The nonlinear optical response of bismuth (Bi) in the nonperturbative regime is studied by phase-resolved two-dimensional terahertz (THz) spectroscopy. A (111)-oriented rhombohedral Bi film of 45-nm thickness is excited by a pair of THz pulses with center frequencies of 1.1 THz, electric field amplitudes of 300 and 600 kV/cm, and pulse durations of 1 ps. The phase-resolved nonlinear signal field, emitted by the sample and recorded in a transmission geometry, allows for a separation of different components of the total nonlinear response, including higher harmonics of the THz pulses and pump-probe signals with few-picosecond decay times. The pump-probe signals originate from irreversible electron-hole pair generation and display a sixfold amplitude pattern in the azimuthal sample orientation. The linearly polarized pump pulses generate an unequal transient carrier population in the six $L$ valleys of the band structure, resulting in a reduction of symmetry of the excited crystal and a backfolding of phonons from the $X$ to the $\mathrm{\Gamma }$ point. Wave packets of back-folded acoustic phonons, which are displacively excited by the THz pump pulse, give rise to coherent pump-probe signals oscillating with a frequency of 0.8 THz.

• Received 31 March 2023
• Accepted 2 June 2023

DOI:https://doi.org/10.1103/PhysRevB.107.245140