The out-of-plane current density Jz is the convolution (denoted by *) of the excitation pulse and the impulse current response as described in the main text: Jz(t) = αeΦ(t) * η(t), where α is the absorption coefficient of the heterostructure, e is electron charge, and Φ(t) is the photon flux of the excitation pulse on the sample. The charge transfer efficiency ξ, which is included in the impulse response, is defined as the net electron charge transferred across the vdW interface per absorbed photon. Note that the value of ξ is independent on the respective absorption of the individual layers for a given total absorption, because the interfacial current from a photogenerated electron in WS2 moving into MoS2 is equivalent to the effect of a photogenerated hole in MoS2 moving into WS2.

The transient electric field immediately above the sample surface was given by the relation E(t) = ςZ0d Jz(t) (14), where ς = 0.108 is an out-coupling efficiency that depends on the angle of incidence (60°) and the THz dielectric function of the sample (εsapphire_THz ~ 10; for simplicity, we take εTMDC⊥_THz ~ 10), Z0 = 376.73 ohms is the impedance of free space, and d = 0.62 nm is the average distance the current flows. In our measurement, the THz field propagated away from the surface, passed through collection optics of finite size and a high-resistivity Si wafer that blocks the reflected excitation beam, and was refocused at the front surface of the EO crystal. These propagation effects were treated as a high-pass filter that only depends on the geometry of the apparatus and were calibrated experimentally.

Last, we modeled the process of EO sampling by applying the transfer function GEO(f) = Atr(f) dEO(f) r41(f) in frequency domain, where Atr(f) is the amplitude transmission coefficient of the interface between air and the EO crystal, dEO(f) is the effective thickness of the EO crystal, taking into account the phase mismatch between the THz pulse and the optical probe pulse, and r41(f) is the frequency-dependent EO coefficient of the material. We followed the procedure in (29) with the experimentally determined optical group index (ng = 3.57) and THz refractive index for GaP (fig. S6). The result was then convolved with a normalized probe intensity profile to obtain the final simulation of the measured THz waveform. The total transfer function connecting Jz and ΔI/I0 for our high-bandwidth apparatus is shown in fig. S7.

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