Teraherz Field Effects Overview

The induced terahertz response of semiconductor systems is investigated with a microscopic theory. In agreement with recent terahertz experiments, the developed theory fully explains the ultrafast build up of the plasmon resonance and the slow formation of incoherent excitonic populations. For incoherent conditions, it is shown that a terahertz field exclusively probes the correlated electronhole pairs via a symmetry breaking between many-body correlations with even and odd functional form.
The light-matter coupling of semiconductor systems is usually mediated by the optical polarization generated by band-to-band excitations. This polarization - i.e. the induced coherence between the optically coupled valence and conduction bands - is influenced and modified by already existing or excitation generated populations of quasiparticles. However, since optical methods probing band-to-band transitions cannot directly measure populations, such approaches provide only indirect information about the characteristics of the semiconductor excitations. Usually it is therefore very di.cult, if not impossible, to unambiguously attribute the observed changes in the interband optical response to their genuine origin. Hence, to learn about the true nature of optically generated excitations and quasi-particles, one needs supplementary information from other methods. With this respect, recent experimental efforts [28,29,30,31,32] have extended semiconductor optics toward the regime where transitions between quasi-particle states can be probed directly with far infrared fields at terahertz (THz) frequencies which are orders of magnitude lower than the usual band-to-band transitions. Especially, the combination of interband optical excitation and intraband measurement of the induced THz absorption allowed the experimentalists to discuss seemingly different questions such as the ultrafast build-up of plasma screening4 and the formation of excitonic correlations [32]. To provide a fundamental basis for the analysis of the semiconductor THz response, we develop in this Letter a comprehensive microscopic theory that consistently includes Coulombic many-body interactions, coupling to optical and THz fields as well as lattice vibrations. The developed theory is applied to compute the time-resolved THz response after optical interband excitation and as special cases, we investigate the build up of the plasmon resonance and the gradual formation of exciton population transitions. Our results demonstrate that the incoherent THz response can be attributed to transitions between specific many-body states of the correlated electron-hole pairs, establishing this technique as uniquely qualified to identify the genuine nature and dynamics of these quasi-particle excitations. In general, the optical response of semiconductors to a classical transversal electric field E(z, t) can be solved from Maxwell's wave equation which couples the light-field to the (optical) interband polarization P and to the (THz) intraband current J.

FIG. 1: (a) Time evolution of carrier density (solid line) and exciting pulse |E|² (shaded area). (b) Real (solid line) and imaginary part (shaded area) of -1/eT for different THz probe delays (solid circles in frame above) as function of THz energy (E_B = 4.2meV). Inset shows density dependence of -1/eT resonance; n₀ and w_PL,0 correspond to frame (b).

FIG. 2: Terahertz absorption (shaded area) and refractive index change (solid line) for di.erent THz probe delays after nonresonant excitation. Here, E₂₁ = 5meV and final density is 6 x 10⁴ cm^-1.

FIG. 3: Terahertz absorption of QW with di.erent postulated exciton fractions. Carrier system at 40 K with density 4 x 10⁹ cm^-2, and E₂₁ = 7meV.