# Radiative Corrections to Quantum Sticking on Graphene

## TL;DR

This paper investigates the quantum sticking rate of atomic hydrogen on suspended graphene, comparing multiple theoretical methods to address infrared problems and soft-phonon effects, revealing size-dependent behaviors of the sticking rate.

## Contribution

It introduces and compares four different theoretical approaches to calculate the quantum sticking rate, addressing infrared divergences and soft-phonon effects in large membranes.

## Key findings

- NCA, IBMA, and SPR methods yield consistent, finite results for large membranes.
- Sticking rate mildly suppressed relative to the lowest-order rate for micromembranes.
- SPR rate decreases to zero with increasing membrane size, unlike NCA and IBMA rates.

## Abstract

We study the sticking rate of atomic hydrogen to suspended graphene using four different methods that include contributions from processes with multiphonon emission. We compare the numerical results of the sticking rate obtained by: (1) the loop expansion of the atom self-energy, (2) the non-crossing approximation (NCA), (3) the independent boson model approximation (IBMA), and (4) a leading-order soft-phonon resummation method (SPR). 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 three methods remedy this infrared problem and give results that are finite in the limit of an infinite membrane. We find that for micromembranes (sizes ranging 100 nm to 10 $\mu$m), the latter three methods give results that are in good agreement with each other and yield sticking rates that are mildly suppressed relative to the lowest-order golden rule rate. Lastly, we find that the SPR sticking rate decreases slowly to zero with increasing membrane size, while both the NCA and IBMA rates tend to a nonzero constant in this limit. Thus, approximations to the sticking rate can be sensitive to the effects of soft-phonon emission for large membranes.