Quantum capacitance measurements of electron-hole asymmetry and next-nearest-neighbor hopping in graphene

The next-nearest-neighbor hopping term ${t}^{\ensuremath{'}}$ determines a magnitude, and, hence, the importance of several phenomena in graphene that include self-doping due to broken bonds and the Klein tunneling, which in the presence of ${t}^{\ensuremath{'}}$, is no longer perfect. Theoretical estimates for ${t}^{\ensuremath{'}}$ vary widely, whereas a few existing measurements by using polarization-resolved magnetospectroscopy have found surprisingly large ${t}^{\ensuremath{'}}$, close to or even exceeding the 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 ${t}^{\ensuremath{'}}$ \ensuremath{\approx} \ensuremath{-}0.3 eV\ifmmode\pm\else\textpm\fi{}15$%$, in agreement with the high end of theory estimates. We discuss the role of electron-electron interactions in determining ${t}^{\ensuremath{'}}$ and overview phenomena, which can be influenced by such a large value of ${t}^{\ensuremath{'}}$.