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Register a new userRadiative Corrections to Quantum Sticking on Graphene
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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.
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A continuum model for low-energy physisorption on a membrane under tension is proposed and studied with variational mean-field theory. A discontinuous change in the energy-dependent sticking coefficient is predicted under certain conditions. This singularity is a result of the bosonic orthogonality catastrophe of the vibrational states of the membrane. The energy-dependent sticking coefficient is predicted to have exponential scaling in 1/E above the singularity. The application of this model to the quantum sticking of cold hydrogen to suspended graphene is discussed. The model predicts that a beam of atomic hydrogen can be completely reflected by suspended graphene at ultralow energies.
The probability that a particle will stick to a surface is fundamental to a variety of processes in surface science, including catalysis, epitaxial growth, and corrosion. At ultralow energies, how particles scatter or stick to a surface affects the performance of atomic clocks, matter-wave interferometers, atom chips and other quantum information processing devices. In this energy regime, the sticking probability is influenced by a distinctly quantum mechanical effect: quantum reflection, a result of matter wave coherence, suppresses the probability of finding the particle near the surface and reduces the sticking probability. We find that another quantum effect can occur, further shaping the sticking probability: the orthogonality catastrophe, a result of the change in the quantum ground state of the surface in the presence of a particle, can dramatically alter the probability for quantum sticking and create a superreflective surface at low energies.
The sticking probability of cold atomic hydrogen on suspended graphene calculated by Lepetit and Jackson [Phys. Rev. Lett. {bf 107}, 236102 (2011)] does not include the effect of fluctuations from low-frequency vibrations of graphene. These fluctuations suppress the sticking probability for low incident energies ($lesssim 15$ meV).
The differential conductance of graphene is shown to exhibit a zero-bias anomaly at low temperatures, arising from a suppression of the quantum corrections due to weak localization and electron interactions. A simple rescaling of these data, free of any adjustable parameters, shows that this anomaly exhibits a universal, temperature- ($T$) independent form. According to this, the differential conductance is approximately constant at small voltages ($V<k_BT/e$), while at larger voltages it increases logarithmically with the applied bias, reflecting a quenching of the quantum corrections. For theoretical insight into the origins of this behavior, we formulate a model for weak-localization in the presence of nonlinear transport. According to this, the voltage applied under nonequilibrium induces unavoidable dephasing, arising from a self-averaging of the diffusing electron waves responsible for transport. By establishing the manner in which the quantum corrections are suppressed in graphene, our study will be of broad relevance to the investigation of nonequilibrium transport in mesoscopic systems in general. This includes systems implemented from conventional metals and semiconductors, as well as those realized using other two-dimensional semiconductors and topological insulators.
The quantum localization in the quantum Hall regime is revisited using Graphene monolayers with accurate measurements of the longitudinal resistivity as a function of temperature and current. We experimentally show for the first time a cross-over from Efros-Shklovskii Variable Range Hopping (VRH) conduction regime with Coulomb interactions to a Mott VRH regime without interaction. This occurs at Hall plateau transitions for localization lengths larger than the interaction screening length set by the nearby gate. Measurements of the scaling exponents of the conductance peak widths with both temperature and current give the first validation of the Polyakov-Shklovskii scenario that VRH alone is sufficient to describe conductance in the Quantum Hall regime and that the usual assumption of a metallic conduction regime on conductance peaks is unnecessary.
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