  The strong ellipticity dependence of high-harmonic generation in gases
enables numerous experimental techniques that are nowadays routinely used, for
instance, to create isolated attosecond pulses. Extending such techniques to
high-harmonic generation in solids requires a fundamental understanding of the
microscopic mechanism of the high-harmonic generation. Here, using extensive
first-principles simulations within a time-dependent density-functional
framework, we show how intraband and interband mechanisms are strongly and
differently affected by the ellipticity of the driving laser field. The complex
interplay between intraband and interband effects can be used to tune and
improve harmonic emission in solids. In particular, we show that the energy
cutoff of the high-harmonic plateau can be increased by as much as 30\% using a
finite ellipticity of the driving field, opening a new avenue for better
understanding and control of HHG in solids based on ellipticity. Also, we
demonstrate the possibility to generate, from a single circularly polarized
driving field, circularly polarized harmonics with alternating helicity. Our
work shows that ellipticity provides an additional knob to experimentally
control high-order harmonic generation in solids.
