Revealing the ultrafast light-to-matter energy conversion before heat diffusion in a layered Dirac semimetal

There is still no general consensus on how one can describe the out-of-equilibrium phenomena in matter induced by an ultrashort light pulse. We investigate the pulse-induced dynamics in a layered Dirac semimetal ${\mathrm{SrMnBi}}_2$ by pump-and-probe photoemission spectroscopy. At $\lesssim 1$ ps, the electronic recovery slowed upon increasing the pump power. Such a bottleneck-type slowing is expected in a two-temperature model (TTM) scheme, although opposite trends have been observed to date in graphite and in cuprates. Subsequently, an unconventional power-law cooling took place at $\sim 100$ ps, indicating that spatial heat diffusion is still ill defined at $\sim 100\mathrm{ps}$. We identify that the successive dynamics before the emergence of heat diffusion is a canonical realization of a TTM scheme. Criteria for the applicability of the scheme is also provided.

Figure 1

Band dispersions of ${\mathrm{SrMnBi}}_2$ extending into the unoccupied side. (a) Crystal structure of ${\mathrm{SrMnBi}}_2$. The unit cell of $485{\AA }^3$ is indicated by a rectangular frame. (b) Temperature profiles of the resistivity. (c) Fermi-surface mapping. Spectral weight at $\pm 5$ meV around $E_F$ is mapped in $k$ space. See the Supplemental Material movie file for the spectral-weight map from the occupied to unoccupied side [45]. (d) Band dispersions recorded before ($-1.3$ ps) and after (0.17 ps) the pumping ($P=30$ mW). The cut was along the Brillouin-zone diagonal indicated by an arrow in (c). (e) Second derivative of the images in (d) with respect to $k$. The calculated Dirac bands adopted from Ref. [46] are overlaid on the left image.

Figure 2

TARPES of ${\mathrm{SrMnBi}}_2$. (a) TARPES images. Top panels show band dispersions, and bottom panels show difference to the averaged image before pumping. (b), (c) Mappings of angle-integrated photoemission intensity (b) and its pump-induced difference (c) as functions of energy and delay time for three pump-power values $P=30$, 60, and 90 mW (top to bottom). $P=30$ mW corresponds to the pump fluence of $0.24\text{mJ}/{\text{cm}}^2$. (d) Photoemission intensity variation as functions of $t$ for the three pump-power values.

Figure 3

Electronic recovery dynamics and its pump-power dependence. (a) Variation of the electronic energy $\mathrm{\Delta }U$ (see text) normalized to the pump power $P$. (b) Variation of the electronic temperature $T_e$. The solid and dashed lines are numerical simulations of $T_e$ and $T_p$, respectively. The inset shows the calculated $\mathrm{\Delta }{U}_e\left(t\right)$ that are normalized to the peak heights. (c) Sketch of the energy flow in the TTM scheme. The conductance of the energy flow from the heated electrons to coupled phonons is described by the coupling constant $\lambda$. (d) Double logarithmic plots of $T_e$ versus $t$. Power-law exponents of $-1, -1/2$, and $-0.21$ are indicated by slopes. (e) Sketch of the lateral-diffusion cooling (top) and on-site cooling (bottom) after the sample is pumped by a finite pump-beam size. Note, the lateral spread of heat is absent in the latter.