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.
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