Two-dimensional THz spectroscopy of nonlinear phononics in the topological insulator ${\mathrm{M}\mathrm{n}\mathrm{B}\mathrm{i}}_2{\mathrm{T}\mathrm{e}}_4$

The interaction of a single-cycle THz electric field with the topological insulator ${\mathrm{M}\mathrm{n}\mathrm{B}\mathrm{i}}_2{\mathrm{T}\mathrm{e}}_4$ triggers strongly anharmonic lattice dynamics, promoting fully coherent energy transfer between the otherwise non-interacting Raman-active $E_g$ and infrared (IR)-active $E_u$ phononic modes. Two-dimensional (2D) THz spectroscopy combined with modeling based on the classical equations of motion and symmetry analysis reveals the multi-stage process underlying the excitation of the Raman-active $E_g$ phonon. In this process, the THz electric field first prepares a coherent IR-active $E_u$ phononic state and subsequently interacts with this state to efficiently excite the $E_g$ phonon.