Superconducting Phases in Lithium Decorated Graphene LiC6.

A study of possible superconducting phases of graphene has been constructed in detail. A realistic tight binding model, fit to ab initio calculations, accounts for the Li-decoration of graphene with broken lattice symmetry, and includes s and d symmetry Bloch character that influences the gap symmetries that can arise. The resulting seven hybridized Li-C orbitals that support nine possible bond pairing amplitudes. The gap equation is solved for all possible gap symmetries. One band is weakly dispersive near the Fermi energy along Γ → M where its Bloch wave function has linear combination of [Formula: see text] and dxy character, and is responsible for [Formula: see text] and dxy pairing with lowest pairing energy in our model. These symmetries almost preserve properties from a two band model of pristine graphene. Another part of this band, along K → Γ, is nearly degenerate with upper s band that favors extended s wave pairing which is not found in two band model. Upon electron doping to a critical chemical potential μ1 = 0.22 eV the pairing potential decreases, then increases until a second critical value μ2 = 1.3 eV at which a phase transition to a distorted s-wave occurs. The distortion of d- or s-wave phases are a consequence of decoration which is not appear in two band pristine model. In the pristine graphene these phases convert to usual d-wave or extended s-wave pairing

On the Positive Effect of Delay on the Rate of Convergence of a Class of Linear Time-Delayed Systems

This paper is a comprehensive study of a long observed phenomenon of increase in the stability margin and so the rate of convergence of a class of linear systems due to time delay. We use Lambert W function to determine (a) in what systems the delay can lead to increase in the rate of convergence, (b) the exact range of time delay for which the rate of convergence is greater than that of the delay free system, and (c) an estimate on the value of the delay that leads to the maximum rate of convergence. For the special case when the system matrix eigenvalues are all negative real numbers, we expand our results to show that the rate of convergence in the presence of delay depends only on the eigenvalues with minimum and maximum real parts. Moreover, we determine the exact value of the maximum rate of convergence and the corresponding maximizing time delay. We demonstrate our results through a numerical example on the practical application in accelerating an agreement algorithm for networked~systems by use of a delayed feedback

On Robustness Analysis of a Dynamic Average Consensus Algorithm to Communication Delay

This paper studies the robustness of a dynamic average consensus algorithm to communication delay over strongly connected and weight-balanced (SCWB) digraphs. Under delay-free communication, the algorithm of interest achieves a practical asymptotic tracking of the dynamic average of the time-varying agents' reference signals. For this algorithm, in both its continuous-time and discrete-time implementations, we characterize the admissible communication delay range and study the effect of the delay on the rate of convergence and the tracking error bound. Our study also includes establishing a relationship between the admissible delay bound and the maximum degree of the SCWB digraphs. We also show that for delays in the admissible bound, for static signals the algorithms achieve perfect tracking. Moreover, when the interaction topology is a connected undirected graph, we show that the discrete-time implementation is guaranteed to tolerate at least one step delay. Simulations demonstrate our results