Valley polarization (VP), an induced imbalance in the populations of a
multi-valley electronic system, allows emission of second harmonic (SH) light
even in centrosymmetric crystals such as graphene. Whereas in systems such as
MoS2 or BN this adds to their intrinsic quadratic response, SH
generation in a multi-valley inversion-symmetric crystal can provide a direct
measure of valley polarization. By computing the nonlinear response and
characterizing theoretically the respective SH as a function of polarization,
temperature, electron density, and degree of VP, we demonstrate the possibility
of disentangling and individually quantifying the intrinsic and valley
contributions to the SH. A specific experimental setup is proposed to obtain
direct quantitative information about the degree of VP and allow its remote
mapping. This approach could prove useful for direct, contactless, real-space
monitoring of valley injection and other applications of valley transport and
valleytronics.Comment: Updating with published version, including typesetting corrections to
eqs 3 and 4; 7 pages, 5 figure
