Giant spin-selective bandgap renormalization in ${\mathrm{CsPbBr}}_3$ colloidal nanocrystals

The spin-dependence of the strongly correlated phenomena and many-body interactions play an important role in quantum information science. In particular, it is quite interesting but unclear how the spin degree of freedom ramifies the bandgap renormalization, one of the fundamental many-body phenomena. We report the first room-temperature observation of giant spin-selective bandgap renormalization (SS-BGR) in $\mathrm{Cs}\mathrm{Pb}{\mathrm{Br}}_3$ colloidal nanocrystals using time-resolved circularly polarized femtosecond pump-probe spectroscopy. The SS-BGR results from many-body interactions among carriers with the same spin that renormalize their joint density of states by $57\pm$ 1 meV, visualized here as photoinduced absorption (PIA) below band-edge transition energy when the pump and probe are co-polarized. The hallmark result of spectrally resolved SS-BGR is in stark contrast to the usually submerged signal in II-VI and III-V semiconductors and is 3 orders of magnitude larger than that observed in Ge/SiGe quantum wells, highlighting the unique and beneficial band structure of the metal-halide semiconductors. We propose that the PIA, due to SS-BGR, can be used to describe the spin-polarization and spin-relaxation dynamics. The experimental and theoretical findings open up new possibilities for optical manipulation of spin degrees of freedom and their many-body interactions in metal-halide perovskite nanocrystals for potential room-temperature applications.

Figure 1

Ground state OA spectrum together with theoretical fit using Elliott's model. The exciton absorption is centered at 2.42 eV, and the binding energy is 10 meV. Blue line is the photoluminescence spectrum which shows sharp exciton emission of FWHM 85 meV centered at 2.42 eV (at the exciton position obtained from Elliott's model).

Figure 2

The pseudocolor $\mathrm{\Delta }\mathrm{A}$ spectrum of $\mathrm{Cs}\mathrm{Pb}{\mathrm{Br}}_3$ nanocrystals for $\mathrm{\Delta }$ = 130 meV at a fixed pump fluence of 25 $\mu \mathrm{J}/{\mathrm{cm}}^2$, for (a) ${\sigma }^{+}{\sigma }^{+}$ and (b) ${\sigma }^{+}{\sigma }^{-}$. The corresponding cross-sections at pump-probe delay time ($\mathrm{\Delta }\mathrm{t}$) of 0.5 and 7 ps are shown in the bottom panel. The inset in (b) shows the zoomed-in image of the PIA.

Figure 3

(a) Illustration of the optical selection rules: ${\sigma }^{+}$ polarized probe monitors the change in $\uparrow$ band, i.e., change in the transition from $|\frac{1}{2},-\frac{1}{2}\rangle$ VB to $|\frac{1}{2},+\frac{1}{2}\rangle$ CB, while ${\sigma }^{-}$ polarized probe monitors the change in $\downarrow$ band, i.e., transition from $|\frac{1}{2},+\frac{1}{2}\rangle$ VB to $|\frac{1}{2},-\frac{1}{2}\rangle$ CB. The black up and down arrows manifest the angular momentum orientation of the electrons. (b) Population of the $\uparrow$ band (dark blue region) by ${\sigma }^{+}$ pump pulse as per the optical selection rules. (c) The renormalization of the $\uparrow$ band due to interactions among spin-carriers in $\uparrow$ band and no shift in $\downarrow$ band since the band is empty at early time scale. (d) Spin-flipping of carriers from $\uparrow$ band to $\downarrow$ band and the corresponding decay of BGR in $\uparrow$ band with simultaneous growth in $\downarrow$ band, providing the direct evidence of spin-selective BGR.

Figure 4

(a) The leftmost panel shows the continuum in the Excited state (orange) and Ground state (magenta) and the modified (wine) continuum states as per the Fermi-distribution function (black dashed line). Middle panel shows the exciton bleach by free-carriers. The rightmost panel shows the simulated $\mathrm{\Delta }\mathrm{A}$ (green) from the combined effect of SS-BGR (red) and exciton bleach (blue). The symbols present the experimental $\mathrm{\Delta }\mathrm{A}$ for $\uparrow$ band at $\mathrm{\Delta }\mathrm{t}=0.5$ ps (for $\mathrm{\Delta }=130$ meV, pump fluence $25\mu \mathrm{J}/{\mathrm{cm}}^2$) that is in agreement with our model. (b), (c) Pseudocolor plot of $\mathrm{\Delta }\mathrm{A}$ (b) experimental and (c) modeled corresponding to $\uparrow$ band at $\mathrm{\Delta }\mathrm{t}=0.5$ ps as a function of fluence at constant $\mathrm{\Delta }=130$ meV; (d) The JDOS shift evaluated using Eqs. (1, 2, 3) at different fluence exhibiting saturation at $\mathrm{\Delta }\mathrm{t}=0.5$ ps for $\uparrow$ band (top panel) and $\mathrm{\Delta }\mathrm{t}=7$ ps for $\uparrow$ band and $\downarrow$ band (bottom panel).

Figure 5

(a), (b) Pseudocolor plot of $\mathrm{\Delta }\mathrm{A}$ at 0.5 ps as a function of $\mathrm{\Delta }$ at constant fluence of 15 $\mu \mathrm{J}/{\mathrm{cm}}^2$ for (a) $\uparrow$ band and (b) $\downarrow$ band. (c), (d) The BGR shift evaluated using Eqs. (1, 2, 3) at different $\mathrm{\Delta }$ for $\uparrow$ band and $\downarrow$ band at (c) $\mathrm{\Delta }\mathrm{t}=0.5$ ps and (d) $\mathrm{\Delta }\mathrm{t}=7$ ps.