【AIGC One Sentence Reading】:Zn-doping in Cd3As2 modifies photocarrier dynamics, with heavy doping leading to prolonged relaxation due to interband recombination, enabling electronic structure engineering.
【AIGC Short Abstract】:Zn-doping in 3D Dirac semimetal Cd3As2 modifies photocarrier dynamics, revealed by time-resolved spectroscopy. Light doping shortens relaxation time, while heavy doping prolongs it due to interband recombination, indicating a transition to a trivial phase. Doping provides a versatile approach to tune electronic structure and carrier dynamics for optoelectronic applications.
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Abstract
Element doping can break the crystal symmetry and realize the topological phase transition in quantum materials, which enables the precise modulation of energy band structure and microscopic dynamical interaction. Herein, we have studied the ultrafast photocarrier dynamics in Zn-doped 3D topological Dirac semimetal utilizing time-resolved optical pump-terahertz probe spectroscopy. Comparing to the pristine , we found that the relaxation time of the lightly doped alloy is slightly shorter, while that of the heavily doped alloy exhibits a significant prolongation. Pump-fluence- and temperature-dependent transient terahertz spectroscopy indicated that in pristine and lightly doped samples within nontrivial semimetal phase, the photocarrier dynamics are dominated by the cooling of Dirac fermions. In heavily doped alloy, however, the observed longer relaxation process can be attributed to interband electron-hole recombination, which is a result of doping-induced transition into a trivial semiconductor phase. Our investigation highlights that Zn-doping is an effective and flexible scheme for engineering the electronic structure and transient carrier relaxation dynamics in , and offers a control knob for functional switching between diverse optoelectronic devices within the realm of practical applications.
1. INTRODUCTION
In the past decade, three-dimensional (3D) topological Dirac semimetals, with their nontrivial band structure and topologically or symmetry-protected relativistic electrons, have served as a fantastic test bed for investigating intriguing topological phase transition (TPT) and various unprecedented phenomena in solids, significantly enriching and propelling the advancement of condensed matter physics [1–6]. Among the known 3D Dirac semimetals, has garnered extensive research interests and exhibited considerable application value in nano-optoelectronics [7,8] and nonlinear optics field [9,10] by virtue of its superior properties, such as ultrahigh carrier mobility [11], strong optical nonlinearity [12,13], commendable chemical stability in air [6], gate-tunable Berry curvature [14], and so on. More importantly, is a neighbor state to diverse quantum states including a Weyl semimetal, topological insulator, and regular semiconductor, rendering it an ideal platform for studying TPT [1]. Prior experimental studies have demonstrated that applying a strong magnetic field [15,16] or high pressure [17] can induce a TPT in from a Dirac semimetal to a Weyl semimetal or a trivial semiconductor.
Light-matter interaction plays a crucial role in revealing the fundamental dynamic coupling among various microscopic degrees of freedom or elementary excitations, and it also holds the capability to trigger novel phase transitions and tailor the materials’ physical properties [18–21]. A profound understanding of the transient dynamics upon light irradiation is the prerequisite for designing and developing innovative functional devices. Especially, the precise control of carrier lifetimes stands out as a key in enhancing the performance of optoelectronic devices such as photodetectors, solar cells, and light-emitting diodes. To date, the ultrafast carrier dynamics following photoexcitation in pristine have been widely investigated using time-resolved optical spectroscopy [22–25], terahertz (THz) spectroscopy [5,26–29], high-harmonic-generation spectroscopy [30–33], angle-resolved photoemission spectroscopy (ARPES) [34], and others. The widespread consensus is that the principal relaxation process in exhibits metallic behavior and can be described using a two-temperature model (TTM). However, we note that the nonequilibrium carrier dynamics in after a TPT have yet to be uncovered. An in-depth exploration of the carrier dynamics both preceding and succeeding a TPT is anticipated to yield profound insights into the unique properties of and may reveal strategies for carrier manipulation related to topological phases.
Element doping in has been proven to be an intrinsic and efficient approach to modify the band structure compared to other extreme conditions [35,36]. Doping can open a bandgap and induce a TPT to a regular semiconductor, depending on the doped element and concentration. This is expected to yield distinct dynamic behaviors compared to the pristine . To date, few studies focused on the impact of doping on nonequilibrium dynamics in . Zhu et al. conducted a study on the photocarrier dynamics of Cr-doped using optical pump-probe spectroscopy, in which they found that the relaxation time is significantly shorter than that of intrinsic and attributed this phenomenon to additional doping-induced carrier-phonon scattering channels [9]. In contrast, Sun et al. observed a long-lived decay component in Mn-doped , which was assigned to the Mn impurity states [37]. However, neither study involves the case that , upon doping, opens a bandgap and transitions into a trivial semiconductor. How the transient relaxation dynamics of doped alloys with an opened gap differ from those of pristine semimetal , and whether they exhibit semiconductor behavior, are fundamental questions that remain to be unraveled. Addressing these questions will not only deepen our understanding on the intricate interplay between electronic structure and transient characteristics but also elucidate the pivotal role of TPT in modulating carrier dynamics.
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Recent researches show that doping Zn into to substitute Cd can effectively suppress energy band inversion and reduce spin-orbit coupling, finally realizing a TPT of from a nontrivial Dirac semimetal to a trivial semiconductor with non-zero bandgap [36,38,39]. The critical doping concentration, , is estimated to be within the range of 0.17–0.21, as determined through transport measurements [36,38,40]. This provides an excellent opportunity to explore the transient dynamics of before and after TPT. Time-resolved THz spectroscopy has been proven to be a powerful spectral tool for capturing diverse ultrafast dynamic responses upon photoexcitation in 3D Dirac semimetals [41–44].
In this study, the pristine as well as lightly and heavily doped films was fabricated by a molecular beam epitaxy (MBE) technique, and the related ultrafast carrier dynamics were systematically investigated via transient optical pump-THz probe spectroscopy (OPTP). The experimental results demonstrate that the transient dynamics differ dramatically between the lightly and heavily doped samples. We propose that both the intrinsic and lightly doped samples exhibit metallic behavior, with their relaxation process dominated by electronic cooling. In contrast, the heavily doped sample undergoes a phase transition, entering a semiconductor phase with an open bandgap, whose transient relaxation process can be interpreted by defect-mediated Auger recombination. This study reveals the fundamental dynamic information of Zn-doped and offers a representative paradigm for manipulating the relaxation pathways and rates of nonequilibrium photocarriers through the controllable element doping in topological semimetals.
2. EXPERIMENTAL METHODS
High-quality film samples were fabricated via the MBE method. Before growing the film, a 10 nm thick CdTe buffer layer was deposited on a sapphire substrate to assist the nucleation. The intrinsic film was grown epitaxially on the buffer layer at 170°C. The alloy films, with different doping concentrations denoted by x, were grown by regulating the Zn-doped evaporation temperature. Eventually, the lightly () and heavily () doped samples were synthesized at temperatures of 180°C and 215°C, respectively. The samples’ thickness was approximately 50 nm determined using an RHEED system.
Time-resolved OPTP measurements were carried out to explore the relaxation dynamics of photocarriers in a home-built experimental setup. The optical pump pulses are delivered from a Ti:sapphire regenerative amplifier (Spectra Physics, Spitfire) operating at a repetition rate of 1 kHz, with a central wavelength of 780 nm (1.59 eV) and a pulse duration of 120 fs. The THz probe pulses are generated and detected based on a pair of 1 mm thick, (110)-oriented ZnTe crystals. All experiments were performed in a dry nitrogen atmosphere, and the specimens were placed in a cryostat. For more details see Appendix A.
3. RESULTS AND DISCUSSION
We first conducted a series of characterizations on the three experimental samples. Energy dispersive spectroscopy (EDS) revealed the doping concentrations of the lightly doped and heavily doped samples to be and , respectively. The high doping level of ensures that the sample has undergone a TPT and becomes a trivial semiconductor. In contrast, the lightly doped with a concentration of remains in nontrivial semimetal phase. Figures 1(a) and 1(b) present the EDS mapping of Zn element distribution, from which it is seen that the distribution of the Zn element is uniform in our alloy samples. Figure 1(c) shows the normalized X-ray diffraction (XRD) patterns, which exhibit a pronounced (224) characteristic peak for all three samples. The peak width keeps constant regardless of the Zn doping level, suggesting that the crystallinity is unaffected by Zn doping. The peak position shifts towards a larger diffraction angle, indicating that the lattice constant shrinks with Zn doping, which is consistent with the expectation since Zn has a smaller atomic radius than its congener element Cd. Figure 1(d) displays the Raman spectra of the three samples, which clearly reveal characteristic phonon modes that are in concordance with previous reports [45,46]. Figure 1(e) illustrates the schematic diagram of the transient OPTP and the sample structure. The pump and probe pulses collinearly focus on the sample, with the spot size of the optical pump being larger than that of the THz probe. Figure 1(f) illustrates the primitive tetragonal unit cell structure of .
Figure 1.EDS mapping of Zn element distribution in (a) lightly doped () and (b) heavily doped () films. (c) Normalized XRD patterns of films with different doping concentration. (d) Raman spectra of the three samples. (e) Schematic diagram of our OPTP experimental setup and sample structure. (f) Tetragonal unit cell of .
Next, the free carrier responses of the intrinsic and doped film samples upon 1.59 eV photoexcitation are systematically studied on picosecond timescale. This is done by tracking the photoinduced differential transmission signals of the probe THz pulse (, where the and denote the transmitted THz electric field peak value without photoexcitation and that of the change with photoexcitation, respectively) as a function of pump-probe delay time. We chose the temperature of 5 K for the pump-fluence-dependent measurements to minimize the effect of ambient thermal excitation. Figures 2(a)–2(c) show the pump-fluence-dependent THz transmission response of the films with , 0.14, and 0.31 versus pump-probe delay time. Figure 2(d) plots the maximum value of the THz transmission response, denoted as , with respect to pump fluence for the three samples. The differences in the transient maxima () observed under identical pump fluence originate from different absorption coefficients. It is necessary to mention that the CdTe buffer layer shows a negligible transient transmission response according to our previous work [47]. And the dips observed in transient dynamic traces at the delay time of about 18 ps are attributed to the re-excitation of the samples caused by the undesirable echo of the pump pulses.
Figure 2.Pump-fluence-dependent differential THz transmission, , as a function of delay time in (a) intrinsic, (b) lightly doped, and (c) heavily doped sample; the solid lines are the curves derived from a convoluted mono-exponential fitting. (d) The maximal versus pump fluence for three samples. The circles denote experimental data, and the solid lines represent the linear fitting curves. (e) Fitted decay time constants of three samples using a single exponential decay function at various pump fluences; the solid lines serve as guide to the eye. (f) The decay rate is plotted with respect to pump fluence for the heavily doped sample, with the solid line representing a linear fit to the data.
Overall, when the pump pulses arrive, a sharp decrease in THz transmission arises for all samples. Subsequently, the transient THz response relaxes back to zero from the negative maximum. From Figs. 2(a)–2(c), one can see that the transient recovery rate is obviously different among the three samples, depending on the Zn doping level. To quantitatively evaluate the relaxation lifetimes of photocarriers, we employ a mono-exponential decay function convoluted with the instrument response function, as follows, to fit the temporal evolution profile [48,49]: Here, is the delay time between the pump and probe pulses. and present the relaxation time constant and amplitude, respectively. The erf refers to the error function. and are pulse temporal duration and a time-independent offset, respectively.
As shown by the solid lines in Figs. 2(a)–2(c), the experimental data can be well reproduced with the aforementioned equation. The extracted pump-fluence-dependent photocarriers’ lifetimes of films with different doping level are plotted in Fig. 2(e). For the intrinsic specimen, the relaxation lifetime increases with the pump fluence, which is consistent with previous reports [26,31]. In the case of the lightly doped specimen, the relaxation lifetime exhibits a similar dependence on pump fluence but is shorter than that of the intrinsic specimen under identical pump fluence. Surprisingly, for the heavily doped specimen, we found that the relaxation lifetime is three to five times longer than that of the intrinsic specimen. Moreover, the relaxation lifetime shows a negative correlation within the applied pump fluence, indicating that the carrier dynamics are associated with a high-order process. This phenomenon, where the photocarriers’ lifetime first becomes shorter and then becomes longer with the increase of Zn doping level, differs from the case of Cr-doped , in which the lifetime exhibits a monotonically decreasing trend with the increase of Cr doping level [9]. This abrupt transformation in transient dynamics usually implies the occurrence of a TPT, which coincides with our case that experiences a TPT as the Zn doping concentration rises from to . Our measurements manifest that nonequilibrium carriers in the nontrivial semimetal phase and the trivial semiconductor phase possess distinct relaxation times and relaxation mechanisms. The decay rates of the heavily doped specimen, i.e., , are presented in Fig. 2(f). It is seen that the decay rates are linearly dependent on pump fluence, which is a clear signature of a two-particle process [50,51].
To better comprehend the mechanism hiding behind the observed transient dynamics, the temperature-dependent OPTP measurements were further carried out on the three samples at a fixed pump fluence of μ. Figure 3(a) shows the normalized transient THz trace of the heavily doped sample at various temperatures, and the THz transmission kinetics of the intrinsic and lightly doped samples are presented in Fig. 5 of Appendix B. Obviously, the relaxation rate drops with increasing temperature. We extracted the relaxation lifetimes using Eq. (1) at different temperatures for the three samples, which are plotted in Fig. 3(b). It is observed that the decay times of the photocarriers generally increase with temperature. Furthermore, compared to the intrinsic sample, the relaxation lifetime of lightly doped is shorter, while that of the heavily doped is longer, irrespective of the temperature. We will next comprehensively analyze the relaxation pictures of films at two distinct phases.
Figure 3.(a) Temperature-dependent transient THz transmission response of the heavily doped alloy, excited at a fixed pump fluence of μ. (b) Temperature dependence of the fitted decay time constants, where the solid lines are guide to the eye.
Upon exposure to near-IR ultrashort optical pulses, the electrons and holes undergo an immediate redistribution within the momentum space, resulting in a deviation from equilibrium state. Subsequently, physical processes such as electron-electron (e-e) scattering, electron-phonon (e-p) coupling, and electron-hole (e-h) recombination, could occur over ultrafast timescales. Right after photoexcitation, the observed transient drop in THz transmission signifies enhanced absorption of THz pulses. This can be ascribed to the contribution of two effects: photoinjected free carriers (which stem from interband transition) and thermalized carriers that undergo e-e scattering (the thermalization of electrons broadens the Fermi distribution over a wider energy range, which in turn leads to an increase of free carriers’ absorption of THz pulses due to intraband transitions having larger momentum and energy conservation phase space [26,42,52]). In general, there are two potential scenarios to describe the nonequilibrium dynamical relaxation after rapid e-e thermalization depending on the interband scattering rate [23,53,54]. (i) If the interband recombination rate is faster than or similar to the intraband scattering rate, the resultant quasi-equilibrium can be described by a Fermi-Dirac distribution with an elevated carrier temperature. The subsequent relaxation process is dominated by the cooling of hot carriers and can be further interpreted by a TTM. This scenario is generally applicable to metals or semimetals with a high carrier concentration. (ii) If intraband scattering rate outpaces interband recombination rate, the electrons and holes establish separate Fermi-Dirac distribution with electrons populating the conduction band and holes remaining in the valence band. The relaxation process is primarily governed by e-h recombination, and this scenario typically occurs in semiconductor materials. In our intrinsic and lightly doped samples within nontrivial semimetal phase, we ascribe the observed relaxation dynamics to the aforementioned first scenario, namely, the cooling of Dirac fermion via e-p coupling. This assignment aligns with previous explanations regarding intrinsic [23,26,55], and is now robustly corroborated by the following three pieces of evidence. (i) In the previous Tr-ARPES study, Bao et al. observed that interband Auger recombination rate is approximately twice as fast as the intraband relaxation rate of Dirac fermions near the Fermi surface [34]. (ii) The decay time constant increases with pump fluence as shown in Fig. 2(e). Higher pump fluence means higher electronic temperature, which naturally results in a longer time to release the excess energy to the lattice through e-p scattering. (iii) The decay lifetime increases with temperature as shown in Fig. 3(b). Consequently, the transient dynamics observed in both intrinsic and lightly doped samples align with the characteristics of the TTM framework, and it is rational to attribute the relaxation process to the cooling of Dirac fermions. What should be mentioned is that, for intrinsic and lightly doped , the interband relaxation is realized through the Auger recombination process. Although the scattering phase space near the Dirac point is restricted due to the minimal density of states, the gapless linear dispersing band structure can greatly facilitate the Auger process, since energy and momentum conservation conditions automatically satisfy along a straight line in momentum space compared to conventional parabolic bands [56,57]. Thus, the relaxation time for interband Auger recombination is relatively short, which escapes from the temporal resolution of our THz probe pulse. As a result, the overall transient signal is predominated by electronic cooling and can be described with a single-exponential decay function. Note that the authors in Ref. [27] observed a fast decay component, as fast as a few hundred fs to 1 ps, and interpreted it as Auger recombination. This observation is consistent with our above claims. Lastly, for the fact that the recovery lifetime of the lightly Zn-doped sample is shorter than that of the intrinsic one, we attribute it to the lightly doped sample’s smaller optical absorption coefficient at 780 nm, which results in a lower thermalization temperature for electrons. Furthermore, doping could introduce additional electron-defect scattering channels, leading to a higher cooling efficiency of thermal electrons.
Next, we focus on the peculiar relaxation dynamics observed in the heavily doped sample. According to transport measurements, at a doping concentration of , the ternary alloy is in the trivial semiconductor phase, characterized by a non-zero bandgap and lacking a linear dispersing band structure [36,38,40]. To underpin the reliability and support our forthcoming proposal, we carried out first-principle electronic structure calculations for the heavily doped . The result indicates that a bandgap of several tens meV is indeed opened, as shown in Fig. 6. More details can be found in Appendix C. The introduction of a bandgap can considerably reduce the phase space available for Auger recombination. This reduction strongly suppresses the Auger recombination process, as seen in bilayer graphene [57,58]. Therefore, we attribute the observed abrupt prolongation of photocarriers’ relaxation lifetime in the heavily doped sample to a strong relaxation bottleneck induced by the presence of a bandgap. Accordingly, the interband relaxation process is no longer primarily driven by Auger recombination, unlike the case in intrinsic and lightly doped , which can also be discerned from the temperature-dependent transient dynamics. This is due to the fact that Auger recombination rate generally increases with temperature according to the Arrhenius law, (where and represent bandgap energy and Boltzmann constant, respectively, and is a constant dependent on the electronic structure) [59–61], which is contrary to our experimental observations, as shown in Fig. 3(a).
We also measured the THz time-domain transmission signals of the heavily doped film upon photoexcitation (see Fig. 7 in Appendix D), and extracted the complex conductivity in investigated THz frequency range (see Fig. 8 in Appendix D). We analyzed the THz photoconductivity dispersion utilizing the Drude-Smith model and found that the model describes the data well. The fitted plasma frequency, , increases with pump fluence and decreases with pump-probe delay time (see Fig. 8 in Appendix D). This trend indicates that the transient dynamics of the heavily doped sample are dominated by the generation and annihilation of free carriers.
The experimental results and the above analysis suggest that the relaxation behavior of the heavily doped sample matches the characteristics of semiconductors, and relaxation process aligns with the aforementioned semiconductor-like scenario, where the transient dynamics are dominated by e-h annihilation. Pump-fluence-dependent decay rate, as shown in Fig. 2(f), indicates that the observed carrier dynamics conform to a two-particle process. Representative bimolecular processes encompass exciton-exciton annihilation, radiative e-h recombination, phonon-assisted e-h recombination, and defect-mediated Auger recombination [62]. Firstly, the possibility of exciton-exciton annihilation can be readily dismissed, as the THz pulse is insensitive to a charge-neutral exciton. Secondly, radiative recombination is also an unlikely candidate for photocarriers’ recovery, since this process usually takes place on a much longer timescale (typically a few nanoseconds) [63], rather than tens of picoseconds as witnessed in Figs. 2(c) and 3(a). Thirdly, it is well known that the phonon population is a strong function of lattice temperature according to the Bose-Einstein statistics . Elevating temperature will accelerate phonon-assisted e-h recombination, leading to a shorter e-h recombination time. Therefore, the possibility of phonon-assisted e-h recombination can be ruled out, as the temperature-dependent relaxation time shown in Fig. 3 contradicts the expected behavior of this mechanism. Finally, considering such high doping level of , the presence of defect or impurity is inevitable. We thus propose that defect-assisted Auger recombination is responsible for the prolonged relaxation process observed in the heavily doped sample. It is noteworthy that this mechanism has been widely applied to explain the e-h annihilation process in various systems so far [64–69]. Strictly speaking, defect-mediated Auger recombination is a three-particle process requiring the participation of three carriers: two free carriers and one trapped carrier. However, since the density of trapped carriers barely changes with time, the process can be reduced to a two-particle recombination model [62,70]. We argue that the defect level is located in the bandgap. Electrons at the defect level have the probability to transition to the bottom of the conduction band by absorbing phonons [71,72]. When the lattice temperature rises, more electrons at the defect level can be thermally excited to the conduction band, which mitigates the rate of free carrier depletion. This scenario qualitatively explains the observed increase in relaxation lifetime with temperature.
To provide an intuitive understanding, the schematic diagrams encapsulating carrier relaxation dynamics discussed earlier are presented in Fig. 4. For the intrinsic and lightly doped , a pair of mirror-symmetric Dirac cones exists near the Fermi level along direction, and the recovery dynamics after photoexcitation are governed by the cooling of thermalized Dirac electrons through emitting optical phonons. For the heavily doped sample, the significant weakening of spin-orbit coupling leads to the liberation of band inversion, triggering the TPT accompanied by the opening of a bandgap. Upon photoexcitation, e-e scattering, e-p scattering, and electron trapping are rapidly completed. Subsequently, the transient relaxation is dominated by defect-mediated Auger recombination.
Figure 4.Schematics for relaxation dynamics of photoexcited carriers near the Fermi level in (a) Dirac semimetal phase and (b) trivial semiconductor phase. It should be noted that the relaxation of holes in (b) is similar to that of electrons.
To the best of our knowledge, this is the first observation of photocarrier dynamics both before and after a TPT induced by chemical doping in 3D Dirac semimetals. By controlling the band structure and topological phase with different Zn doping levels, we have realized the shortening or the prolonging of the characteristic lifetime of photocarriers, as well as the regulation of photocarriers’ relaxation channels in Dirac semimetal . Our findings demonstrate that the alloy is an excellent functional material with the capability for various applications in the fields of high-speed optoelectronic devices and nonlinear optics. For example, the lightly doped alloy, which has an ultrashort relaxation time, can be applied as an ultrafast saturable absorber of a pulsed laser or an ultrafast optical switch. Alternatively, the long relaxation time and population inversion in the heavily doped alloy may enhance the potential for achieving the stimulated light amplification.
4. CONCLUSIONS
In summary, we have successfully fabricated the Zn-doped alloy films and systematically investigated the impact of Zn doping on the photocarrier dynamics using an OPTP setup. The experimental results emphasize the vital role of Zn doping in engineering the band structure and tuning the photocarrier recovery time and relaxation channels in . Our findings provide deep insights into the ultrafast carrier dynamics before and after a TPT in 3D topological Dirac semimetal, thereby paving the way for the design of novel ultrafast optoelectronic devices based on Dirac semimetal materials.
APPENDIX A: TIME-RESOLVED OPTP EXPERIMENTAL SYSTEM
The ultrafast OPTP measurements were carried out to explore the relaxation dynamics of photocarriers in a home-built setup [42]. The optical pulses are delivered from a Ti:sapphire regenerative amplifier (Spectra Physics, Spitfire) operating at a repetition rate of 1 kHz with a central wavelength of 780 nm (1.59 eV) and a pulse duration of 120 fs. The laser pulse is split into three beams. One acts as the source for generating THz pulse, another functions as the THz radiation detecting beam, and the remaining one is utilized to excite the sample, serving as optical pump pulse. The THz pulse is generated and detected based on a pair of 1 mm thick, (110)-oriented ZnTe crystals. The optical pump and THz probe pulse are collinearly propagated with a spot size of 6.5 mm and 2.0 mm on the surface of the sample, respectively. The optical chopper frequency is set to 500 Hz. An optical power attenuator is utilized to adjust the pump fluence of the excitation beam, enabling the conduction of pump-fluence-dependent experiments. All experiments were performed in a dry nitrogen atmosphere, and the specimens were placed in a cryostat (Oxford Instruments, OptistatDRY BL4), with the temperature ranging from 5 to 300 K.
APPENDIX B: TEMPERATURE-DEPENDENT TRANSIENT THz TRANSMISSION DYNAMICS OF INTRINSIC AND LIGHTLY DOPED SAMPLES
The normalized THz transmission kinetics for the intrinsic and lightly doped samples, measured at various temperatures, are presented in Fig. 5. Generally, the relaxation rate is observed to decrease with increasing temperature.
Figure 5.Normalized THz differential transmission responses at various temperatures under a fixed pump fluence of μ in (a) intrinsic and (b) lightly doped samples.
APPENDIX C: CALCULATION OF ENERGY BAND STRUCTURE OF THE HEAVILY DOPED (Cd1?xZnx)3As2 BASED ON DENSITY-FUNCTIONAL THEORY
Geometry optimizations and band structure calculations were carried out using the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation [73], as implemented in the Vienna Ab initio Simulation Package (VASP) [74]. The interactions of electrons with ionic cores were described using projector augmented wave (PAW) pseudopotentials [75,76]. For all of these calculations, we chose an energy cutoff of 500 eV, and the maximum force of each ion was less than 0.01 eV/Å. Γ-centered k-grid samplings [77] were adopted for the system. The ground state is a centrosymmetric crystal structure derived from an underlying antifluorite lattice (space group No. 142, I41/acd, 80 atoms per unit cell) [78,79]. By using a special quasi-random structure method, we replace 15 Cd atoms with Zn () to simulate 31% doping in the experiment. The optimized has a lattice constant of Å with and . Note that the band structure was calculated by taking into consideration spin-orbit coupling (SOC).
Figure 6.Calculated electronic band structure of 0.31-Zn-doped based on VASP.
APPENDIX D: PHOTOEXCITED THz TIME-DOMAIN SPECTRA, COMPLEX THz PHOTOCONDUCTIVITY, AND DRUDE-SMITH FITTING OF THE HEAVILY DOPED (Cd1?xZnx)3As2
To further investigate the nonequilibrium state dynamics of the heavily doped , the photoexcited THz time-domain spectra were measured with the OPTP setup, which are shown in Fig. 7. According to the thin-film approximation, the frequency-dependent complex THz photoconductivity can be calculated by the following relation [80,81]: where and are the transmitted frequency-domain THz fields under pump on and pump off, respectively. and denote the refractive index of the substrate and the thickness of the photoexcited region, and is the impedance of free space. Figures 8(a) and 8(b) present the real and imaginary parts of THz photoconductivity with respect to frequency under different pump fluences and delay times.
We employed the Drude-Smith model [80,82], as given below, to fit the complex THz photoconductivity : where , , and are the plasma frequency, vacuum permittivity, and momentum scattering time, respectively. represents the backscattering constant with a range from to 0. One can see that the complex photoconductivity in the heavily doped film fits well with the Drude-Smith model, with the fitting plasma frequencies shown in Figs. 8(c) and 8(d).
Figure 7.Transmitted THz time-domain signals of the heavily doped thin film under different pump fluences and delay times. Inset shows the zoom-in around the THz peak.
Figure 8.Complex THz photoconductivity dispersion and Drude-Smith model fitting under (a) various pump fluences at a delay time of 1 ps and (b) various delay times at μ. Blue square and red circle denote real and imaginary parts, respectively, and solid lines are fitting curves with the Drude-Smith model. The fitted plasma frequency versus (c) pump fluence and (d) delay time.