Ultrafast relaxation dynamics of photoexcited Dirac fermions in the three-dimensional Dirac semimetal $\mathrm{C}{\mathrm{d}}_3\mathrm{A}{\mathrm{s}}_2$

Three-dimensional (3D) Dirac semimetals that can be seen as 3D analogues of graphene have attracted enormous interest in research recently. In order to apply these ultra-high-mobility materials in future electronic/optoelectronic devices, it is crucial to understand the relaxation dynamics of photoexcited carriers and their coupling with lattice. In this paper, we report ultrafast transient reflection measurements of the photoexcited carrier dynamics in cadmium arsenide ($\mathrm{C}{\mathrm{d}}_3\mathrm{A}{\mathrm{s}}_2$), which is one of the most stable Dirac semimetals that have been confirmed experimentally. By using the low-energy probe photon of 0.3 eV, we probed the dynamics of the photoexcited carriers that are Dirac-Fermi-like approaching the Dirac point. We systematically studied the transient reflection on bulk and nanoplate samples that have different doping intensities by tuning the probe wavelength, pump power, and lattice temperature and find that the dynamical evolution of carrier distributions can be retrieved qualitatively by using a two-temperature model. This result is very similar to that of graphene, but the carrier cooling through the optical phonon couplings is slower and lasts over larger electron temperature range because the optical phonon energies in $\mathrm{C}{\mathrm{d}}_3\mathrm{A}{\mathrm{s}}_2$ are much lower than those in graphene.

Figure 1

Schematic diagrams of transient reflection experiment on (a) a bulk crystal and (b) a nanoplate. Both samples are pumped by 800 nm and probed by 2 μm and 4 μm unless in a probe wavelength dependent measurements. Reproduced with permission [64], copyright 2015, American Chemical Society. (c) Band diagram of $\mathrm{C}{\mathrm{d}}_3\mathrm{A}{\mathrm{s}}_2$ and pump/probe photon transition configuration; the Fermi levels of the bulk and nanoplate $\mathrm{C}{\mathrm{d}}_3\mathrm{A}{\mathrm{s}}_2$ are denoted as red and blue dash lines, and the 800 nm, 2 μm, and 4 μm photon relevant transitions are denoted as red, blue, and green arrows, respectively. Reproduced with permission [59], copyright 2015, American Chemical Society. Inset shows the crystal structure of the $\mathrm{C}{\mathrm{d}}_3\mathrm{A}{\mathrm{s}}_2$.

Figure 2

The typical transient reflection spectra of $\mathrm{C}{\mathrm{d}}_3\mathrm{A}{\mathrm{s}}_2$ bulk sample and nanoplate at room temperature for (a) 2-μm probe and (b) 4-μm probe, respectively. (c) Probe wavelength dependence of transient reflection spectra for 2000 nm, 2115 nm, 3880 nm, and 4000 nm on bulk $\mathrm{C}{\mathrm{d}}_3\mathrm{A}{\mathrm{s}}_2$ at 77 K. The pump power is 5 mW. (d) Normalized plot of (c) according to the negative peak signals at time zero ($\mathrm{\Delta }R/R{{|}_t}_{=0}$).

Figure 3

(a) Pump power dependent transient reflection spectra for 4-μm probe on bulk $\mathrm{C}{\mathrm{d}}_3\mathrm{A}{\mathrm{s}}_2$ at 10 K. The pump power is varied from 1 mW to 10 mW. The inset is an enlargement of the positive $\mathrm{\Delta }R/R$ signals. (b) Normalized plot of (a) according to the negative peak signals at time zero. The spectra are fitted by exponential decay function: $\mathrm{\Delta }R/R=A_0+A_1\times \exp (-t/\tau )$ from time zero to the delay times $\left(t_c\right)$ that cross zero with τ as the decay constant. (c) Pump power dependence of $t_c$ (red) and maximum positive signals (dark blue). (d) Pump power dependence of the decay constant τ. The lines in (c) and (d) are guides to the eye.

Figure 4

(a) Normalized temperature dependent transient reflection spectra according to the negative peak signals at time zero for a 4-μm probe on bulk $\mathrm{C}{\mathrm{d}}_3\mathrm{A}{\mathrm{s}}_2$ sample at 10 K, 78 K, 150 K, and 300 K, respectively. The pump power is 5 mW. The decay of $\mathrm{\Delta }R/R$ from the negative peak is fitted by a biexponential decay function: $\mathrm{\Delta }R/R=A_0+A_1\times \exp (-t/{\tau }_1)+A_2\times \exp (-t/{\tau }_2)$ with a fast time constant ${\tau }_1$ and a slow time constant ${\tau }_2$. (b) The temperature dependence of ${\tau }_1$ and ${\tau }_2$ extracted from the fitting of (a), the lines are guide to the eye.

Figure 5

Schematic diagrams of the carrier distribution around the Fermi level. (a) Before the pump excitation, (b) after pump excitation and initial thermalization through e-e scattering, and (c) after cooling with e-p scattering. (d) The carrier distribution difference of (a) and (b). (e) Transient reflectivity of bulk at 4 μm as a function of $T_e$ deduced from the temperature dependent measurement (Fig. 4).