Giant deformation potential induced small polaron effect in Dion-Jacobson two-dimensional lead halide perovskites

Abstract

Halide perovskites have attracted substantial attention recently. However, the strong lattice distortion effects in these materials have led to debates regarding the nature of charge carriers. While the behavior of carriers in bulk three-dimensional materials is well-documented, the characteristics of carriers in two-dimensional perovskites remain less well understood. In this study, we provide direct and clear evidence of small polaron formation through transient spectroscopic analysis of deformation potential and dynamic lattice screening. Coherent acoustic phonon wave signals reveal a strong coupling between carriers and lattice degrees of freedom, leading to small polaron formation and a spin lifetime enhancement of up to 10-fold. Utilizing optical Kerr spectroscopy and theoretical modeling, we observed a notably long polarization response time at room temperature, attributed to lattice distortion and small polarons approximately two-unit cells in size. Temperature-dependent coherent phonon dynamics and X-ray diffraction further confirmed the presence of small polarons. This discovery underscores the significance of the cooperative interplay between exciton dynamics and the small polaron field, particularly in influencing the Coulomb exchange interaction of excitons.

Keywords: coherent acoustic phonon; deformation potential; polaronic carriers; spin polarization; ultrafast spectroscopy.

Figure 1.

(a) Schematic illustration of small polaron characterization experiments (CP in panel a stands for circular polarized). (b) Crystal structures of (4AMP) (MA)_n−1Pb_nI_3n+1 (n = 1, 2 and 3) series samples are reported here, where 4AMP is 4-(aminomethyl)piperidinium. Pseudo color maps of TR spectra of n = 1 sample with (c) same circularly polarized pump and probe pulses (ϕ⁻ and ϕ⁻) and (d) counter circularly polarized pump and probe pulses (ϕ  ⁺ and ϕ⁻). Spin relaxation dynamics of (e) n = 1, (f) n = 2 and (g) n = 3, where Diff denotes the net spin contribution obtained from SC–CC signals, and Fit denotes the fitted curves for spin-relaxation time using a single exponential decay model. (h) Exciton binding energy and spin lifetime of n = 1–3 samples.

Figure 2.

(a–c) Calculated phonon dispersions and the corresponding phonon density of states of n = 1, 2 and 3 sample. (d) Schematic of the generation of coherent acoustic phonon (CAP) wave and deformation potential model. (e) Pseudo color map of TR spectrum at a delay of 3 ps of n = 1 excited at 515 nm with a fluence of 8.42 μJ cm⁻². (f) Pump fluence-dependent ΔR/R for CAP oscillation after subtracting contributions for these three samples. Fitting parameter of the CAP wave amplitude according to the strain function in the Supplementary Data. (g) The oscillation amplitude as a function of the pump fluence. (h) CAP amplitude functions of carrier concentration (the dashed lines represent Hooke's law with different deformation potentials). (i) Acoustic phonon wave velocity, which, according to , can be calculated by the fitted slope, and strain function in the Supplementary Data, respectively. Comparison of crystal distortion, including (j) different hydrogen bonding, (k) average axial and equatorial angles, (l) distortion index and bond angle variance parameter.

Figure 3.

Small polaron properties characterization of n = 1–3 samples. (a) Time-resolved optical Kerr effect response measurement. (b) Photoluminescence peak locations as a function of the temperature. The solid lines represent the two Bose–Einstein oscillators model. (c) Exciton-phonon coupling strength (A_EP) obtained the fitting parameters of the temperature-dependent peak location. (d) Fast Fourier transform (FFT) of the oscillation observed for n = 1–3 samples. (e) Complex THz photoinduced reflection spectra after excitation at 515 nm for n = 1 sample. The calculated charge distribution of (f) holes polaron and (g) electron polaron in 4 × 4 × 1 supercell of n = 1 samples.

Figure 4.

(a) CAP at a few typical temperatures ranging from 4 to 295 K and (bottom) temperature-dependent CAP lifetime obtained from strain function fitting. (b) Spin relaxation dynamics at different temperatures and (bottom) temperature dependence of their spin lifetime. (c) Temperature dependence of FFT amplitude. (d) The low-temperature powder XRD with a magnified pattern from 25° to 26° (2θ°) in the temperature range of 120–295 K. (e) Temperature-dependent lattice parameters obtained from refinement.

Figure 5.

Comparison of spin-relaxation rate with theoretical curve and schematic diagram of small polaron effect.