Strongly Coupled Electron–Phonon Dynamics in Few-Layer TiSe2

Article Cite This: ACS Photonics XXXX, XXX, XXX−XXX

Strongly Coupled Electron−Phonon Dynamics in Few-Layer TiSe2 Exfoliates Tony E. Karam,† Jianbo Hu,†,‡ and Geoffrey A. Blake*,†,§ †

Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States Laboratory for Shock Wave and Detonation Physics Research, Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang, Sichuan 621900, China § Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, California 91125, United States ‡

S Supporting Information *

ABSTRACT: Ultrafast electron diffraction is used to probe the time-resolved dynamics in a few-layer TiSe2 sample. At normal incidence, the suppression of the Bragg diffraction peak intensities following photoexcitation displays strongly biexponential behavior. For tilted samples, changes in the diffraction peak positions reveal coherent acoustic vibrations that are dependent on the sample thickness and that further permit a calculation of the Young’s modulus. The complex room temperature lattice dynamics observed are attributed to strong electron−phonon coupling and electron−lattice equilibration processes, which support a Jahn−Teller origin of the charge density wave behavior in TiSe2. Additionally, the significant role that the related Kohn anomalies may play in the electron transport dynamics and transition mechanism of this material is emphasized. These results demonstrate the importance of strongly coupled electron−phonon dynamics in the relaxation of electronically excited room temperature TiSe2, which is expected to impact its applicability in optoelectronics. KEYWORDS: ultrafast electron diffraction, transition metal dichalcogenides, charge-density waves

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dynamics following laser excitation can provide unique insights into the properties of these layered materials.17−21 Titanium diselenide (TiSe2) is a semimetal TMDC with exotic properties such as charge density waves (CDW) and superconductivity at low temperatures,22−24 whose dynamics are dominated by electron−phonon interactions. Phonon softening and Kohn anomalies have been reported in TiSe2 above the CDW transition temperature Tc (∼189 K) for the lowest phonon mode L−1 at the Brillouin zone boundary.25,26 The CDW transition and the phonon softening strongly depend on the thickness of the layered sample,27 and the mechanism behind the CDW transition in TiSe2 is still under intense debate.28−32 Several studies point to a Jahn−Teller effect as the likely explanation of CDW in TiSe2 rather than an excitonic insulator mechanism.25,33,34 The former should, in principle, include strong electron−lattice interactions.35,36 Recently, through the

ayered transition metal dichalcogenides (TMDCs) possess unique optoelectronic, mechanical, chemical, and thermal properties that make them the subject of active research.1−5 TMDC semiconductors (of the form MX2, where M = metal and X = S, Se), such as molybdenum disulfide (MoS2) and tungsten disulfide (WS2), are characterized by a bulk indirect bandgap that increases to a direct bandgap for monolayer films.6,7 Furthermore, valley polarization in molybdenum disulfide (MoS2) monolayers has been reported and proposed to arise from their distinctive electronic structure.8,9 Semiconductor TMDCs possess a bandgap energy comparable to that of silicon, which makes them ideal for potential applications in transistors.10,11 The electronic and optical properties of TMDC monolayers are extensively tunable through covalent functionalization by phase engineering.12 While various ultrafast spectroscopy techniques have been used to investigate the electronic dynamics of thin layer and bulk TMDCs,13−16 studies of the transient behavior of nonequilibrium structures via probes of the ultrafast lattice © XXXX American Chemical Society

Received: August 4, 2017 Published: February 7, 2018 A

DOI: 10.1021/acsphotonics.7b00878 ACS Photonics XXXX, XXX, XXX−XXX

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ACS Photonics inclusion of exact, nonlocal exchange in density functional theory (DFT) calculations, strong electron−phonon coupling and lattice distortions are predicted to drive the CDW formation in TiSe2.37 Thus, detailed examinations of the transient structural dynamics of layered TiSe2 could better elucidate the nature of these transitions, in particular those techniques that can provide windows into the correlated atomic motions, bond dilation, and structural transformation(s) that are expected to accompany CDW behavior on the time scale of nuclear motion. Ultrafast electron diffraction (UED) provides such a distinct window into these correlated motions and relaxation processes by recording the transient nonequilibrium diffraction patterns with femtosecond temporal resolution following laser excitation of a sample.38 Using UED, paradigms that correlate structure, dynamics, and functionality can be established, leading to better understanding of light−matter interactions in materials.39−46 Additionally, electron diffraction is uniquely advantageous for the study of the transient structural dynamics in monolayers and few-layer (that is, several monolayer) samples due to the large scattering cross section of electrons as compared to, for example, X-ray diffraction.47−49 In this article, ultrafast electron diffraction is used to investigate the transient structural dynamics of few-layer TiSe2 exfoliates at room temperature. As discussed below, a strongly biexponential suppression of the diffracted intensity is observed and is attributed to the ultrafast response generated by strong electron−phonon coupling that results from the presence of a Kohn anomaly for the lowest phonon mode L−1 at the Brillouin zone boundary (that persists to >290 K), followed by electron−lattice equilibration. Out-of-plane acoustic breathing modes are also observed from oscillatory changes in position of the Bragg diffraction spots that are attributed to the excitation of the lowest order longitudinal acoustic phonons quantized by the sample thickness. These results provide new insights into the strongly coupled optical modes and lattice dynamics of few-layer TiSe2 materials. Using UED to probe the lattice degrees of freedom rather than the electronic response provides a fuller understanding of the complex electron−phonon coupling dynamics in TiSe2. Characterizing the impact of strongly coupled electron− phonon modes on the transport and energy relaxation of “hot” electrons is essential for future applications of layered TMDCs in superconductors, electronics, and optoelectronics, as such modes can limit their time-dependent electrical conductivity. Furthermore, these results present strong evidence of the importance of strong electron−lattice interactions and Kohn anomalies in the electron transport dynamics of few-layer TiSe2 films by probing the transient structural dynamics of the crystal lattice, leading to an improved understanding of these dynamics through a mechanism based on lattice modulations associated with the Jahn−Teller effect. The TiSe2 samples used in this study are commercially purchased and repeatedly exfoliated on a thermal release tape to a thickness of less than ten nanometers. The samples are then released into water by heating and transferred to copper TEM grids. The grids are subsequently scanned for the best diffraction patterns. Figure 1A shows the crystal structure of a TiSe2 unit cell consisting of Ti atoms arranged in a hexagonal planar network that is sandwiched between two layers of Se atoms. A scheme of the UED setup in the transmission geometry composed of laser pump and electron probe pulses is shown in Figure 1B. The dynamics are initiated by 100 fs laser

Figure 1. (A) Crystal structure of a TiSe2 until cell. c is the layer spacing in bulk. (B) Scheme of the UED setup in the transmission geometry composed of a laser pump and electron probe.

pulses centered at 800 nm at a repetition rate of 2 kHz. The intensity of the Bragg diffraction peaks as well as their position is monitored with 30 keV electron pulses at different pump− probe time delays. Details of the experimental setup are included in the Methods section. As we will show below, the out-of-plane dynamics observed at non-normal incidence angles yield an estimated thickness of ∼5.7 nm, or about 5−6 monolayers, in the probed area of the sample. A representative electron diffraction pattern of TiSe2 exhibiting a single-crystalline sample is shown in Figure 2A. Figure 2B displays a typical diffraction intensity spectrum obtained by azimuthally averaging the Bragg diffraction spots. A one-dimensional diffraction curve is obtained as a function of the scattering vector. Any time-dependent changes in the diffraction pattern are then recovered by fitting the location and area of the diffraction peaks at various pump−probe time delays using a piecewise-linear background and a Lorentzian function. The time-resolved intensity change of the Bragg diffraction spots are shown in Figure 2C at a laser excitation fluence of 1.4 and 2.3 mJ/cm2. These temporal profiles are obtained by averaging over the six first-order diffraction spots shown in Figure 2A. A biexponential function of the form I = I0 + A1 e−τ1/t + A2 e−τ2/t is used to fit the transient decay. The lifetimes values obtained from the fit are τ1 = 1.8 ± 0.3 and τ2 = 12.6 ± 1.1 ps, respectively, at 1.4 mJ/cm2. For a laser excitation fluence of 2.3 mJ/cm2, these lifetime values become 2.4 ± 0.3 and 10.2 ± 1.1 ps. Detailed results of the biexponential fits over a range of fluences and extending to longer pump−probe time delays are shown in the Supporting Information. In UED, following the ultrafast rise in electron temperature, electron−phonon interactions result in the population of optical phonons, followed by the generation of acoustic waves, which in turn leads to lattice heating. The lattice dynamics following the impulsive excitation are coherent and characterized by a single exponential decay that can be described using a two-temperature approximation that treats the electron and lattice degrees of freedom in a coupled fashion.50−52 For cases such as that presented here, a biexponential change of the intensity of the Bragg diffraction spots is attributed to lattice fluctuations or instabilities such as strong electron−phonon interactions and/or phase transitions.38,44,53−555 Since no change in the position of the Bragg diffraction spots is observed, then we can confidently rule out the latter. Hence, the fast decay in the case of TiSe2 is attributed to strong electron−phonon interactions, which are known to arise from the L−1 at the Brillouin zone boundary and to persist at room temperature.25,26 In this case, UED is the ideal technique to investigate the transient structural dynamics by B

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by the coherent modulation of the diffracted intensity due to carrier relaxation through further electron−phonon and phonon−phonon scattering once these lattice instabilities reach thermal equilibrium with the electronic system. That is, the biexponential suppression of the Bragg diffraction spot intensities consists of a faster component due to a lattice instability caused by strong electron−lattice coupling that leads to incoherent optical phonon modes, followed by coherent electron−lattice equilibration at longer times.53,57 Such biexponential behavior is not observed in other semiconductor TMDCs samples currently under investigation in our laboratory such as WSe2 and MoS2. Previous UED work reported single exponential decay for the suppression of the intensity of the Bragg spots with lifetimes of 15 ps for monolayer graphene,48 5 ps in carbon nanotubes,58 and 5 ps/17 ps for 2 nm-/11 nm-thick gold nanofilms, respectively.49 Biexponential suppression of the intensity of the diffraction spots has been previously reported in VO2 samples exhibiting phase transitions,38,54 in graphite where SCOP modes are present,53,57,59 and in CeTe3 for which CDW arises from strong electron−phonon coupling.55 Here, we argue that the laserinduced strong electron−lattice dynamics in layered TiSe2 samples lead to incoherent optical phonons dynamics and lattice instabilities that can be revealed from the biexponential suppression of the Bragg diffraction spots. Hence, this report presents compelling experimental evidence that the transient structural dynamics induced by the ultrafast photoexcitation of TiSe2 exfoliates are governed by strong electron−phonon coupling and lattice instabilities. Both recent DFT simulations37 and extensive previous work on TiSe2 suggests that such strong coupling of the electronic and lattice degrees of freedom is to be expected.31,35,60 Indeed, such strong electron−phonon interactions are proposed to be the driving mechanism behind the CDW in TiSe2 that leads to phonon softening of the transverse mode at the L point.25,31,35,36,61−63 Similarly strong electron−phonon coupling has been previously reported in different high temperature superconductors,64−68 but to the best of our knowledge, these results present the first decisive experimental evidence of these dynamics in TiSe2 by probing the transient lattice rearrangement following laser excitation. Dynamic Umklapp effects associated with the Kohn anomaly for the lowest phonon mode L−1 at the Brillouin zone boundary form a natural explanation for the observed results, as they are expected to persist at room temperature in TiSe2.25,26 The Kohn anomaly leads to a strong renormalization of the phonon optical bands, on a time scale order of a few ps, as observed in the τ1 lifetime (Figure 2C). Fluence-dependent measurements are carried out to further unravel the transient structural dynamics of TiSe2. Fitting the fluence-dependent decay with a biexponential function yields variations in the distinct lifetimes. The faster lifetime τ1 attributed to carrier relaxation through strongly coupled electron−phonon modes is seen to increase with the excitation fluence, while the second lifetime τ2 attributed to further electron−lattice equilibration through electron−phonon and phonon−phonon scattering is found to decrease. The percentage of the amplitude of the diffracted intensity suppression at 2 and 20 ps at different 800 nm excitation fluence is shown in Figure 3A. The amplitudes at each time delay increase linearly with slopes of 0.73 ± 0.04 and 1.04 ± 0.04 at 2 and 20 ps, respectively.

Figure 2. (A) Electron diffraction image of the layered TiSe2 sample. (B) Representative diffraction intensity spectrum obtained by azimuthally averaging the diffraction pattern and its curve fitting. (C) Time-resolved intensity change at laser excitation fluences of 1.4 (red dots) and 2.3 (blue dots) mJ/cm2. The dynamics are characterized by a biexponential fit.

directly probing the lattice due to the large scattering cross section of electrons and their strong interaction with matter.52 Similar behavior of the Bragg diffraction spot intensities was observed for CeTe3 at Tc, which exhibits CDW with a fast decay of 1.5 ps and is attributed to lattice instabilities.55 The suppression of the diffracted intensity is due to the displacement of the atoms following laser excitation due to thermal vibrations, which is described by the Debye−Waller factor e−2M, for which 2M = ⟨|K⃗ ·u ⃗(n)|2 ⟩

(1)

and where u⃗(n) is displacement of the nth atom and K⃗ is the difference between the initial and the final wave vectors.56 The faster lifetime, τ1, is attributed to the initial hot carrier relaxation, and likely dominated by strong electron−phonon coupling that leads to lattice instabilities such as the strongly coupled optical phonon (SCOP) modes that were previously reported in graphite,53 while the biexponential decay is caused C

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as shown in Figure 4. These isotropic out-of-plane oscillations are observed from the change of the c-axis lattice constant. The

Figure 4. Acoustic breathing modes observed following the coherent excitation with 800 nm laser pulses. These oscillations are due to excitation of the lowest order longitudinal acoustic phonons quantized by the sample thickness.

experimental results are fit using an exponentially decaying sine function given by I(t) = A e−t/τ3 sin(2πft + φ), where f, φ, and τ3 are the frequency, the phase shift, and the oscillation lifetime, respectively. The oscillation period (Tp = 1/f) and lifetime τ3 are determined to be 3.3 ± 0.2 and 14.5 ± 2.7 ps, respectively. The period of the acoustic phonon oscillations is dependent on both the sample thickness, d, and Young’s modulus, Y, via53,71,72

Figure 3. (A) Percentage of the intensity suppression at different excitation fluences for pump−probe delays of 2 and 20 ps. (B) Plot of the lifetimes obtained from the biexponential fit of the transient intensity change versus laser excitation fluence.

1/2 1 nυ n ⎛Y ⎞ = = ⎜ ⎟ Tp 2d 2d ⎝ ρ ⎠

Figure 3B displays the lifetimes obtained from the biexponential fit of the change in the diffraction intensity as the excitation fluence is increased. The longer lifetime τ2 attributed to electron−lattice equilibration is seen to decrease with the excitation fluence, which can be explained by an increase in the phonon−phonon scattering at higher pump power.48 Interestingly, the shorter lifetime τ1 increases with the excitation fluence, as shown in Figure 3B. This effect follows from the fact that the incoherent phonon modes are populated more efficiently than their decay, such that they are overpopulated at higher excitation, thereby “blocking” their relaxation channels.59,69 This strong electron−lattice coupling at the lowest phonon mode L−1 at the Brillouin zone boundary leads to a temperature-dependent softening of the phonon frequencies. The observed behavior strongly indicates that a Jahn−Teller effect is responsible for the formation of CDW in TiSe2 in the absence of traditional Fermi surface nesting.35,36 Furthermore, it has recently been reported that the lattice distortions due to strong electron−phonon coupling in TiSe2 play a significant role in the CDW formation mechanism.70 These observations are characteristic to TiSe2, in contrast to other CDW-prone TMDCs. Interestingly, the atomic displacement and lattice instabilities behind the CDW transition, as probed by density functional theory, occur in the in-plane direction only.70 By tilting the normal direction of the sample surface by a few degrees away from the propagation direction of the electron beam, out-of-plane coherent oscillations arising from acoustic breathing modes are observed from the residual change in the position of the Bragg diffraction peaks following laser excitation

(2)

where n is a positive integer, with n = 1 for the fundamental resonance, while n > 1 for overtones, ρ is the density of the sample, and υ is the acoustic wave velocity. From the bulk density of ρ = 5.2 g·cm−3 and an acoustic wave velocity of υ = 2740 m·s−1,73 we first derive a thickness of the probed area of 5.7 ± 0.3 nm and thus a Young’s modulus of 42 ± 6 GPa. The calculated Young’s modulus concurs with that reported in the literature for layered TiSe2.73 The calculated sample thickness is valid for the probed area and may not be consistent throughout the sample, and corresponds to approximately 5−6 monolayers of TiSe2. To summarize, the time-resolved diffraction dynamics in a few-layer TiSe2 exfoliate are reported using UED. The timeresolved intensity change of the Bragg diffraction peaks are characterized by a biexponential function with the shorter lifetime attributed to lattice instabilities caused by strongly coupled electron−phonon modes and a longer one attributed to electron−lattice equilibration. The intensities of the suppression of the diffraction peaks increase linearly with laser fluence and have similar slopes for both exponential terms, which shows that the processes are correlated. The positions of the Bragg diffraction peaks exhibit periodic acoustic oscillations, whose frequency enables a derivation of the Young’s modulus and sample thickness. This study demonstrates the advantages of UED approaches to the study of few-layer materials and monolayers by probing the transient structural dynamics of the lattice following laser excitation. The present results provide an enriched understanding of the electron−lattice dynamics in a few-layer sample of TiSe2, especially the strong electron− D

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Research (grant FA9550-16-1-0200). J.H. acknowledges the support from China 1000-Young Talents Plan. The authors gratefully acknowledge Professor Austin Minnich and Dr. Spencer J. Baskin for valuable discussions, and dedicate this manuscript to the memory of our colleague and mentor Professor Ahmed H. Zewail.

phonon coupling in excited TiSe2 that is governed by Kohn anomalies, and how they impact the transport and energy relaxation of electrons in layered-TMDCs. The persistence of such strong coupling at room temperature in few-layer TiSe2 may ultimately limit applicability of these materials in optoelectronics, unless they can be controlled. Furthermore, this study provides strong experimental evidence as to the important role of Kohn anomalies in the temperaturedependent transition mechanism of these materials, with the strong electron−lattice interactions observed pointing to a Jahn−Teller effect behind the CDW behavior in TiSe2.

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METHODS The ultrafast electron diffraction setup consists of 800 nm pump and electron probe pulses in the transmission geometry. An amplified titanium:sapphire laser system produces 100 fs− 800 nm pulses with a repetition rate of 2 kHz. The fundamental laser beam is split into pump and probe arms using a beam splitter. p-Polarized 800 nm pump pulses used to initiate the dynamics are focused into the sample at a 45° angle with respect to the sample surface. The subpicosecond electron probe pulses are obtained by focusing 266 nm UV pulses generated by frequency tripling of the titanium:sapphire fundamental onto a LaB6 photocathode. The subpicosecond photogenerated electrons are subsequently accelerated to 30 keV, and each electron pulse contains around 300 photoelectrons to minimize space-charge effects.52 The spatial overlap between the pump and probe beams is ensured by maximizing the transmission of both beams using a 150 μm aperture. The sample is mounted on a computer-controlled five-axis stage, and the pump−probe temporal delay is generated using a delay line. The time-dependent diffraction patterns are recorded using a microchannel plate/phosphor screen coupled to a CCD working in the gate mode.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsphotonics.7b00878. Additional analyses of the time-resolved intensity behavior of the Bragg diffraction spots at different pump fluences as well as the dynamics of the c-axis lattice constant obtained at non-normal incidence angles (PDF)

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REFERENCES

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: (626) 395-6296. ORCID

Tony E. Karam: 0000-0002-1244-5141 Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Generous financial support for this work was provided by the Gordon and Betty Moore Foundation, as well as the National Science Foundation and the Air Force Office of Scientific E

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