as weak localization, electron-electron interactions, and the Kondo effect [40,41].Recently, Barua et al. [42] observed a similar upturn in resistivity (ρ) of 1T-VSe 2 appearing due to V ions intercalated between the van der Waals gap, which contributed to magnetic susceptibility and acted as localized magnetic scatterers to the conduction electrons.Here, in the case of VSe 2 , the intercalated V 4+ ions with an unpaired electron in the d orbital can provide magnetic moments which can drive the electron transport at low temperatures [39,43,44].This kind of localized magnetic impurity can result in scattering of conduction electrons through s-d exchange interactions and the observed upturn in R(orρ) through such interactions is described as the Kondo effect [42].We have fitted the lowtemperature ρ with ρ = ρ 0 + αT 2 + c m ln( T K T ) + bT 5 , where ρ 0 is the residual resistivity, αT 2 shows the contribution from the Fermi liquid properties, the term bT 5 is from the lattice vibrations, and c m (ln T K T ) represents the contribution from the Kondo effect.Below 6.2 K the logarithmic Kondo term is dominating over other negligible parameters except ρ 0 .Thus fitting of the upturn of R below 10 K is suggesting the existence of Kondo-like behavior in VSe 2 .
To confirm the presence of magnetic moments in 1T-VSe 2 because of the intercalated V 4+ and its effect on the CDW, the temperature-dependent magnetic susceptibility (χ ) has been performed and the data are shown in Fig. 2 T −θ + χ 0 , where χ 0 is the temperature-independent intrinsic contribution to susceptibility from the V bands, C is a Curie constant, and θ is a paramagnetic Curie temperature.The parameters obtained from 1/χ fitting using the modified Curie-Weiss law are χ 0 = 0.000 05 m 3 /kg, C = 0.0009 m 3 /kg K, and θ = 0.5 K .Thus, the intercalated V is contributing to the feeble magnetism in the sample (shown in Fig. S1, in the Supplemental Material [37]).After confirming the quality of the sample and observation of the signature CDW from low-temperature measurements, we have performed the Raman spectroscopy to understand the phenomena in detail [24].
At high temperatures above the CDW transition, the formula unit of VSe 2 has three atoms per unit cell [30,45], and thus has nine zone-center vibrational modes, which can be presented with irreducible representation, = A 1g + E g (2) + 2A 2u + 2E u (2).Here only two modes, A 1g and the doubly degenerate E g (2) modes, are Raman active while the other four are IR active modes.[13] Figure 3(a) shows Raman spectra at 300 K having three peaks at ∼206, ∼257, and ∼332 cm −1 .For VSe 2 , Sugai et al. [46] reported that the sharp peak at ∼206 cm −1 is A 1g symmetry.Due to the lack of group theoretical analysis of vibrational modes for 1T-VSe 2 , the origin of the two peaks, ∼257 cm −1 and ∼332 cm −1 , could not be understood and thus requires further investigations.To confirm the origin of these modes, we have performed the polarized Raman spectra of the VSe 2 crystal (Fig. S2, Supplemental Material [37]), where the laser is incident normal to the ab plane.For parallel polarization (XX) configuration, the incident and the scattered light are polarized along the same axis, while for perpendicular polarization (XY) configuration, they are orthogonal.The sharp A 1g mode is observed only in parallel polarization while the mode ∼257 cm −1 is present in both parallel as well as perpendicular polarization measurements [46].Thus, the mode at ∼257 cm −1 has E g symmetry.Further, considering the fact that 1T-TiSe 2 has similar crystal structure and comparable molecular masses of V and Ti, the origin of these modes can be consigned using the knowledge of the vibrational modes of 1T-TiSe 2 [45,47].Similar to the broad modes, ∼257 cm −1 and 332 cm −1 , in 1T-VSe 2 , weak and broad features are observed at ∼300 cm −1 and 360 cm −1 for 1T-TiSe 2 which are assigned to A 1g symmetry and the two-phonon process [30,47].Therefore, the broad feature ∼332 cm −1 for 1T-VSe 2 can be related with the two-phonon process (2 ph ) [30].
The low-temperature (10 K) Raman spectra [Fig.3(b)] has five Raman modes and is quite distinct from the 300 K spectra.The peaks observed, ∼144 cm −1 , ∼171 cm −1 , ∼211 cm −1 , ∼251 cm −1 , and 320 cm −1 , are assigned to doubly degenerate the E g (2), A 1g , A 1g , E g , and 2 ph modes, respectively [48].The symmetry assigned for all the modes is based on the symmetry operation on an undisturbed 1T-VSe 2 crystal.The schematic of the vibrational modes of A 1g ∼206 cm −1 and E g (2) are shown in Fig. 3(c).Here, the A 1g mode represents out-of-plane vibration (along the c axis) of Se atoms, while the doubly degenerate E g (2) mode is associated with the opposite vibration of Se atoms relative to each other along the a axis and b axis.The E g (2) mode is expected at 300 K as per the irreducible representation; however, owing to the weak scattering, the mode remains hidden in the noise at 300 K and the intensity of this mode enhances below 120 K.The Raman spectrum shown in Fig. 3 is base line corrected and normalized with the intensity of the A 1g mode, ∼206 cm −1 .
To understand the role of the CDW on phonons, we performed a temperature-dependent Raman study from 300 to 10 K, as shown in Fig. 4 (also in Supplemental Material [37], Fig. S3).From 300 to 120 K, three Raman modes, A 1g , E g E g , and 2 ph , have been observed; however, the spectral features are broad and weakly intense for E g and 2 ph .The resemblance in the Raman spectrum from 300 to 120 K confirms the stability of the trigonal structure up to 120 K.However, below 120 K, the intensity of the broad E g mode starts to rise significantly and becomes comparable with the intensity of the most intense A 1g mode.Further, the doubly degenerate E g (2) mode starts to appear prominently between 100 and 10 K (shown in the red rectangle).Such modulation in the Raman spectra with temperature is related with the onset of the CDW transition below 120 K, as the size of the unit cell increases due to the formation of superlattices [46].Thus, the vibrational spectra are dramatically modulated by the formation of superlattices, which have been probed by Raman and Fourier transform infrared (FTIR) studies [49].
In the case of incommensurate distortions, the translational symmetry of the lattice is lost and the restriction of first-order Raman scattering to zone-center phonons is relaxed, resulting in several additional modes in the first-order Raman scattering.Interestingly, a very minor peak of A 1g ∼171 cm −1 appears at the 40 K spectra and grows further in low-temperature spectra (shown in green rectangle), as reflected in R measurement for the onset of the commensurate phase below ∼50 K.The behavior can be understood by the formation of a commensurate superlattice where the size of the Brillouin zone reduces, which results in the folding of phonon dispersion curves [24].This folding can lead to the appearance of new zone-center phonons compared to the undistorted structure.Therefore, the appearance of the out-of-plane A 1g mode below 50 K can be associated with the formation of a commensurate superlattice.Further, earlier studies on x-ray investigation of a superlattice at I-CDW and C-CDW transitions demonstrated the significant variation along the c * axis at the C-CDW transition, whereas the component along the a * axis remains independent of temperature; therefore the appearance of the out-of-plane A 1g mode at ∼50 K is a signature of C-CDW transition.
To explore the correlation between the CDW transition and phonon energy, the variation of the peak position of the E g (2) mode, the A 1g mode ∼211 cm −1 , and the E g mode are shown in Fig. 5 intensity are determined through the Lorentzian peak fitting of each normalized Raman spectrum.The E g (2) mode and the A g mode ∼211 cm −1 show phonon hardening on the lowering of temperature up to 10 K.These modes have been fitted with ω(T ) = ω 0 + mT , where ω 0 is the phonon frequency of the E g (2) and A g modes at absolute zero temperature; m is the first-order temperature coefficient of the two modes [50].The fitted curve is shown as a solid line in Fig. 5(a) and the m values for the E g (2) and A g modes obtained by the linear fitting are -0.0617 and −0.0296 cm −1 /K, respectively.The stiffening of the phonon mode estimated from m depends upon anharmonic coupling of phonons and thermal expansion of the crystal.In contrast to these two modes showing the usual phonon hardening, the broad E g mode does not show a significant change in energy with temperature as shown with the solid blue line in Fig. 5(a).However, the integrated intensity of the E g mode which is active in both the CDW transitions enhances strongly below the I-CDW transition temperature ∼100 K [Fig.5(b)].Further, it is worth noticing that the integrated intensity reaches maxima near C-CDW transition and then starts to decline at further lower temperature suggesting the coupling of Raman modes with CDW transitions.After the CDW transition, the density of electronic states coupled with phonons decreases at the Fermi surface, which results in the decrease of Raman intensity at further lower temperature.Further, the decrease of the Raman intensity below the C-CDW suggests the deformation of the crystal structure [51].Thus, the emergence of new Raman modes represents the formation of a superlattice at the onset of the CDW transition and strong coupling of the E g mode with the CDW, giving evidence of electron-phonon coupling.

IV. CONCLUSION
In summary, the novel phenomenon of the CDW has been investigated in single crystalline 1T-VSe 2 using temperaturedependent resistance measurement and Raman spectroscopy.The hump in resistance measurement below 110 K is related to the onset of the I-CDW, while the existence of the C-CDW ∼ 50 K is confirmed by dR/dT .The appearance of five Raman active modes at low temperature suggested the reduction in the size of the Brillouin zone due to the formation of superlattices.The onset of the C-CDW transition is marked with the appearance of the A 1g mode ∼177 cm −1 .At the onset of the I-CDW, the intensity of the E g mode, ∼257 cm −1 , enhanced significantly and the E g (2) mode ∼114 cm −1 becomes prominent.The rise of the integrated intensity of the E g mode at the onset of the CDW transitions signifies the role of electron-phonon coupling in the CDW transition.
(a).The estimated lattice parameters are a = 3.361 Å and c = 6.101Å, with a unit cell volume = 59.726Å 3 .The difference curve (Y obs − Y calc ) clearly shows the grown VSe 2 crystals are of highquality single phase while the single crystalline nature is confirmed by observation of peaks only along the c

FIG. 1 .
FIG. 1.(a) XRD pattern of single crystal of 1T-VSe 2 ; inset shows the optical image of the grown crystals.(b) Schematic of trigonal crystal structure of P 3m1 space group.(c) FESEM imaging of the layered nature of the crystal.

FIG. 2 .
FIG. 2. (a) Resistance (R) and first derivative of resistance (dR/dT) of 1T-VSe 2 ; inset shows upturn in R below 6.2 K due to Kondo interactions.(b) Variation of magnetic susceptibility (χ ) with temperature showing downturn at the onset of CDW.The inset figure shows the variation of 1/χ with temperature fitted with modified Curie-Weiss law.
FIG. 3. Raman spectra of 1T-VSe 2 at (a) 300 K and (b) 10 K; (c) schematic of main type of lattice vibrations observed in Raman spectra.

FIG. 4 .
FIG. 4. Temperature dependence of Raman spectra from 300 to 10 K.The enclosed red and green rectangles represent the emergence of E g (2) at the I-CDW and A g modes at the C-CDW, respectively.
FIG. 5. Temperature dependence of (a) the peak position of the vibrational modes with temperature, and (b) integrated intensity of E g mode as observed in the normalized Raman spectra.