Supercriticality of charge centers in graphene probed with scanning tunneling microscopy*

The massless Dirac fermion carriers in graphene, with their effective fine structure constant,$\alpha_{g} $, being of order unity, provide fertile ground for exploring the physics of ultra-relativistic particles in the strong coupling limit.In particulara positive charge Z embedded in graphene is expected to exhibit supercritical behavior already for Z\textgreater Z$_{\mathrm{c}}=$0.5/$\alpha_{\mathrm{g}}$, in stark contrast to the atomic case where Z$_{\mathrm{c}}$ $\sim$ 170 is experimentally inaccessible. However due to the significant screening in graphene, attaining the supercritical regime is challenging.\footnote{Y. Wang \textit{et al}, Science, 340, 734 (2013)} We will report on a new method to create charge centerswithin the graphene layer whose charge, Z, can be tuned to exceed the critical value. Using low temperature scanning tunneling microscopy and spectroscopy we study the evolution in the local electronic structure of graphene as a function of Z, from charge neutrality to the supercritical regime, which is identified by comparing to numerical simulations.