N8- polynitrogen stabilized on carbon-based supports as metal-free electrocatalyst for oxygen reduction reaction in fuel cells

The sluggish oxygen reduction reaction (ORR) kinetics at the cathode is one of the key factors limiting the performance of polymer electrolyte membrane fuel cell (PEMFC). Platinum-based materials are the most widely studied catalysts for this ORR reaction while their large-scale practical application in fuel cells is hindered due to their scarcity and low stability. Therefore, highly active, low cost and robust non-Pt catalysts are being developed to overcome the drawbacks. Recently, a novel polynitrogen N8- (PN) stabilized on multiwall carbon nanotube (MWNT) was synthesized under ambient condition for the first time by our group and demonstrated high ORR activities. It is promising for replacing platinum-based catalysts. However, the substrate effect was not covered in our previous work. Moreover, the PN synthesis mechanism and its catalytic properties for ORR and ORR mechanisms are still not fully understood. The main objectives of this research are to investigate the catalytic properties of PN on different carbon-based substrates, to identify the active sites and mechanisms of ORR, and eventually to provide guidelines for optimizing the synthesis of PN-series catalysts as well as increasing the efficiency of ORR. Polynitrogen N8- (PN) deposited on multiwalled carbon nanotubes (PN-MWNT) are synthesized by cyclic voltammetry (CV) with UV irradiation and further used for oxygen reduction reaction (ORR). Compared to the sample synthesized without UV, a larger amount of N8- is synthesized and is found to distribute more uniformly on MWNT with 254nm UV irradiation (PN-MWNT-254nm); this indicates the production of more azide radicals as the precursors for synthesis of N8- by photoexcitation of azide ions is a rate-limiting step for PN synthesis. The PN-MWCNT-254nm sample shows higher ORR current density than that from a commercial Pt catalyst. Kinetic studies indicate a four-electron pathway on N8- while a two-electron one on N3- . In situ Shell-Isolated Nanoparticle-Enhanced Raman Spectroscopy (SHINERS) analysis reveals that the side-on and end-on 02 adsorption occurs at N8- and N3-, respectively, confirming the electron transfer process. Calculation results from natural bonding orbital (NBO) analysis are used to identify the possible active sites for oxygen chemisorption and further clarify the ORR mechanism. PN deposited on graphene (G), nitrogen-doped graphene (NG) and boron-doped graphene (BG) are synthesized experimentally. The formation of PN on G, NG and BG is confirmed by ATR-FTIR and temperature-programmed desorption (TPD). Moreover, a larger amount of N8- is obtained on NG and BG substrates than that over pure G. Electrochemical tests show that PN-NG and PN-BG possess superior activity toward the ORR and favored a four-electron pathway. This work provides facile strategies to efficiently synthesize PN under ambient condition and deep understanding of its intrinsic oxygen reduction activity

Microscopic theory of quantum anomalous Hall effect in graphene

We present a microscopic theory to give a physical picture of the formation of quantum anomalous Hall (QAH) effect in graphene due to a joint effect of Rashba spin-orbit coupling $\lambda_R$ and exchange field $M$. Based on a continuum model at valley $K$ or $K'$, we show that there exist two distinct physical origins of QAH effect at two different limits. For $M/\lambda_R\gg1$, the quantization of Hall conductance in the absence of Landau-level quantization can be regarded as a summation of the topological charges carried by Skyrmions from real spin textures and Merons from \emph{AB} sublattice pseudo-spin textures; while for $\lambda_R/M\gg1$, the four-band low-energy model Hamiltonian is reduced to a two-band extended Haldane's model, giving rise to a nonzero Chern number $\mathcal{C}=1$ at either $K$ or $K'$. In the presence of staggered \emph{AB} sublattice potential $U$, a topological phase transition occurs at $U=M$ from a QAH phase to a quantum valley-Hall phase. We further find that the band gap responses at $K$ and $K'$ are different when $\lambda_R$, $M$, and $U$ are simultaneously considered. We also show that the QAH phase is robust against weak intrinsic spin-orbit coupling $\lambda_{SO}$, and it transitions a trivial phase when $\lambda_{SO}>(\sqrt{M^2+\lambda^2_R}+M)/2$. Moreover, we use a tight-binding model to reproduce the ab-initio method obtained band structures through doping magnetic atoms on $3\times3$ and $4\times4$ supercells of graphene, and explain the physical mechanisms of opening a nontrivial bulk gap to realize the QAH effect in different supercells of graphene.Comment: 10pages, ten figure

Two-Dimensional Topological Insulator State and Topological Phase Transition in Bilayer Graphene

We show that gated bilayer graphene hosts a strong topological insulator (TI) phase in the presence of Rashba spin-orbit (SO) coupling. We find that gated bilayer graphene under preserved time-reversal symmetry is a quantum valley Hall insulator for small Rashba SO coupling $\lambda_{\mathrm{R}}$, and transitions to a strong TI when $\lambda_{\mathrm{R}} > \sqrt{U^2+t_\bot^2}$, where $U$ and $t_\bot$ are respectively the interlayer potential and tunneling energy. Different from a conventional quantum spin Hall state, the edge modes of our strong TI phase exhibit both spin and valley filtering, and thus share the properties of both quantum spin Hall and quantum valley Hall insulators. The strong TI phase remains robust in the presence of weak graphene intrinsic SO coupling.Comment: 5 pages and 4 figure

Topological phases in gated bilayer graphene: Effects of Rashba spin-orbit coupling and exchange field

We present a systematic study on the influence of Rashba spin-orbit coupling, interlayer potential difference and exchange field on the topological properties of bilayer graphene. In the presence of only Rashba spin-orbit coupling and interlayer potential difference, the band gap opening due to broken out-of-plane inversion symmetry offers new possibilities of realizing tunable topological phase transitions by varying an external gate voltage. We find a two-dimensional $Z_2$ topological insulator phase and a quantum valley Hall phase in $AB$-stacked bilayer graphene and obtain their effective low-energy Hamiltonians near the Dirac points. For $AA$ stacking, we do not find any topological insulator phase in the presence of large Rashba spin-orbit coupling. When the exchange field is also turned on, the bilayer system exhibits a rich variety of topological phases including a quantum anomalous Hall phase, and we obtain the phase diagram as a function of the Rashba spin-orbit coupling, interlayer potential difference, and exchange field.Comment: 15 pages, 17figures, and 1 tabl

Intrinsic Riemannian Functional Data Analysis for Sparse Longitudinal Observations

A novel framework is developed to intrinsically analyze sparsely observed Riemannian functional data. It features four innovative components: a frame-independent covariance function, a smooth vector bundle termed covariance vector bundle, a parallel transport and a smooth bundle metric on the covariance vector bundle. The introduced intrinsic covariance function links estimation of covariance structure to smoothing problems that involve raw covariance observations derived from sparsely observed Riemannian functional data, while the covariance vector bundle provides a rigorous mathematical foundation for formulating the smoothing problems. The parallel transport and the bundle metric together make it possible to measure fidelity of fit to the covariance function. They also plays a critical role in quantifying the quality of estimators for the covariance function. As an illustration, based on the proposed framework, we develop a local linear smoothing estimator for the covariance function, analyze its theoretical properties, and provide numerical demonstration via simulated and real datasets. The intrinsic feature of the framework makes it applicable to not only Euclidean submanifolds but also manifolds without a canonical ambient space.Comment: 36 pages, 8 figure

Spin Polarized and Valley Helical Edge Modes in Graphene Nanoribbons

Inspired by recent progress in fabricating precisely zigzag-edged graphene nanoribbons and the observation of edge magnetism, we find that spin polarized edge modes with well-defined valley index can exist in a bulk energy gap opened by a staggered sublattice potential such as that provided by a hexagonal Boron-Nitride substrate. Our result is obtained by both tight-binding model and first principles calculations. These edge modes are helical with respect to the valley degree of freedom, and are robust against scattering, as long as the disorder potential is smooth over atomic scale, resulting from the protection of the large momentum separation of the valleys.Comment: 4 pages, 4 figure