In this proceedings we describe our recent results on semiconductor nonlinear optics, investigated using single-cycle
THz pulses. We demonstrate the nonlinear absorption and self-phase modulation of strong-field THz pulses in doped
semiconductors, using n-GaAs as a model system. The THz nonlinearity in doped semiconductors originates from the
near-instantaneous heating of free electrons in the ponderomotive potential created by electric field of the THz pulse,
leading to ultrafast increase of electron effective mass by intervalley scattering. Modification of effective mass in turn
leads to a decrease of plasma frequency in semiconductor and produces a substantial modification of THz-range material
dielectric function, described by the Drude model. As a result, the nonlinearity of both absorption coefficient and
refractive index of the semiconductor is observed. In particular we demonstrate the nonlinear THz pulse compression
and broadening in n-GaAs, as well as an intriguing effect of coexisting positive and negative refractive index
nonlinearity within the broad spectrum of a single-cycle THz pulse. Based on Drude analysis we demonstrate that the
spectral position of zero index nonlinearity is determined by (but not equal to) the electron momentum relaxation rate.
Single cycle pulses of light, irrespective of the frequency range to which they belong, inherently have an ultrabroadband
spectrum covering many octaves of frequencies. Unlike the single-cycle pulses in optical domain, the THz pulses can be
easily sampled with sub-cycle resolution using conventional femtosecond lasers. This makes the THz pulses accessible
model tools for direct observation of general nonlinear optical phenomena occurring in the single-cycle regime.