Open Access
Add to BibSonomy
Abstract
We use an ultrafast optical pump-probe spectroscopy to study quasiparticle (QP) dynamics in a topological insulator LaBi. Temperature-dependent optical measurements have been carried out, by which we observed nearly constant fast component (with a lifetime of 0.15 ps) and slow component (with a lifetime of 1.5 ps) for the whole range from 10 K to 295 K. The laser fluence dependence result shows that there is no saturation for the QP dynamics up to 3.3 mJ /cm2. Moreover, an Eg mode transverse optical (TO) coherent phonon has also been observed, with a frequency of 2.8 THz. Our results provide for the first time the ultrafast dynamics information of both the QPs and coherent phonons in a nodal line topological material.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Topologically nontrivial quantum materials, such as topological insulators [1], topological semimetals [2], and topological superconductors [3], provide a platform for investigating intriguing symmetry-protected topological (SPT) phases. To date four-fold degenerate Dirac semimetals (DSM) [4], two-fold degenerate Weyl semimetals (WSM) [2], three-fold degenerate semimetals [5] and nodal line semimetals (NLSM) [6] have been discovered. Among them, the crossing points can form crossing lines or rings (i.e. nodal lines or nodal rings [6]) in momentum space. In past several years, rare-earth monopnictide LaBi has been predicted and experimentally verified to be a topological insulator [7–10]. LaBi has a relatively small gap, making it instead similar to a semimetal. The Dirac cones [8] and large magnetoresistance [11] of LaBi have been observed, which are similar to those of topological semimetals, such as WTe2 [12], TaAs [13] and NbP [14]. More recently, it has been reported that LaBi exhibits nodal line like surface states [10], which in theory can lead to long-range Coulomb interaction and flat Landau levels [15,16]. Despite of the various investigations nearby the Fermi surface, to date there has been no report on the studies of its excited state far above the Fermi surface. So far, the ultrafast QP dynamics and coherent phonons in LaBi and other nodal line topological quantum materials are unclear.
In the meantime, ultrafast optical spectroscopy investigation of topological materials is developing rapidly [17–19]. It is known that the carrier dynamics in solid is sensitively influenced by the electronic dispersions, gaps, and many-body interactions among the charge, lattice, spin, and orbital degrees of freedoms. Ultrafast pump-probe spectroscopy has been successfully employed to trace the intrinsic ultrafast relaxation processes in time domain for photo-excited carriers [20–26], coherent phonons [27,28], squeezed magnons [29,30], etc.
In this work, we carry out a time-resolved ultrafast pump-probe investigation on a single crystal topological insulator LaBi. We obtain the QP lifetimes and find they do not prominently vary with temperature, indicating a constant electron-phonon coupling (EPC) strength for the whole temperature range. In the fluence-dependent experiment, we observe that the fast component amplitude increases linearly with increased photo-carrier density at higher excitation fluences. Furthermore, an Eg mode TO coherent phonon mode is also observed. Our results show a comprehensive ultrafast spectroscopy characterization of LaBi, which facilitates potential applications of nodal line semimetal-like topological insulators.
2. Methods
An experimental setup similar to that we previously reported in Refs. [22,29] is employed in this work. A femtosecond regenerative amplifier system is employed to generate laser pulses with 250 kHz repetition rate, 800 nm central wavelength, and ∼70 fs pulse duration. The laser beam is split into a pump and a probe beam, which spatially overlap on the sample surface. A regular photo diode is employed to detect the relative differential reflectivity ΔR/R0 of the probe beam. An auto-balanced detector and a lock-in amplifier is used to enhance the signal-to-noise ratio. The pump pulse fluence is 1.13 mJ/cm2, and the probe fluence is 1 mJ/cm2. The average powers for the pump and probe beams are 1.7 mW and 1.0 mW, respectively. Lower repetition rate of pump pulses generates much weaker thermal effect [23,31]. The thermal effect in our 250 kHz experimental setup is relatively small. The quantitative criteria is whether the value of |ΔR/R|max deviates from a linear relation with fluence.
Black LaBi single crystal (face centered cubic crystal structure) of millimeter size is grown using the metal fluxes method [8]. The sample is polished to have an optical-flat surface, which is the (001) surface and is shown in the upper inset of Fig. 1(a). The sample is glued on a copper sample holder by using cryogenic varnish, which is mounted on the cold finger of an open cycle cryostat.
Fig. 1. (a) Time resolved ΔR/R0 of LaBi at different temperatures. The red solid curves are the fitting curves. The insets are the sample surface morphology (upper) and the schematic of the LaBi crystal structure (lower), respectively. (b) and (c) depict lifetimes τfast and τslow as a function of temperature, respectively.
3. Results and discussion
The ultrafast dynamics of LaBi obtained at different temperatures are shown in Fig. 1(a), which are slightly offset for clarity. The red spot on the sample surface in the inset indicates the spot for the laser pulse incidence. In Fig. 1(a), the temperature varying is indicated with colour gradient: light blue dots represent data from higher temperatures, while dark blues are from lower temperatures. Two distinct relaxation processes constitute the photo-induced change of reflectivity. Because the lifetime of fast component of the dynamics is comparable to the pump pulse duration, we consider the de-convolution of the signal using a finite width Gaussian pump pulse. The data are fitted with
By using Eq. (1), we obtain the QP lifetimes τfast and τslow for all the temperatures, which are summarized in Figs. 1(b) and 1(c), respectively. The fitting results clearly show that both the fast and slow component lifetimes do not vary prominently with temperature. The fast component of the dynamics reflects the decay of photo- and thermal-carriers in the excited state, whose excess energy transfers to the lattice through EPC, with an interaction time of 0.1∼10 ps [32]. The strength of EPC can be interpreted from the lifetime of the electron-phonon thermalization. The temperature independence of τfast indicates that the EPC strength does not change with temperature, which is normal in many cases [33]. The slow component of the dynamics is as usual attributed to the phonon-phonon scattering, and the lifetime τslow is of typical value for phonon-phonon scattering. In some cases, electron-hole recombination or carrier diffusion can also result in a slow component. The electron-hole recombination process is greatly sensitive to temperature, as demonstrated in many semimetals [21], whereas τslow exhibits temperature independence in our experiment. The relaxation time of carrier diffusion (at the order of 100 ps, [34,35]) is much longer than the scattering time (about 1.5 ps) in our result. We subsequently attribute the slow component in the dynamics to the phonon-phonon scattering [36]. Our result indicates that the electron-phonon and phonon-phonon scatterings in the sample do not vary much with temperature. We note that the nodal line surface state only exists in the very few surface layers of atoms, thus we are mainly probing the bulk states of the sample.
We further investigate the laser fluence dependence of the QP dynamics. The ultrafast relaxation process of LaBi under different irradiation laser fluence are measured at 7 K, and the results are shown in Fig. 2(a). We obtain the lifetimes and the densities of the photon-carriers at different fluences, depicted in Figs. 2(b) and (c), respectively. The lifetimes of the fast decay process follow a radical function, as indicated by the red curve, and the dashed part is the extrapolation of the measured data. This feature has been observed in many solids, such as semimetals and superconductors [33], at relatively higher laser fluence, which indicates a constant EPC strength. The density of photon-carriers increases linearly with fluences, as demonstrated by the red straight line, which indicates that the laser pulse does not cause a thermally-induced saturation phenomena during the experiment. Another noticeable feature of the fluence dependence result is that the slow component becomes more prominent with enhanced fluence, leading to the overall negative amplitude portion of the dynamics at longer than 1.0 ps. We attribute this to the enhanced phonon-phonon scattering at high laser fluences, such as the anharmonic optical-to-acoustic phonon decay.
Fig. 2. (a) The carrier dynamics in LaBi measured under different pump fluence at 7 K. The red solid curves are the fitting of the carrier dynamics; (b) and (c) denote the fluence dependence of the Afast and the τfast, respectively.
Furthermore, we analyze the coherent phonon in LaBi at 7 K, which is superimposed on the QP dynamics scanning trace [ Fig. 3(a)]. The optical phonon modes can be extract by subtracting the QP dynamics from the total dynamics trace, which is illustrated as the inset of Fig. 3(a). The red curve in the inset is the fitting curve based on a damped oscillation function
Fig. 3. Coherent optical phonon extracted from the dynamics. Red curve: Fitting result of the electronic dynamics. Inset: Coherent phonon oscillation obtained after subtracting the electronic relaxation. (b) Raman spectroscopy of our LaBi crystal at room temperature. (c) FFT result of the time-resolved oscillation shown in the inset of (a). Red curve: a Gaussian fitting curve.
Under our experimental configuration, both A1g and Eg coherent phonon modes can be detected. An ab initio study shows there is only one TO phonon mode in LaBi at Г point, which is along the [100] direction with a frequency of 3.05-3.10 THz [37]. The phonon frequency is roughly consistent with our result. Thus we can exclude the A1g mode and assign it to the Eg mode TO phonon, where the La-Bi-La-Bi-La atomic chain oscillates transversely along the [100] direction within the a-b plane (Fig. 4). It is heuristic to compare our result with that of topological insulator Bi2Se3 [38]. The crystal structure of Bi2Se3 is rhombohedral with the R$\bar{3}$m space group, and there is a single A1g mode observed, which is a breathing mode between the layers along the c-axis.
Fig. 4. Schematic diagram of the in-plane Eg vibration mode in LaBi. The red arrows indicate the vibration directions of the La and Bi atoms.
4. Conclusion
In summary, we have investigated the ultrafast dynamics of a topological insulator LaBi, along with the dependence on temperature and laser fluence. We find a fast component with a lifetime of 0.15 ps and a slow component with a lifetime of 1.5 ps in the relaxation process. Both the fast and slow components do not change prominently with temperature. No sign of thermal saturation is observed for laser fluences up to 3.3 mJ/cm2. Moreover, we also observe an Eg mode TO coherent phonon with a frequency of 2.8 THz. Our investigation provides for the first time an ultrafast dynamics study of a nodal line topological insulator, which facilitates potential applications of such materials in various optoelectronics and photonics devices.
Funding
National Key Research and Development Program of China (2017YFA0303603, 2016YFA0300300); National Natural Science Foundation of China (11774408, 11574383); Beijing Natural Science Foundation (4191003); External Cooperation Program, Chinese Academy of Sciences (GJHZ1826); Chinese Academy of Sciences Interdisciplinary Innovation Team.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
References
1. M. Z. Hasan and C. L. Kane, “Colloquium: Topological insulators,” Rev. Mod. Phys. 82(4), 3045–3067 (2010). [CrossRef]
2. B. Q. Lv, H. M. Weng, B. B. Fu, X. P. Wang, H. Miao, J. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, Z. Fang, X. Dai, T. Qian, and H. Ding, “Experimental Discovery of Weyl Semimetal TaAs,” Phys. Rev. X 5(3), 031013 (2015). [CrossRef]
3. N. Hao and J. P. Hu, “Topological quantum states of matter in iron-based superconductors: from concept to material realization,” Natl. Sci. Rev. 6(2), 213–226 (2019). [CrossRef]
4. Z. J. Wang, H. M. Weng, Q. S. Wu, X. Dai, and Z. Fang, “Three-dimensional Dirac semimetal and quantum transport in Cd3As2,” Phys. Rev. B 88(12), 125427 (2013). [CrossRef]
5. B. Q. Lv, Z. L. Feng, Q. N. Xu, X. Gao, J. Z. Ma, L. Y. Kong, P. Richard, Y. B. Huang, V. N. Strocov, C. Fang, H. M. Weng, Y. G. Shi, T. Qian, and H. Ding, “Observation of three-component fermions in the topological semimetal molybdenum phosphide,” Nature 546(7660), 627–631 (2017). [CrossRef]
6. C. Fang, H. M. Weng, X. Dai, and Z. Fang, “Topological nodal line semimetals,” Chin. Phys. B 25(11), 117106 (2016). [CrossRef]
7. M. G. Zeng, C. Fang, G. Q. Chang, Y.-A. Chen, T. Hsieh, A. Bansil, H. Lin, and L. Fu, “Topological semimetals and topological insulators in rare earth monopnictides,” https://arxiv.org/abs/1504.03492 (2015).
8. X. H. Niu, D. F. Xu, Y. H. Bai, Q. Song, X. P. Shen, B. P. Xie, Z. Sun, Y. B. Huang, D. C. Peets, and D. L. Feng, “Presence of exotic electronic surface states in LaBi and LaSb,” Phys. Rev. B 94(16), 165163 (2016). [CrossRef]
9. R. Lou, B. B. Fu, Q. N. Xu, P. J. Guo, L. Y. Kong, L. K. Zeng, J. Z. Ma, P. Richard, C. Fang, Y. B. Huang, S. S. Sun, Q. Wang, L. Wang, Y. G. Shi, H. C. Lei, K. Liu, H. M. Weng, T. Qian, H. Ding, and S. C. Wang, “Evidence of topological insulator state in the semimetal LaBi,” Phys. Rev. B 95(11), 115140 (2017). [CrossRef]
10. B. J. Feng, J. Cao, M. Yang, Y. Feng, S. L. Wu, B. T. Fu, M. Arita, K. Miyamoto, S. He, K. Shimada, Y. G. Shi, T. Okuda, and Y. G. Yao, “Experimental observation of node-line-like surface states in LaBi,” Phys. Rev. B 97(15), 155153 (2018). [CrossRef]
11. T. Kasuya, M. Sera, and T. Suzuki, “Anomalous Magnetoresistance in Ce1-xLax Sb and Ce1-xLax Bi,” J. Phys. Soc. Jpn. 62(8), 2561–2563 (1993). [CrossRef]
12. M. N. Ali, J. Xiong, S. Flynn, J. Tao, Q. D. Gibson, L. M. Schoop, T. Liang, N. Haldolaarachchige, M. Hirschberger, N. P. Ong, and R. J. Cava, “Large, non-saturating magnetoresistance in WTe2,” Nature 514(7521), 205–208 (2014). [CrossRef]
13. C.-L. Zhang, Z. Yuan, Q.-D. Jiang, B. Tong, C. Zhang, X. C. Xie, and S. Jia, “Electron scattering in tantalum monoarsenide,” Phys. Rev. B 95(8), 085202 (2017). [CrossRef]
14. C. Shekhar, A. K. Nayak, Y. Sun, M. Schmidt, M. Nicklas, I. Leermakers, U. Zeitler, Y. Skourski, J. Wosnitza, Z. Liu, Y. Chen, W. Schnelle, H. Borrmann, Y. Grin, C. Felser, and B. Yan, “Extremely large magnetoresistance and ultrahigh mobility in the topological Weyl semimetal candidate,” Nat. Phys. 11(8), 645–649 (2015). [CrossRef]
15. Y. Huh, E.-G. Moon, and Y. B. Kim, “Long-range Coulomb interaction in nodal-ring semimetals,” Phys. Rev. B 93(3), 035138 (2016). [CrossRef]
16. J.-W. Rhim and Y. B. Kim, “Landau level quantization and almost flat modes in three-dimensional semimetals with nodal ring spectra,” Phys. Rev. B 92(4), 045126 (2015). [CrossRef]
17. J. Orenstein, “Ultrafast spectroscopy of quantum materials,” Phys. Today 65(9), 44–50 (2012). [CrossRef]
18. Jimin Zhao, “Ultrafast spectroscopy and its application in condensed matter physics,” Wuli 40, 184–193 (2011). [CrossRef]
19. C. Giannetti, M. Capone, D. Fausti, M. Fabrizio, F. Parmigiani, and D. Mihailovic, “Ultrafast optical spectroscopy of strongly correlated materials and high-temperature superconductors: a non-equilibrium approach,” Adv. Phys. 65(2), 58–238 (2016). [CrossRef]
20. J. Orenstein and J. E. Moore, “Berry phase mechanism for optical gyrotropy in stripe-ordered cuprates,” Phys. Rev. B 87(16), 165110 (2013). [CrossRef]
21. Y. M. Dai, J. Bowlan, H. Li, H. Miao, S. F. Wu, W. D. Kong, Y. G. Shi, S. A. Trugman, J. X. Zhu, H. Ding, A. J. Taylor, D. A. Yarotski, and R. P. Prasankumar, “Ultrafast carrier dynamics in the large-magnetoresistance material WTe2,” Phys. Rev. B 92(16), 161104 (2015). [CrossRef]
22. Y. C. Tian, W. H. Zhang, F. S. Li, Y. L. Wu, Q. Wu, F. Sun, G. Y. Zhou, L. L. Wang, X. C. Ma, Q. K. Xue, and Jimin Zhao, “Ultrafast Dynamics Evidence of High Temperature Superconductivity in Single Unit Cell FeSe on SrTiO3,” Phys. Rev. Lett. 116(10), 107001 (2016). [CrossRef]
23. Q. Wu, H. X. Zhou, Y. L. Wu, L. L. Hu, S. L. Ni, Y. C. Tian, F. Sun, F. Zhou, X. L. Dong, Z. X. Zhao, and Jimin Zhao, “Ultrafast Quasiparticle Dynamics and Electron-Phonon Coupling in (Li0.84Fe0.16)OHFe0.98Se,” https://arxiv.org/abs/1910.09859 (2019).
24. R. Wang, T. Wang, Y. Zhou, Y. L. Wu, X. X. Zhang, X. Y. He, H. L. Peng, Jimin Zhao, and X. H. Qiu, “Layer-dependent ultrafast dynamics of α-In2Se3 nanoflakes,” 2D Mater. 6(3), 035034 (2019). [CrossRef]
25. L. Zhang, D. W. He, J. Q. He, Y. Fu, A. Bian, X. X. Han, S. Y. Liu, Y. S. Wang, and H. Zhao, “Ultrafast charge transfer in a type-II MoS2-ReSe2 van der Waals heterostructure,” Opt. Express 27(13), 17851 (2019). [CrossRef]
26. Y. L. Wu, X. Yin, J. Hasaien, Y. Ding, and J. Zhao, “High-Pressure Ultrafast Dynamics in Sr2IrO4: Pressure-Induced Phonon Bottleneck Effect,” Chin. Phys. Lett. 37, 047801 (2020). [CrossRef]
27. F. Sun, Q. Wu, Y. L. Wu, H. Zhao, C. J. Yi, Y. C. Tian, H. W. Liu, Y. G. Shi, H. Ding, X. Dai, P. Richard, and Jimin Zhao, “Coherent helix vacancy phonon and its ultrafast dynamics waning in topological Dirac semimetal Cd3As2,” Phys. Rev. B 95(23), 235108 (2017). [CrossRef]
28. L. L. Hu, M. Yang, Y. L. Wu, Q. Wu, H. Zhao, F. Sun, W. Wang, R. He, S. L. He, H. Zhang, R. J. Huang, L. F. Li, Y. G. Shi, and Jimin Zhao, “Strong pseudospin-lattice coupling in Sr3Ir2O7: Coherent phonon anomaly and negative thermal expansion,” Phys. Rev. B 99(9), 094307 (2019). [CrossRef]
29. Jimin Zhao, A. V. Bragas, D. J. Lockwood, and R. Merlin, “Magnon squeezing in an antiferromagnet: reducing the spin noise below the standard quantum limit,” Phys. Rev. Lett. 93(10), 107203 (2004). [CrossRef]
30. Jimin Zhao, A. V. Bragas, R. Merlin, and D. J. Lockwood, “Magnon squeezing in antiferromagnetic MnF2 and FeF2,” Phys. Rev. B 73(18), 184434 (2006). [CrossRef]
31. N. Gedik, M. Langner, J. Orenstein, S. Ono, Y. Abe, and Y. Ando, “Abrupt Transition in Quasiparticle Dynamics at Optimal Doping in a Cuprate Superconductor System,” Phys. Rev. Lett. 95(11), 117005 (2005). [CrossRef]
32. R. H. Groeneveld, R. Sprik, and A. Lagendijk, “Femtosecond spectroscopy of electron-electron and electron-phonon energy relaxation in Ag and Au,” Phys. Rev. B 51(17), 11433–11445 (1995). [CrossRef]
33. B. Mansart, D. Boschetto, A. Savoia, F. Rullier-Albenque, F. Bouquet, E. Papalazarou, A. Forget, D. Colson, A. Rousse, and M. Marsi, “Ultrafast transient response and electron-phonon coupling in the iron-pnictide superconductor Ba(Fe1−xCox)2As2,” Phys. Rev. B 82(2), 024513 (2010). [CrossRef]
34. N. Gedik, J. Orenstein, R. Liang, D. A. Bonn, and W. N. Hardy, “Diffusion of Nonequilibrium Quasi-Particles in a Cuprate Superconductor,” Science 300(5624), 1410–1412 (2003). [CrossRef]
35. R. Wang, B. A. Ruzicka, N. Kumar, M. Z. Bellus, H. Y. Chiu, and H. Zhao, “Ultrafast and spatially resolved studies of charge carriers in atomically-thin molybdenum disulfide,” Phys. Rev. B 86(4), 045406 (2012). [CrossRef]
36. M. Hase and M. Kitajima, “Interaction of coherent phonons with defects and elementary excitations,” J. Phys.: Condens. Matter 22(7), 073201 (2010). [CrossRef]
37. G. Gökoglua and A. Erkisi, “Lattice dynamics and elastic properties of lanthanum monopnictides,” Solid State Commun. 147(5-6), 221–225 (2008). [CrossRef]
38. H.-J. Chen, K. H. Wu, C. W. Luo, T. M. Uen, J. Y. Juang, J.-Y. Lin, T. Kobayashi, H.-D. Yang, R. Sankar, F. C. Chou, H. Berger, and J. M. Liu, “Phonon dynamics in CuxBi2Se3 (x = 0, 0.1, 0.125) and Bi2Se2 crystals studied using femtosecond spectroscopy,” Appl. Phys. Lett. 101(12), 121912 (2012). [CrossRef]
