  The next-nearest neighbor hopping term t' determines a magnitude and, hence,
importance of several phenomena in graphene, which include self-doping due to
broken bonds and the Klein tunneling that in the presence of t' is no longer
perfect. Theoretical estimates for t' vary widely whereas a few existing
measurements by using polarization resolved magneto-spectroscopy have found
surprisingly large t', close or even exceeding highest theoretical values. Here
we report dedicated measurements of the density of states in graphene by using
high-quality capacitance devices. The density of states exhibits a pronounced
electron-hole asymmetry that increases linearly with energy. This behavior
yields t' approx -0.30 eV +-15%, in agreement with the high end of theory
estimates. We discuss the role of electron-electron interactions in determining
t' and overview phenomena which can be influenced by such a large value of t'.
