Radiative Corrections to Quantum Sticking for Cold Atoms on Suspended Graphene

We study the adsorption rate of atomic hydrogen to suspended graphene using three different methods that include contributions from processes with multiple soft-phonon emissions. We compare the numerical results of the adsorption rate obtained by: (1) the loop expansion of the atom self-energy, (2) the non-crossing approximation (NCA) and (3) the independent boson model approximation (IBMA). The loop expansion reveals an infrared problem, analogous to the infamous infrared problem in QED. The 2-loop contribution to the sticking rate gives a result that tends to diverge for large membranes. The latter two methods remedy this infrared problem and give results that are finite in the limit of an infinite membrane. We find that for micromembranes, the methods of NCA and IBMA give results that are in good agreement with each other. Lastly, we provide detailed results for the effect of finite temperature on the adsorption rate of cold atoms. [1] S.Sengupta and D.P. Clougherty, Phys Rev B.96.035419