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Anisotropic Coherent Acoustic Phonon Dynamics of Black Phosphorus Studied by Transient Absorption Microscopy

Due to its corrugated hexagonal lattice structure, Black phosphorus (BP) has unique anisotropic physical properties, which provides an additional freedom for designing devices. Many body interactions, including interactions with phonon, is crucial for heat dissipation and charge carrier mobility in device. However, the rich properties of the coherent acoustic phonon, including anisotropy, propagation and generation, were not fully interrogated. In this paper, the polarization-resolved transient absorption microscopy was conducted on BP flakes to study the anisotropic coherent acoustic phonon dynamics. It is found that the damping of the coherent acoustic phonon oscillation was anisotropic, which was revealed to be originated from the anisotropic absorption by pump power dependent experiment. The initial oscillation amplitude of coherent acoustic phonon was found to be anisotropic, from which we believed that the direct photoelastic mechanism dominated the generation of coherent acoustic phonons in our experiment. Besides, we calculated the sound velocity of the coherent acoustic phonon from the oscillation frequency and the acoustic echo, respectively, which well agreed with each other. These findings provide significant insights into the rich acoustic phonon properties of BP, and promise important application for BP in polarization-sensitive optical and optoelectronic devices.


Introduction
Black phosphorus (BP) is a promising two-dimensional semiconductor material with thickness dependent direct bandgap from 0.3 (bulk) 1 to ~2 eV (single layer) 2 and high carrier mobility (on order of 10 4 cm 2 V -1 s -1 ), [3][4][5] which endows BP a promising candidate for further applications such as electronic device with high speed and on-off current ratios, 6-10 mid-infrared optoelectronic device with lower noise. [11][12][13][14][15] Besides, its corrugated hexagonal lattice structure provides unique anisotropic physical properties, such as optical responses, 16 carrier mobility [4][5] and thermal conductivity, [17][18] which brings a new direction in designing novel and polarization sensitive electronic, optoelectronic and optomechanical devices. 5,13,15,[19][20][21][22] A lot of angle-resolved optical techniques have been used to study the anisotropic response of BP, such as Raman spectroscopy, 19,[23][24] photoluminescence spectroscopy 19,25 and scanning polarization modulation microscopy. [26][27] But due to far lower vibrational energy than optical phonons, acoustic phonons were difficult to be detected by traditional Raman spectroscopy. 28 Transient absorption method based on pump-probe technique provides a good choice for observing coherent acoustic phonons in solids when the probe energy resonates with the transient absorption. [29][30][31] By transient absorption method, ultrafast charge carrier dynamics of BP has been investigated. [32][33][34][35][36] These ultrafast studies showed anisotropic charge carrier dynamics. 32,34,36 For designing better device based on these unique anisotropic properties, it is far from being enough just making clear the behavior of charge carriers. It is remarkably necessary to elucidate the many body interactions in BP, including interactions with the phonon, which were crucial for heat dissipation and charge carrier mobility in device. [37][38] One recent study revealed layerdependent coherent acoustic phonon behaviors of BP using transient absorption microscopy. 29 However, the rich properties of the coherent acoustic phonon, including anisotropy, propagation and generation, were not fully interrogated.
In this paper, we performed polarization-resolved transient absorption microscopy to investigate the anisotropic dynamics of photoexcited charge carriers and coherent acoustic phonon in BP. The transient absorption signal with oscillation at acoustic phonon frequency induced by pump excitation was detected as a function of pump-probe delay.
The damping time of coherent acoustic phonon oscillation was found to be beam polarization dependent. By the pump power dependent experiment, we attributed the polarization dependence of the damping to anisotropic absorption. Meantime, the polarization-resolved transient absorption dynamics shows larger coherent acoustic phonon oscillation amplitude for beam polarization along zigzag direction than along armchair direction, from which we deduced that direct photoelastic modulation of refractive index dominated the generation of coherent acoustic phonon. Besides, we calculated the sound velocity of the coherent acoustic phonon from the oscillation frequency and the "acoustic echo", respectively, which well agreed with each other.

Methods
The schematic diagram of home-built transient absorption microscope was shown in Figure 1. A Ti: Sapphire oscillator (Micra, Coherent) provides ~350 fs laser pulse at repetition rate of 80 MHz with a wavelength of 800 nm, which was split into two beams by a beam splitter. One of the beams (70% of the total energy) was doubled by a β-barium borate (BBO) crystal and used as the pump pulse, while the other beam (30% of the total energy) served as the probe pulse. An acousto-optic modulator (R23080-1-.85-LTD, Gooch & Housego) modulated the pump beam at 100 kHz. After passing the polarizer and half-wave plate to make the polarization direction of the pump and probe beams parallel to each other, the two beams were spatially overlapped and conducted into an -5 -inverted microscope (Ti-U, Nikon) equipped with a 60×, 1.49 numerical aperture (NA) oil-immersion objective and a piezo stage (Nano-View/M-100-3, MadCity Lab) which was used for scanning. By the high NA objective, we could get a small laser spot with spatial resolution of ~200 nm. The same objective was used to collect the reflected beams.
After filtering the pump beam, only the reflected probe beam was detected by an avalanche photodiode (APD120A/M, Thorlabs). The reflectivity changes (ΔR) of the probe beam due to the pump beam monitored with a lock-in amplifier (SR830, Stanford Research Systems). Finally, the signal was input into the computer for further processing.
Using this setup, we can do localized excited states study on BP flakes with low shotnoise and high sensitivity, and perform excited states imaging of BP flakes.

Results and Discussion
Thin BP fakes on glass substrate were prepared by standard mechanical exfoliation from bulk BP. Subsequently, freshly exfoliated thin BP flakes were used directly for Computer characterization and optical measurements at temperature of ~21 °C and relative humidity of <10%. Figure 2a shows a typical optical image of thin BP flake with size in tens of microns. Angle-resolved polarized Raman spectra (ARPRS) were collected to determine the crystalline orientation by exciting the BP flake with 532 nm laser line. From the polarized Raman spectra of the BP flake excited at different polarization angles and the polar plot of the integrated intensity of A 2 mode (see Figure S1 in Supporting Information), we could obtain that the armchair direction is along the yellow line in Figure   2a, which has a cross angle of 6° with horizontal direction rotated anticlockwise. Atomic force microscopy (AFM) image in Figure 2b shows that the BP flake is mainly composed of a few flat terraces, with thickness of two large terraces labelled (500 nm and 392 nm).
To obtain rich spatial-temporal information of the BP flake, the piezo stage was used for scanning the sample at fixed pump-probe delays. Figure

(d)
Beam polarization In addition to the usual photoinduced charge carrier relaxation, a strongly coherent acoustic phonon oscillation was clearly observed in the traces as the probe laser energy 1.55 eV was in resonance with the transient absorption. 29 Meantime, the oscillation amplitude was gradually damped, which could be attributed to three factors [39][40][41]   It is well known that BP exhibits distinct anisotropic optical properties due to its wave plate and made sure that they were parallel to each other, so that we could obtain the anisotropic dynamics response of the BP flake from armchair to zigzag direction. As shown in Figure 3, when θ was 0°, the BP flake showed strong positive PB signal and an abrupt decrease. The positive PB signal was due to pump pulse induced ground state depletion. Subsequently, the positive PB signal decayed slowly with a long lifetime.
When the laser polarization was getting close to the zigzag (90°) direction, the initial signal was positive PB signal, but rapidly decreased and switched to negative PA signal.
We attributed the negative PA signal to the phonon-assisted intraband (Drude) absorption (because of the excess carrier population induced by the pump pulse), which gave rise to excited states absorption counteracting pure transient bleaching of interband ground state absorption, as reported in graphene. 50 Subsequently, the negative PA signal decayed slowly with a long lifetime. The gradual change of the transient absorption signal from PB to PA was attributed to the anisotropic carrier mobility of BP, which further leads to different weights of the intraband absorption depending on the probe polarization. 51 Furthermore, ΔR/R at 0 ps decreased when laser polarization changed from armchair direction to zigzag direction, which is due to larger absorption coefficient for light polarized along armchair direction than zigzag direction. 34 Besides, we could see the coherent acoustic phonon oscillation damped more and more quickly, when the beam polarization was gradually changed from armchair to zigzag direction. The above results demonstrate that the transient absorption dynamics, including both the charge carrier and the coherent acoustic phonon, is anisotropic.
To obtain the many body interactions time, the transient absorption traces for beam polarization along armchair and zigzag direction were fitted by three exponential decays superposed on one damped oscillation term: where An is proportionality constants, t1, t2 and t3 are the lifetime of three photoinduced carrier relaxation processes in BP flake. The first process was attributed to the energy relaxation of hot carriers though carrier-carrier and carrier-phonon scattering after photoexcitation, 35 which was very fast and formed a thermalized Fermi-Dirac distribution.
The second process was attributed to the carrier recombination and lattice heating. 35 The third process was attributed to the cooling of lattice temperature through dissipation of heat to the substrate. 34 B is the initial amplitude of the coherent acoustic phonon oscillation. wc and tc are the periodic oscillation frequency and lifetime of the damped coherent acoustic phonon oscillation. The fitting results are shown in Table 1 and in Figure S3. t1 for beam polarization along armchair and zigzag direction are 0.73 ps and 0.84 ps, respectively, which are very fast and roughly the same. Therefore, there are no obvious anisotropic effects in the carrier-carrier and carrier-phonon interactions. t2 for beam polarization along armchair and zigzag direction is 7.67 ps and 23.89 ps, respectively, meaning the carrier recombination and lattice heating is more slowly when the beam polarization gradually changed from armchair direction to zigzag direction. We attributed the slower process to the low carrier mobility in the zigzag direction than the armchair direction. 32, 36 t3 for beam polarization along armchair and zigzag direction are 175.64 ps and 160.85 ps, respectively, which are very slow and roughly the same. It is reasonable since heat conductance is a very slow process and the heat dissipation to the substrate is independent of the beam polarization. The slightly larger t3 for the beam polarization along armchair direction is possibly due to stronger absorption.   Table 2. It can be seen that for beam polarization along armchair direction, the damping time of the coherent acoustic phonon oscillation increased from 145.19 ps to 193.41 ps, and for beam polarization along zigzag direction, the damping time increased from 32.54 ps to 46.64 ps, when the pump power was increased from 50 μW to 90 μW. High pump power means more heat was generated due to absorption of more photons, which is believed to account for longer damping time in Figure 4. On the other hand, it is well known that the absorption coefficient is larger for light polarized along armchair direction than along zigzag direction. 52 Hence, more heat was supposed to be generated for light polarized along armchair direction than along zigzag direction, giving rise to longer damping time for light polarized along armchair direction. Therefore, we deduce that anisotropic absorption is responsible for the -12 -anisotropic coherent acoustic phonon damping.
Different from the damping time, as shown in Table 1, the coherent acoustic phonon oscillation frequencies for beam polarization along armchair and zigzag direction are roughly the same, 43.69 GHz and 43.84 GHz, respectively. This means that it is insensitive to the beam polarization, which is reasonable because the oscillation frequency is inherent of the coherent acoustic phonon. Meantime, they are consistent with the fast Fourier transform results (shown in the inset of Figure 2d).
Furthermore, it is remarkably noted that the coherent acoustic phonon oscillation reappeared at pump-probe delay of ~185 ps as labeled by the black arrow in Figure 3.
This phenomenon could be attributed to the "acoustic echo". 53 Now we turn to examine the generation mechanism of the coherent acoustic phonons in our experiment. Although BP was absorptive to the 400 nm pump photons due to its small band bap, the pump pulse could also penetrate deep into the BP flake in our experiment.
Therefore, the acoustic phonon oscillation could be excited in two distinct mechanisms. [56][57] First, the pump pulse photoelastically modulates the dielectric constant directly. Second, the pump pulse induces thermal expansion that converts into strain and modulates the dielectric constant indirectly. In order to examine which is the dominant mechanism, we extracted the initial oscillation amplitude of the coherent acoustic phonon in transient absorption dynamics in Figure 4. As shown in Table 2, the initial oscillation amplitude were 0.039×10 -6 , 0.055×10 -6 , and 0.067×10 -6 for pump power of 50, 70 and 90 μW, respectively, when the pump pulse was polarized along armchair direction. The initial oscillation amplitude were 0.086×10 -6 , 0.098×10 -6 , and 0.135×10 -6 for pump power of 50, 70 and 90 μW, respectively, when the pump pulse was polarized along zig direction. We could see that the initial oscillation amplitude for pump pulse polarization along armchair direction was smaller than that along zigzag direction at each pump power. As stated previously, the absorption coefficient of BP is larger for light polarized along armchair direction than along zigzag direction, 52 producing more heat for light polarized along armchair direction. According to the indirect mechanism, this would lead to larger initial oscillation amplitude for light polarized along armchair direction, which is contradictory to the experiment results. Therefore, we believe that the direct photoelastic mechanism dominated the generation of coherent acoustic phonons in our experiment.

Conclusions
In this paper, the polarization-resolved transient absorption microscopy based on pumpprobe technique was conducted on BP flakes in a reflection geometry to study the anisotropic coherent acoustic phonon dynamics. Due to anisotropic carrier mobility and absorption in BP, a remarkable beam polarization dependent charge carrier and coherent acoustic phonon dynamics was observed. First, the damping time was decreased when the beam polarization was changed from armchair to zigzag direction, indicating the damping time of the coherent acoustic phonon oscillation was anisotropic. The pump power dependent experiment revealed that anisotropic absorption led to the anisotropic damping. Second, the initial oscillation amplitude of the coherent acoustic phonon was smaller for beam polarized along armchair direction than along zigzag direction, from which we believed that the direct photoelastic mechanism dominated the generation of coherent acoustic phonons in our experiment. Besides, we calculated the sound velocity of the coherent acoustic phonon from the oscillation frequency and the "acoustic echo", respectively, which well agreed with each other. These findings provide significant insights into the rich acoustic phonon properties of BP, and promise important application for BP in polarization-sensitive optical and optoelectronic devices.

Supporting Information
The

Notes
The authors declare no competing financial interest.

ACKNOWLEDGEMENT
This work was financially supported by the National Natural Science Foundation of China